Composite Sheet Forming (Composite Materials Series)

COMPOSITE SHEET FORMING COMPOSITE MATERIALS SERIES Series Editor: R. Byron Pipes, Center for Composite Materials, Un...

Author: D. Bhattacharyya

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COMPOSITE SHEET FORMING

COMPOSITE MATERIALS SERIES

Series Editor: R. Byron Pipes, Center for Composite Materials, University of Delaware, Newark, Delaware, USA Vol. Vol. Vol. Vol. Vol. Vol.

1 2 3 4 5 6

Vol. Vol. Vol. Vol.

7 8 9 10

Friction and Wear of Polymer Composites (K. Friedrich, Editor) Fibre Reinforcements for Composite Materials (A.R. Bunsell, Editor) Textile Structural Composites (T.-W. Chou, Editor) Fatigue of Composite Materials (K.L. Reifsnider, Editor) Interlaminar Response of Composite Materials (N.J. Pagano, Editor) Application of Fracture Mechanics to Composite Materials (K. Friedrich, Editor) Thermoplastic Composite Materials (L.A. Carlsson, Editor) Advances in Composite Tribology (K. Friedrich, Editor) Damage Mechanics of Composite Materials (R. Talreja, Editor) Flow and Rheology in Polymer Composites Manufacturing (S.G. Advani, Editor)

Cover illustration- Arrow diagram for a [0,9012s blister fairing, 61max- 35.3%, (for details see p. 233).

t~Zmax = - 2 5 . 9 %

Composite Materials Series, 11 COMPOSITE SHEET FORMING edited by

D. Bhattacharyya Department of Mechanical Engineering, School of Engineering, University of Auckland, Auckland, New Zealand

1997 ELSEVIER Amsterdam

m

Lausanne

m

New

York

m

Oxford

m

Shannon

--

Tokyo

ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands

ISBN ISBN

0-444-82641-6 (Vol. 11) 0-444-42525-X (Series)

9 1997 Elsevier Science B.V. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science B.V., Copyright and Permissions Department, P.O. Box 521, 1000 AM Amsterdam, The Netherlands. Special regulations for readers in the U S A - This publication has been registered with the Copyright Clearance Center Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside the USA, should be referred to the copyright owner, Elsevier Science B.V., unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-free paper. Printed in The Netherlands.

PREFACE Sheet forming is one of the most used processes in metal forming and hence it is not surprising to see considerable efforts being put into adapting or modifying the existing sheet metal forming techniques to suit the needs of forming composite sheets. With the increasing availability of various types of fibre-reinforced polymeric sheets, especially with thermoplastic matrices, the scope of using such materials is rapidly expanding in the automobile, building, sports and other manufacturing industries beyond the traditional areas of aerospace and aircraft applications. Their good structural and anti-corrosion properties with available design versatility give them many advantages over traditional metallic sheets. However, to realise the full potential of these materials, it is often necessary to redesign the component with subsequent manufacturing in mind. For economic competitiveness it is also desirable to develop rapid manufacturing techniques suitable for different types of composite sheets. Thus the understanding of their fundamental deformation behaviour, along with the capability of developing analytical models, is essential for efficient and defect-free forming of this relatively new generation of materials. This book contains twelve chapters and attempts to cover different aspects of sheet forming including both thermoplastic and thermosetting materials. In view of the expanded role of fibre-reinforced composite sheets in the industry, the book also describes some non-traditional applications, processes and analytical techniques involving such materials. It has often been noted by the Editor and his research colleagues that familiarity with the basic principles and ideas of sheet metal forming is somewhat lacking among the researchers of composite sheet forming. Although there are fundamental differences in nature between metallic and composite sheets, there are many concepts and techniques, originally developed for sheet metal forming, that can be successfully utilised for composites. Hence the first chapter has been dedicated to a brief introduction to the principles of sheet metal forming. The next two chapters introduce the various forms of materials, manufacturing techniques and the fundamentals of computer simulation. Chapter 4 describes the different aspects of thermoforming of continuous fibre-reinforced thermoplastics and the following chapter studies the shear and frictional behaviour of composite sheets during forming. Grid strain analysis is an established technique for sheet metals; Chapter 6 explores the possibility of applying this method in continuous fibre-reinforced polymeric sheets. For an efficient manufacturing process development, finite element modelling and an understanding of rheology play extremely important roles; the next two chapters address these topics with the fundamental concepts reviewed and the recent developments discussed. Chapter 9 introduces the theory of bending, which is an

vi

Preface

integral mechanism of most sheet forming processes, of thermoplastic composite sheets and shows a novel way of determining both longitudinal and transverse viscosities through vee-bend tests. A significant expansion of the usage of composite materials is taking place in biomedical areas and Chapter 10 discusses the thermoforming of knitted fabric-reinforced thermoplastics for load-bearing, anisotropic bio-implants. Chapter 11 studies the forming of thermoset composites, a new technique of manufacturing composite components, and highlights the phenomenological similarities with those found with thermoplastics. The last chapter introduces roll forming, a commonly used rapid manufacturing process for sheet metals, and discusses the possibility of applying it economically for continuous fibre-reinforced thermoplastic sheets. I would like to thank Dr R. B. Pipes, editor-in-chief of this Elsevier series on composite materials, for inviting me to organise and edit this particular volume. Thanks are also due to the authors of the various chapters for making their learned contributions and complying with the necessary publication schedule. Finally I wish to thank the University of Auckland, the German Science Foundation, the University of Kaiserslautern and my family for their support during my sabbatical leave which allowed me to complete the final phase of the editing work. D. Bhattacharyya

LIST OF CONTRIBUTORS

S.G. ADVANI

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA B. Tomas ASTROM

Department of Aeronautics, Division of Lightweight Structures, Royal Institute of Technology, S-IO0 44 Stockholm, Sweden D. B H A T T A C H A R Y Y A

Composites Research Group, Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand G.R. CHRISTIE

Composites Research Group, Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand T.S. CREASY

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA (currently at University of Southern California, Los Angeles, CA,

USA) J.L. D U N C A N

Composites Research Group, Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand R.J. DYKES

Composites Research Group, Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand K. F R I E D R I C H

Institute for Composite Materials Ltd. (IVW), University of Kaiserslautern, 67663 Kaiserslautern, Germany M.O. G H A F U R

Polydynamics Inc., 1685 Main St. West, Suite 305, Hamilton, Ontario, Canada L8S 1G5 vii

viii

List of contributors

Timothy G U T O W S K I

Laboratory for Manufacturing and Productivity, Massachusetts Institute of Technology, Cambridge, MA 02139, USA M. HOU

Centre for Advanced Materials Technology, Department of Mechanical Engineering, University of Sydney, Sydney, N S W 2006, Australia B.L. K O Z I E Y

Polydynamics Inc., 1685 Main St. West, Suite 305, Hamilton, Ontario, Canada L8S 1G5 J. KREBS

Institute for Composite Materials Ltd. (IVW), University of Kaiserslautern, 67663 Kaiserslautern, Germany Haorong LI

Laboratory for Manufacturing and Productivity, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Patrick J. M A L L O N

Mechanical and Aeronautical Engineering Department, University of Limerick, Limerick City, Ireland S.J. M A N D E R

Composites Research Group, Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand (currently at McKinsey & Company, Sydney, NSW, Australia) T.A. M A R T I N

Composites Research Group, Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand J. M A Y E R

Biocompatible Materials Science and Engineering, Department of Materials, Swiss Federal Institute of Technology, ETH Zurich, Wagistrasse 23, 8952 Schlieren, Switzerland S.P. McENTEE

Composites Research Unit, University College, Galway, Ireland G.B. McGUINNESS

Composites Research Unit, University College, Galway, Ireland F.A. M I R Z A

Faculty of Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7

Lbt of contributors

ix

Adrian M. M U R T A G H Engineering Department, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UK C.M. 6 BR,~DAIGH Composites Research Unit, University College, Galway, Ireland S.M. P A N T O N

Composites Research Group, Department of Mechanical Eng&eer&g, University of Auckland, Private Bag 92019, Auckland, New Zealand S.F. SHULER Department of Mechanical Eng&eering, University of Delaware, Newark, DE 19716, USA (currently at General Electric Co., Pittsfied, MA, USA) J. V L A C H O P O U L O S

Faculty of Eng&eering, McMaster University, Hamilton, Ontario, Canada L8S 4L7 E. W I N T E R M A N T E L

Biocompatible Materials Science and Eng&eering, Department of Materials, Swiss Federal Institute of Technology, ETH Zurich, Wagistrasse 23, 8952 Schlieren, Switzerland

This . Page Intentionally Left Blank

CONTENTS

A more detailed contents list is given at the beginning of each chapter.

Preface

v

List of Contributors

vii

Chapter 1 (J.L. Duncan and S.M. Panton) Introduction to sheet metal forming

1

Abstract 1 1.1. Introduction 2 1.2 Introduction to plastic flow theory 2 1.3. Forming characteristics of sheet metals 1.4. Forming limits for sheet metal 12 1.5. Industrial sheet metal forming 15 1.6. Bending and spring-back 19 1.7. Superplasticity 23 References 25

Chapter 2 (B. Tomas Astr6m) Thermoplastic composite sheet forming: materials and manufacturing techniques Abstract 27 2.1. Introduction 28 2.2. Constituents 29 2.3. Properties 48 2.4. Manufacturing techniques Acknowledgement 72 References 72

60

xi

27

Contents

xii

Chapter 3 (B.L. Koziey, M.O. Ghafur, J. Vlachopoulos and F.A. Mirza)

Computer simulation of thermoforming 75 Abstract 75 3.1. Introduction 76 3.2. Sheet production 77 3.3. Thermoforming simulation 3.4. Concluding remarks 88 References 88

78

Chapter 4 (K. Friedrich, M. Hou and J. Krebs)

Thermoforming of continuous fibre/thermoplastic composite sheets Abstract 92 4.1. Introduction 92 4.2. Experimental details and procedures 96 4.3. 2-D stamp forming 100 4.4. 3-D stamp forming 137 4.5. 3-D diaphragm forming of GF/PP laminates 4.6. Summary 159 Acknowledgements 160 References 160

91

146

Chapter 5 (A.M. Murtagh and P.J. Mallon)

Characterisation of shearing and frictional behaviour during sheet forming Abstract 163 5.1. Introduction 164 5.2. Transverse fibre flow 170 5.3. Intra-ply shear 173 5.4. Inter-ply slip 177 5.5. Friction during thermoforming References 214

197

Chapter 6 (T.A. Martin, G.R. Christie and D. Bhattacharyya)

Grid strain analysis and its application in composite sheet forming 217 Abstract 217 6.1. Introduction 218 6.2. Large strain analysis 218 6.3. Method of least squares fitting 224 6.4. Forming a composite spherical dome

226

163

Contents

xiii

6.5. Forming a composite blister fairing 230 6.6. Draping theory of textile fabrics 234 6.7. Diagnostic applications 238 6.8. Concluding remarks 241 References 244

Chapter 7 (C.M. O Brfidaigh, G.B. McGuinness and S.P. McEntee) Implicit finite element modelling of composites sheet forming processes

247

Abstract 248 7.1. Introduction 248 7.2. Modelling of composite sheets during forming 254 7.3. Numerical s o l u t i o n s - plane stress problems 258 7.4. Central indentation of a composite sheet ~ the shear-buckling problem 7.5. Experimental comparisons - - diaphragm forming 286 7.6. Conclusions of plane stress analysis 303 7.7. Numerical s o l u t i o n s - plane deformation problems 305 7.8. Conclusions of plane deformation analysis 315 Acknowledgements 318 Nomenclature 318 References 319

Chapter 8 (S.G. Advani, T.S. Creasy and S.F. Shuler) Rheology of long fiber-reinforced composites in sheet forming

323

Abstract 324 8.1. Introduction 324 8.2. Rheological properties 329 8.3. Rheological measurement techniques 348 8.4. Why the rheological properties are important and how to use them in sheet forming 356 8.5. Outlook 366 References 367

Chapter 9 (T.A. Martin, S.J. Mander, R.J. Dykes and D. Bhattacharyya) Bending of continuous fibre-reinforced thermoplastic sheets Abstract 371 9.1. Introduction 372 9.2. Development of an idealised viscous bending model 9.3. Experimental procedures 380

371

374

263

xiv

Contents

9.4. Results and discussion 382 9.5. Modified constant shear rate tests 9.6. Conclusions 399 Acknowledgements 399 References 400

392

Chapter 10 (J. Mayer and E. Wintermantel) Thermoforming processes for knitted-fabric-reinforced thermoplastics: new manufacturing techniques for load-bearing, anisotropic implants 403 Abstract 404 10.1. General aspects of anisotropic biomaterials for load-bearing implants 10.2. Knitted-carbon-fiber-reinforced composite materials 405 10.3. Net-shape forming of knitted fabrics for load-transmitting implants shown for an ulnar osteosynthesis plate 419 10.4. Deep drawing of knitted-fiber-reinforced organo-sheets 428 10.5. Discussion 432 10.6. Summary and conclusions 435 Acknowledgements 435 References 436

Chapter 11 (H. Li and T. Gutowski) The forming of thermoset composites

441

Abstract 441 11.1. Introduction to thermoset forming 442 11.2. Kinematics 446 11.3. Thermoset forming experiments and forming limit analysis 11.4. Concluding remarks 468 References 471

455

Chapter 12 (S.J. Mander, S.M. Panton, R.J. Dykes and D. Bhattacharyya) Roll forming of sheet materials

473

Abstract 474 12.1. Introduction 474 12.2. Roll forming equipment and tooling 476 12.3. Conventional form roll design 483 12.4. Computer-aided design in roll forming 489 12.5. Deformation analysis of roll forming 491

404

Contents

12.6. Roll forming of thermoplastic material 12.7. Concluding remarks 512 Acknowledgements 513 References 513 Author Index Subject Index

517 525

xv

498


Composite Sheet Forming edited by D. Bhattacharyya 9 Elsevier Science B.V. All rights reserved.

Chapter 1

Introduction to Sheet Metal Forming J.L. D U N C A N and S.M. P A N T O N Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand

Contents Abstract 1 1.1. Introduction 2 1.2. Introduction to plastic flow theory 2 1.2.1. The principal element 2 1.2.2. Yielding of isotropic materials 2 1.2.3. Yielding of anisotropic materials 3 1.2.4. Deformation of principal element 4 1.2.5. Deviatoric stresses 5 1.2.6. The flow rule 5 1.2.7. Anisotropic flow rules 6 1.2.8. Plastic work 6 1.3. Forming characteristics of sheet metals 6 1.3.1. Approximate constitutive relationships 11 1.3.2. The relation between tensile data and multiaxial stress conditions 1.4. Forming limits for sheet metal 12 1.5. Industrial sheet metal forming 15 1.5.1. Stretch forming 15 1.5.2. Deep drawing 17 1.6. Bending and spring-back 19 1.6.1. Bending without tension 19 1.6.2. Bending under tension 22 1.7. Superplasticity 23 References 25

11

Abstract

This chapter is intended to provide a concise introduction to plastic flow theory and the mechanics of sheet metal forming. The influence of material properties on sheet metal "formability" is considered with specific reference to the properties that can be determined from a simple tensile test. The instabilities which limit different forming operations are described and the forming limit diagram introduced. Simple

2

J.L. Duncan and S.M. Panton

models are derived for some practical forming processes, and the forming conditions that result are described. A brief introduction to superplastic forming is given.

1.1. Introduction Sheet metal forming covers a wide variety of operations and consequently many different forming conditions. If we consider a small element of the sheet, as shown in fig. 1.1, it is observed that there are a number of common factors in the state of stress and strain in most of these processes. These can be summarised in the following way: 1. the sheet is formed by tractions transmitted through the sheet; 2. at least one principal stress is tensile; 3. with very few exceptions, the through thickness stress is zero and consequently a state of plane stress exists; 4. the process is limited by the instabilities of local necking or wrinkling (buckling). In this chapter, we first give an introduction to sheet metal forming and in section 1.2 look at some fundamentals of plastic flow theory which is the basis for studying the mechanics of forming. In section 1.3, we examine how the material properties of sheet metal can be described in a way that helps to characterise the formability of the sheet material. In section 1.4, the instabilities which limit the different sheet forming operations will be examined and in section 1.5, we develop simple models for some practical forming processes.

1.2. Introduction to plastic flow theory 1.2.1. The principal element

The state of stress at a point can be expressed in terms of the magnitude and orientation of three principal stresses as shown in fig. 1.2; in what follows, cr3, is the stress normal to the sheet, which, as mentioned, is usually zero. 1.2.2. Yielding of isotropic materials

Plastic yielding is the transition from small and recoverable elastic deformation to irreversible, permanent deformation. In a uniaxial test, the instantaneous value of the yield stress is referred to as the flow stress, of.

Fig. 1.1. A small element taken from a deforming sheet.

Introduction to sheet metal form&g

3

O3

(Yl

(Y2

Fig. 1.2. The principal stresses at a point.

Two well-known criteria for the onset of plastic yielding are (i) the Tresca and (ii) the von Mises yield criteria. The Tresca yield criterion states that yielding will commence when the magnitude of the maximum shear stress is equivalent to the maximum shear stress at yield in a uniaxial test. Relating the maximum shear stress to the principal stresses through Mohr's circle of stress, it can be shown that Tresca's yield criterion can be stated in terms of the principal stresses and the flow stress, 0"1 --0"3 = O f

(1.1)

for the case of al > a2 > a3. As originally stated, the von Mises criterion was based on the assumption that the distortional strain energy in a general state of stress reaches a critical value at yield. One could, however, state that yielding occurs at a critical value of the root-meansquare average of the the maximum shear stresses in an element. This gives the same result, which can be expressed mathematically as (0-1 -- 0"2) 2 "+- (0"1 -- 0"2) 2 + (0"1 -- 0"2) 2 = 20-2

(1.2)

It may be seen from either criterion that in metals, yielding is fundamentally related to the shear stresses in an element and that there is not a great difference between the two criteria. The stress conditions in sheet metal forming are generally those of plane stress and the two criteria can be compared graphically in fig. 1.3. It may be noted that each gives identical results for conditions of uniaxial stress and equal biaxial stress, but for other conditions the von Mises yield criterion predicts higher stresses for the onset of yielding.

1.2.3. Yielding of anisotropic mater&& In the above section, it was assumed that yielding is independent of the orientation of the principal axes. In anisotropic materials this assumption is not valid. A common form of anisotropy is for the material properties in the thickness direction to vary from those in the plane of the sheet. This type of variation of material properties with direction can be characterised by the constant, R which is the ratio of width

4


(Yl Tresca

i,,

__.

if2

V

_ h .

Mises

Fig. 1.3. Comparison of the Tresca and von Mises yield criteria

to thickness strain in a uniaxial tensile test. In this case a suggested plane stress yield locus [1] is (1.3)

O'~ + O'~ + R(ff 1 --if2) a = R(o'f) a

where a is a constant related to the crystal structure of the material (typically about 6 for body-centred cubic materials and 8-10 for face-centred cubic materials). 1.2.4. Deformation of a principal element

A principal element will deform without shear and the strain increments which result are principal ones. With reference to fig. 1.4, the strain increments are, de1

-

da/a

(1.4)

de 2 - db/b de1 - dc/c

A metal deforming elastically undergoes a small volumetric change; during plastic strain, however, the volume change in a typical metal is very small and is often neglected. Therefore, (a + da)(b + db)(c + dc) - abc - 0 2

2

c+~

1

3

1"~

Fig. 1.4. Deformation of a principal element.

~

"~3

Introduction to sheet metal forming

5

Neglecting the product terms of small quantities one obtains da/a + db/b + de/c = 0 so that the sum of the principal strain increments is zero, i.e. (1.5)

del + de2 + de3 = 0 1.2.5. Deviatoric stresses

The principal stresses may be considered as the sum of two components, namely the hydrostatic stress (o"h) and the deviatoric stresses 0"{, 0"~ 0"~ as shown in fig. 1.5. This leads to the following expressions for the deviatoric stresses 0"~ -- 0"1 - 0"h l 0"2 - - 0"2 -- 0-h

0"~ - 0"3 - 0"h

(1.6)

where 0"h = (0-1 + 0"2 + 0"3)/3. 1.2.6. The flow rule The relation between stress and the strain increment during plastic deformation of isotropic materials is given by the flow rule, (1.7)

de]/0"{ - d e 2 / 0 " 2 ' - d e 3 / 0 " 3 ' - d~.

i.e. the principal strain increments are in the same proportion as the deviatoric stresses, .

!

del "de2"de3

/

/

(1.8a)

"0-1 " 0 2 " 0 3

The constant, d)~, indicates the magnitude of the strain increments and and its value is not determined by the stress state. For a given yielding state of stress, the material may not deform, in which case 3~ -- 0 or in a non-strain-hardening material it may deform appreciably at constant stress. In this respect, plastic deformation differs considerably from the elastic state where there is a one-to-one relationship between stress and strain. Furthermore the same strain state, del, de2, de3 may arise from a number of different stress states which differ only in their hydrostatic component. t

~3

03 IL

~h

+

-

t

Ot

a2

Fig. 1.5. Deviatoric and hydrostatic stresses.

02 ~h

~h

6


1.2.7. Anisotropic flow rules

An alternative interpretation of the flow rules is that the vector representing the plastic strain increments is normal to the yield surface (the principle of normality). It follows that in addition to the flow rules described in (1.8a), there are flow rules which correspond to the anisotropic yield criteria described in eq. (1.3). For a situation of plane stress, the anisotropic equivalent of eq. (1.8a) is given [1] by: d e 1 " d e 2 "" (0"1) a - 1 - R ( f f 1 - 0 " 2 ) a - 1 " (0"2) a - 1 -

R(cr 2 -0"1) a-1

(1.8b)

1.2.8. Plastic work

The forces acting on the faces of the principal element shown in fig. 1.4 are ~r1.bc, crz.ac and a3.ab, hence the work done in deforming the element is given by d W = er1bc. da + ~rzac. db + cr3ab, dc

As the volume of the element is abc, from eq. (1.4) we can show that the work done per unit volume is dW/vol = eqdel + crzde2 + cr3de3

(1.9)

This may be rewritten in the form, d W/vol = a . de

(1.1 O)

where a is a generalised stress function called the equivalent, representative or effective stress and de is the equivalent or effective strain increment. It can be shown, using plastic incompressibility and the flow rules, that O" - - 1[(0" 1 -- 0"2) 2 -+" (0" 2 -- 0"3) 2 q- (0" 1 -- 0"3)2]) 0.5

(1.1 la)

and, if the element is deforming, O" : O f

(1.11b)

The equivalent strain increment is de

- - ( 2 [ ( 8 1 - 82) 2 + (82 - 83) 2 -q- (g 1 - 63)2]) 0.5

(1.12)

The equivalent stress and equivalent strain permit material properties determined from a uniaxial test to be applied in problems involving general states of stress. 1.3. Forming characteristics of sheet metals

The most basic test to characterise material behaviour is the tensile test, fig. 1.6. In this section we describe information which can be determined from this test, and explain how it may be related to other stress states which exist in practical forming operations. In the tensile test, a testpiece with a known cross-sectional area and gauge length is subjected to an increasing tensile load until the specimen fails. The extension of the


7

F

T

[ " I]

i

Lgth

Gauge ~ 1

Currentx-sectional area= A

t [ 1

Originalx-seetior~l area = A o

T

engineering strain = 8L / L

F

truestrain= In ((L+b'I_.)/L) engineering stress= F / A o true stress = F / A

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 1.6. Tensile test. gauge length, 8L, is recorded for a given load, F From this information, the engineering stress-engineering strain curve and the true stress-true strain curve may be determined. Initially we consider the engineering stress-strain curve. Different metals exhibit vastly differing stress-strain characteristics, but one may identify three or four distinct regions in the engineering stress-strain curve, fig. 1.7 illustrates the following regions. R e g i o n I. In this region of the stress-strain curve, the deformation is approximately uniform throughout the gauge length and the material remains elastic. The stressstrain relationship is linear and if the load were removed the specimen would return to its original length. In metals, the extension at the limit of elasticity is typically about one part in one thousand. Compared with other materials such as stone or concrete, metals and their alloys have a high stiffness and when they are compared with composites such as wood or with most plastics, they are very stiff. R e g i o n II. Eventually the elastic limit will be reached and the material will begin to

yield plastically. The behaviour of the material in the vicinity of the yield point is complex; however, in fig. 1.8 we observe two distinct types: (a) discontinuous and (b) H'

IH

IV

i i ! i

1 i

', |

,

i

Fig. 1.7. Engineering stress-strain curve.

8


(a)

0,)

Fig. 1.8. (a) Discontinuous and (b) continuous yield point phenomena.

continuous yielding. Discontinuous yielding is associated with ageing and with ludering, in which bands of plastically yielded material become visually apparent within regions which are predominantly elastic. Region III. Beyond the elastic limit and any discontinuous stage, the material will deform plastically and in a homogeneous fashion. The increase in the flow stress of the material during this period is known as work-hardening; however, the crosssectional area also decreases so that the engineering stress-strain curve does not give an accurate picture of the rate of hardening. Region IV. Eventually a point will be reached on the stress-strain curve at which the engineering stress reaches a maximum. Beyond this point, small imperfections will act as initiation sites for necking. Deformation will be concentrated in these regions and eventually lead to failure of the strip. We describe this process in more detail in section 1.4. When interpreting a stress-strain curve, there are various pieces of information which can be observed routinely; these are illustrated in fig. 1.9 and are: 9 yield strength indicating the limit of elastic deformation; 9 the work-hardening characteristic of the material which can be quantified by the ratio of the ultimate tensile strength (UTS) to the yield strength, af; 9 the elastic elongation; 9 the yield point elongation, if present; 9 the maximum uniform elongation Total elongation is a widely used technological indicator of the ability of the material to stretch, but some care must be exercised because this is a function not only of material behaviour but also of specimen geometry. In the same material, shorter, wider testpieces will give greater total elongation than long, narrow ones. As we apply a tensile force to a specimen, there will be strain not only in the axial direction, but also in the width and thickness directions. For an isotropic material, these transverse strains would be equal; prior processing of the sheet may result, however, in directional material properties, and these are characterised by the ratio of width strain to thickness strain as shown in fig. 1.10. This has been denoted by, R, in eq. (1.3) above and it is also known as the r-value. It may be noted that a high rvalue will tend to retard the thinning of the material under tension.


9

Work Hardening UTS / YS typically in the range of

1.2- 2.5 Yield strength typically 150-600 MPa

v

Maximum uniform elongation

l ~ ~ e elongation typically ~ II-"1 around0.1-0.3% II ~ yield point elongation [ I ifpresent

To tal Elongation

Fig. 1.9. A typical engineering stress-strain curve for metals and alloys. F

Thickness

Width

r = width strain / thickness strain

Typically Steels I to 2.5 Aluminium 0.6 to 1.0

F Fig. 1.10. Determination of r-value.

In fig. 1.6, we refer to both true stress-strain and engineering stress-strain curves. The engineering curve is widely used, particularly in specifying material properties. In modelling and analysing the mechanics of sheet forming processes, it is necessary to use the true stress-strain curve. The distinction is as follows. As the specimen will strain in the width and thickness directions as well as axially, the cross-sectional area of the specimen will change; the true stress (the axial load divided by the current cross-sectional) area will differ from the engineering stress (the axial load divided by the original cross-section) particularly when the extension increases to 10% or more. We may also note that for any increase in load, the true strain increment is the resulting change in length divided by the current length (as opposed to the

10


engineering strain increment which is the resulting change in length divided by the original length). If we integrate the true strain increments we obtain true strain defined as;

e~- f de- f dL/L-ln(L/Lo)

(1.13)

If we plot true stress against true strain, fig. 1.11, we see a curve that is very different from the engineering stress-strain diagram; it shows that strain hardening continues at a diminishing rate, but it does not cease at the maximum load. One characteristic of sheet metal behaviour that is often referred to is "formability". There is no precise definition of formability as in general usage, it is taken to mean the response of a particular material to a given forming process; this response is often measured in terms of the percentage of rejects in running the sheet in the press shop. As formability depends on the material, the type of deformation process and the state of the tooling used, it is not a single-valued quantity for any batch of sheet. Variability is a major factor in the perceived formability, but apart from this, the measurable properties that can be derived from the tensile test which are considered to enhance formability are: 9 high strain hardening as indicated by the UTS/yield ratio or the slope of the true stress-strain curve; 9 resistance to thinning in terms of a high r-value. Typical values of these properties are given in table 1.1 for different grades of steel sheet commonly used in sheet metal forming. In general, discontinuous yielding and yield point elongation diminish formability and the effects of temperature and strain rate may also need to be considered.

"

w

g Fig. 1.11. True stress-strain curve. TABLE 1.1 Typical material properties for cold-rolled, low-strength steel Commercial quality

Drawing quality (DQ)

DQ special killed

Interstitial free

230 320 1.35 0.20 1.0 30-35

200 310 1.55 0.21 1.2-1.5 38-42

180 300 1.75 0.22 1.6-1.8 40-45

150 320 2.25 0.24 2.0-2.2 45-48

Yield strength (MPa) Ultimate tensile strength (MPa) UTS / YS n r Total elongation (%)


11

1.3.1. Approximate constitutive relationships

In this section we will look at simple approximations to the uniaxial stress-strain curve. Figure 1.12a shows a rigid-perfectly plastic approximation which is particularly useful for approximate load calculations. In fig. 1.12b, we consider an elasticperfectly plastic model used in studying small strain processes such as bending and springback. In fig. 1.12c, a power hardening law has been fitted to the true stresstrue strain curve over the plastic range. In terms of the uniaxial stress and strain, this can be expressed as (1.14)

al = Ke'~

where K is a coefficient indicating the strength of the material and n is the strain hardening index. It is found that this expression will fit true stress-strain curves of annealed sheet very well except at very low values of strain near initial yielding. In fig. 1.12d, we see a model for the stress-strain-rate characteristics of strain-rate sensitive materials such as superplastic alloys. These empirical relations are presented in order to show that tensile test results, although containing much data, can be summarised by simple models; in certain situations even a model as simple as the rigid-perfectly plastic may give quite acceptable results.

1.3.2. The relation between tensile data and multiaxial stress conditions

The uniaxial stress-strain properties determined from tensile testing as shown in fig. 1.13 can be used in the analysis of the multiaxial stress conditions in general sheet forming operations. In the elastic region (I) the stress-strain characteristics are defined by the wellknown generalised Hooke's laws. The pertinent material properties are Young's modulus and Poisson's ratio. o=-Ke"

v v

o

Log o

(b)

e "-

Bi~m

(d) Log t

Fig. 1.12. Approximate constitutive relationships: (a) Rigidly perfectly plastic, (b) elastic-perfectly plastic, (c) power hardening, (d) non-Newtonian fluid.

12

.


.

t,f

.

|~

~Work Hardening/

(II) C,e.,neralised - I Hooke's l (I)

a

-[ w

s

~ "

Fig. 1.13. Relating tensile test data to multiaxial states of stress. The conditions for initial yield (II) are determined using either of the yield criteria described in section 1.2. In the plastic region (III) the stress conditions continue to satisfy the yield criterion and the generalised stress function, a, is equal in magnitude to the instantaneous value of the uniaxial yield strength, i.e. the flow stress of the material, af. The strains in the uniaxial and generalised process are el and e as defined above. For an isotropic material, the generalised stress-strain curve and the uniaxial curve are identical. 1.4. F o r m i n g

l i m i t s for s h e e t m e t a l

The forming of sheet metal is limited by two types of instability, tensile instability (necking) and wrinkling (buckling). In any sheet material, there will always be imperfections in the form of areas which are slightly thinner or weaker than the surrounding sheet. These form the focus of potential necks and we consider first a small geometric imperfection in a tensile test as shown in fig. 1.14. The reduction in the cross-sectional area causes a greater stress in this locality and hence a greater strain; the increased strain will reduce the crosssectional area. The deformation of the whole testpiece will remain stable so long as the force required to deform the imperfection continues to increase with extension of the specimen. At some point, the increase in strength due to strain hardening will be overcome by the reduction in cross-sectional area and deformation will become unstable. For an incompressible material, it can be shown that this occurs when dal/de1
n In the tensile strip, a neck will develop at this point which will cover a region in length roughly equal to the width of the specimen. This is termed a diffuse neck. Once a neck has developed, extension of the testpiece is accommodated by deformation in the neck; this causes an increase in the local strain-rate and with ratesensitive materials the development of necking is slowed and it becomes more diffuse. For materials having the kind of behaviour modelled in fig. 1.12d with high "m" values, such as superplastic alloys, this effect is large and the rate of growth of a neck in a material is imperceptible. In such situations, the strip stretches in a nearly uniform manner giving the useful property of permitting high strains. It is stated above that diffuse necking is associated with a maximum in the load carrying capacity of a region of the testpiece, i.e. the product of stress, trl, and area, A, reaches a maximum. Some non-metals, such as certain polymers, have a stressstrain relation which is convex upwards, as shown in fig. 1.15; the same load can be sustained at the initiation of diffuse necking at A as at B. Deformation is therefore only unstable between these points and the neck will draw out until conditions reach the point B and then the neck will travel along the testpiece in a stable manner. This phenomenon is not seen in metals although, in aged materials, Ltider's bands will travel along the strip in a roughly analogous manner. In general sheet forming processes, a diffuse neck is prevented from developing by the constraint of the surrounding material; therefore the sheet will strain in a quasistable manner until a local neck or groove develops with a width of the order of the sheet thickness, as shown in fig. 1.16. If one of the principal strains in the plane of the sheet is zero or negative, then there is a direction of zero extension in the sheet. A ." Constant 10ad line

i3

Fig. 1.15. Stress-strain curve for a polymer which will deform by drawing out a neck.

Fig. 1.16. Imperfection in a continuous sheet.

14


local neck, as postulated by Hill [2], is most likely to develop in this direction when the strains satisfy the relation,

(1.15)

81 + 8 2 -" n

If both of the principal strains are tensile, then there is no direction of zero strain. In this case, the Marciniak model [3] shows that the shape of the yield locus can stabilise the process so that necking is delayed. The Hill and Marciniak models when combined give rise to a line in the strain diagram, fig. 1.17, which indicates the onset of local necking. This is called the "forming limit curve". The existence of this curve can also be established experimentally; the standard procedure is to form strips of various width over a hemispherical punch and observe the strain at which necking occurs by use of a circular grid. The use of differing strip widths creates strain conditions which vary from plane strain through to biaxial tension. The whole diagram, fig. 1.17, is commonly known as the "forming limit diagram" and it is widely used in the diagnosis of sheet forming problems. Strains in various regions of the sheet can be measured using some gridding technique and plotted in this diagram. As an example, a typical draw die operation as shown in fig. 1.18, the sheet is clamped around the edge and drawn in by the action of the punch. When the punch bottoms in the die, the region in the centre of the sheet will be stretched in biaxial tension as shown. In the side walls, the sheet is stretched in plane strain while

Hill

Major Principal Strain A E1

Marciniak

El+ez=n

.

9

Biaxial

Tension

/

s t I, s s, f ,,,

Minor Principal Strain

Fig. 1.17. Forming limits imposed by necking.

Stretc~ng

Plane Strain

Drawing Fig. 1.18. Press forming (with draw die).


15

in the corners, the sheet is stretched in the radial direction and compressed circumferentially. A grid circle at each of these regions will be deformed as shown in fig. 1.19 and the strains in the part will fall within the envelope shown. The importance of leaving a safety zone between this envelope and the forming limit curve is clear. It should be accepted as inevitable that small variations in process characteristics such as friction will cause some variation in strain, and if this variation in strain causes failure of the parts, then the process should be considered incapable. For this reason the forming limit diagram is.an important process control tool. The forming limit diagram is also an important tool during die try-out and can indicate appropriate modifications to the tooling. In general, these modifications will attempt to pull the critical strains away from the forming limit curve for the material.

1.5. Industrial sheet metal forming Industrial applications cover a wide spectrum of processes and, as shown in fig. 1.18, in any one process different regions will have different straining paths. It is not possible here to deal with the whole range of industrial forming operations, but it is useful to look at the idealised cases that exist at either end of this s p e c t r u m - these are two-dimensional stretch forming and axisymmetric deep drawing. The basic mechanics of each will be introduced and from this it is possible to identify the kind of material behaviour that is most advantageous for the particular operation.

1.5.1. Stretch forming In forming shallow, smoothly contoured shells such as autobody panels the sheet is stretched over a punch in a double-acting press as illustrated in the twodimensional model in fig. 1.20. The strains necessary to achieve the desired shape Plane Strain

Equal Biaxial

, s

Drawing

""

""

(Shear)

Typical envelope of strains in a formed part Fig. 1.19. Typical envelope of strains on a forming limit diagram.

16


Fig. 1.20. Two-dimensionalmodel of stretch forming. are often quite small, but in order to ensure that the shape of the part is properly fixed without excessive spring-back and in some cases to gain strength in the part by strain hardening the sheet, the strains are often much greater than those required just by geometry. In this type of forming, the part required is contained within the trim line shown; the edges of the sheet under the blankholder are used to provide the appropriate tension to stretch the sheet over the punch and this material is discarded after trimming. The restraint at the flange is created in two ways: one is by friction between the sheet and the blankholder and the other by means of the draw bead shown. In a draw bead, the sheet is bent and unbent as it passes through the bead; the plastic work done results in additional tension on the downstream side. The difference between the two methods of restraining the sheet is that the friction effect will depend on both the coefficient of friction and the blankholder force while the draw bead will create a tension which is proportional to the yield stress and the thickness of the sheet, as may be inferred from section 1.6. In a three-dimensional stretch forming die, the important feature is that the flange is not clamped rigidly, but is allowed to move inward in a controlled fashion. In order to obtain sufficient tension to stretch the sheet over the punch, the tension in the side wall between the blankholder and the punch must be very high and to prevent tearing here the material must have good strain-hardening properties. In the two-dimensional case, the minimum strain will be at the centreline. Due to friction between the sheet and the punch, the tension will build up away from the centre. The equation governing this behaviour can be summarised with the aid of fig. 1.21. If the sheet element subtends an angle, d4~, and is being stretched by a tension, T, (force per unit length in a direction perpendicular to the plane of the diagram), then equilibrium in the radial direction gives that q = T/R

(1.16)

where, q, is the tool contact pressure and R the local radius of curvature of the tool. In the tangential direction, dT --/zq. Rd~b = / z T . dq~

(1.17)

The tension in the sheet is T -- tcr

(1.18)


17

Fig. 1.21. Element of a sheet being stretched over a punch.

Differentiating and substituting, we obtain

d T / T =/x(dcr/~r + dt/t) dqb

(1.19)

The first term in the brackets in eq. (1.19) is the rate of strain hardening and the second term is the rate of thinning. In order to obtain good stretching over the punch without excessive thinning in the most highly stressed regions, we require a low coefficient of friction and good strain hardening. The latter requirement often means that the sheet must be in a fully annealed condition and referring to table 1.1, it is clear that IF steel will behave well in this application. (In this case, formability is traded off against strength as well as cost.)

1.5.2. Deep drawing In drawing an axisymmetric cup as shown in fig. 1.22, most of the deformation takes place in the outer region or flange which is drawn in to create the cylindrical walls of the cup. The blankholder is used to keep the flange flat and avoid wrinkling; some frictional restraint is inevitable but this is kept a small as possible.

To

BlankH o l ~

Punch ]

--~..T,+OT,

Die

To (a)

Fig. 1.22. Deep drawing a cylindrical cup.

(b)

18


The equilibrium equation for an element in the flange shown in fig. 1.22b is

dT~o To-T~o= T~

r

0

(1.20)

The stress state in the flange is illustrated in the yield locus in fig. 1.23a. At the outside, A, a state of uniaxial compression will exist; at the inner part of the flange, B, the radial tension, T~, causes the radial stress to approach the yield stress in uniaxial tension, ~rf. The corresponding strain paths are shown in fig. 1.23b. It may be seen that the strains in the centre of the part are small, indicating that in deep drawing most of the deformation is confined to the flange. The forming limit curve is also shown in this diagram and it will be seen that necking is unlikely to limit the process. Furthermore as the level of the forming limit curve depends on the strain-hardening index, n, a low value of n can be accommodated and it is possible to deep draw fully cold-worked sheet. In the diagram in fig. 1.23b, the left-hand diagonal is a path of constant thickness deformation; in drawing the flange, its thickness will be unchanged or slightly increased. It may also be shown that a high r-value is advantageous in deep drawing as it increases the strength of the cup wall, which would deform by stretching and thinning, and decrease the strength of the flange. This brief examination of two idealised processes at the extremes of the spectrum of practical forming operations shows that different material properties such as the strain-hardening index, n, and the normal anisotropy ratio, the r-value, influence different processeses in different ways. In general, the magnitude of the tractions or tension that is developed in the sheet can be understood by examining the loading

r,

A

(a)

Fig. 1.23. Axisymmetricdeep drawing.

TO

(b)


19

paths in a stress diagram such as fig. 1.23a and the deformation of the sheet and the limits imposed by necking anticipated from the forming limit diagram, as in fig. 1.23b. 1.6. Bending and spring-back Sheet bending is generally considered as a plane strain-plane stress process and the variables are indicated in fig. 1.24. The moment, M, and the tension, T, are values per unit length along the bend. Except for very small radius bends, the strain distribution is assumed to be linear, i.e. el - ln(1 + y/R)

(1.21)

where y is the distance from the neutral axis. Since y/R is small, el is approximately equal to y/R [4].

1.6.1. Bending without tension The neutral axis is at the mid-plane, and the strain distribution is as shown in fig. 1.25. The stress distribution depends on the stress-strain relationship for the material, and it is convenient to express this in terms of the major stress and strain, i.e. 0"1 = f(el) (82

(1.22)

- - 0" 3 - - 0 ) .

z"

~.':.~~~..-~:

t~2

....

9

t

/

,'-,'l

"

'~,~',,

-:'~::~:~:~.:~

"

_

"

,4

"l

/ I / s /

I / I

I

/

',.

0

." R

." /

I 9

/

I

Fig. 1.24. Variables in sheet bending.

, ; : ~

M

20

J.L. Duncan and S.M. Panton 01 - E'81

M

~

,~ 9

(Plastic/ power hardening)

Fig. 1.25. Stress and strain distributions in bending. For an elastic-perfectly plastic material: (i) the stress in the elastic region is given by or1 = E ' e l

(1.23)

where E ' = E/(1 - v 2) and v is Poisson's ratio. (ii) the stress in the plastic region is given by o1 = S

(1.24)

where for a perfectly plastic, von Mises material of constant flow stress, S is related to the flow stress (~rf) by S = (4/3) ~ If the material is elastic, the following well-known equation applies M I I = cqly = E ' I R

(1.25)

At the limiting elastic curvature, ~r1 = S at y = t/2 and hence the limiting elastic curvature and the corresponding moment are given by, (1/R)E -- 2 S / E ' t , ME -- St2/6

(1.26)

As the curvature increases, the material will progressively contain more material in the plastic region, fig. 1.26. From the right-hand drawing of fig. 1.26c, the fully plastic moment, can be determined as Mp = St2/4

(1.27)

A typical moment-curvature characteristic is shown in fig. 1.27. It may be noted that as Mp = 1.5ME, the change in curvature upon unloading A(1/R) = 1.5 (1/R)E. Hence A(1/R) = 3S/E't

(1.28)


21

Increasing Moment v

PI

.Elastic

M,

M P

Limiting Elastic

Elastic- Plastic

Fully Plastic

Fig. 1.26. Stress distributions with increasing moment and curvature in an elastic-perfectly plastic material.

9

I

l

I

I

I

I

I

I

I

t

I

Mp

l

1/R

I

Curvature

E't

A (l/R)

Fig. 1.27. The moment-curvature diagram for an elastic-perfectly plastic sheet.

Unloading the plastic moment from mp to zero is associated with a change in bend angle A0 and a change in radius AR (fig. 1.28); the length of the neutral axis will remain unchanged, hence

(A(1/R)/(1/R)) + (A0/0) = 0

(1.29)

Combining (1.28) and (1.29), we can obtain the change in bend angle or spring-back as

AO = 3(S/E') (R/t)O

(1.30)

Equation (1.30) shows that the spring-back angle is proportional to the ratio of yield stress to elastic modulus. For annealed sheet, this is typically around 1 to 1,000; however, for hard temper sheet it may increase to 1 in 300 or greater. Equation (1.30) also shows that spring-back is proportional to the ratio of radius to sheet thickness. For small radius bends, such as are typical in roll forming, this may be around 2. For large radius bending, such as may be typical with autobody panels, this may be much higher, and spring-back will be large. Because of the variability in S, tl~e process may

22


,

.... 9 --~~"-':~;i~::..'-.',.:m. ~ ~ i ~ : ~ . . , , ~.~i~ii:.'.'~..~..~ i ~ ~ "~'~:~!~....

! 9

,r3,

/

i i i

/

/ R 0

/

/

/

/

/ /

/

/

/

R+Z~R

Fig. 1.28. Spring-back of a sheet upon unloading of a moment. be difficult to control. A technique for avoiding these problems is discussed in the next section. If the unloading process from a fully plastic moment is elastic, there will be a residual stress distribution in the sheet, as shown in fig. 1.29. This is an idealised representation, but sheet metal that has been subjected to various bending, unbending and straightening processes is liable to have significantly more complex residual stress distributions. 1.6.2 9 Bending under tension

Equation (1.30) indicates that if a sheet is given a gentle curvature by the application of a moment, the spring-back would be large. To obtain accurate shape as, for example, in curving an exterior panel for an aircraft, the sheet is curved by stretching over a former, as shown in fig. 1.30. It will be seen from the stress distributions shown in fig. 1.30, that as the tension increases, the m o m e n t required to maintain a curvature less than the limiting elastic curvature will remain constant until the outer fibre stress reaches the yield stress S. When the tension has reached that required to stretch the sheet plastically, i.e.

Fig. 1.29. Residual stresses upon unloading.


(a)

23

t

M

M

(b) (i)

S

(u)

......

(Iv) ~

S

(c) M Me

w

~9

T

St Fig. 1.30. (a) Bending under tension. (b) Stress distribution under increasing tension. (c) Moment required to maintain the curvature as the strip tension increases.

T - S t , the moment has reduced to zero and the spring-back due to bending will also be zero. In practice, the sheet will be stretched plastically by a few per cent and will then take up the radius of the former accurately.

1.7. Superplasticity The characteristic behaviour of metals and their alloys is that at room temperature they can be deformed plastically and will strengthen or work harden as they do so. The resistance to flow depends largely on the amount of deformation imposed and not on the rate of working. At higher temperatures, such as those used in hot forging, their strength will diminish and remain constant during deformation; they do not strain harden, but the flow strength is dependent on the rate of working. As the temperature increases, metals typically have a well-defined melting point and change from a solid with an appreciable, but still low, rate-sensitivity to a low-


24

viscosity liquid. They do not display the semi-fluid highly viscous behaviour of materials such as glass or thermoplastics at the temperatures used for glass-blowing and blow-moulding. The ability to draw out a thin filament of glass from a molten pool or to blow a tube of molten polyethylene out to many times its diameter can be shown to depend on the fact that the resistance to flow is very nearly proportional to the rate of extension, i.e. these materials behave as ideal viscous liquids and imperfections do not become catastrophic. Although highly viscous behaviour is not a characteristic of metals, even at elevated temperatures, certain alloys do show moderate viscosities under unusual conditions. This phenomenon has been termed superplasticity. There are a few alloys which can be produced in a very fine grain condition, less than 10 microns, and this state is stable at temperatures up to about half of their absolute melting temperature. If these alloys are hot worked, they do not strain harden, but have a flow stress which obeys a law of the kind, O- - - B ~ m

where m, the strain-rate sensitivity index, is in the range 0.3 ~ 0.8. The alloys that have received most attention are Zn 22%A1 which is formed at 250~ and Ti 6%A1 4%V which is superplastic between 900 and 980~ If these materials are deformed in an elevated temperature tensile test, extensions of several hundred per cent are possible. The flow stress at these temperatures is low compared with typical hot-working strengths in metals but it is still higher than those observed in thermoplastics in moulding and blow-forming. Vacuum-forming can be used, but for reasonable production times, pressure forming is necessary. In designing superplastic forming processes, it is necessary to keep the strain rate within the range at which the rate-sensitivity index is highest; this may only extend over about a decade in the vicinity of 10 -3 s -1 . A useful example is illustrated in fig. 1.31 which shows the two-dimensional pressure forming of a sheet into a corner. If the sheet is clamped at A and B, the first stage of the process can be considered as uniform stretching of the sheet until it just touched the side-walls of the die; assuming incompressibility, the thickness at this instant is

A / / /

//////7-//t3

/ /

Fig. 1 . 3 1 . 2 - D p r e s s u r e f o r m i n g of a sheet into a c o m e r .

Introduction to sheet metalforming

25

tA -- (2~/2/:r)to F r o m this point onwards, the sheet is often assumed to stick to the die wall without further thinning and the current thickness, t, of the unsupported sheet tangent at the height, h, can be calculated by geometry. If the strain rate prescribed for the process is k0, the membrane stress is cr = p h / t and the required pressure is p -

tB ' /h

If it is desired to form into a small corner radius, the final value of h is small and the pressure could be high. As indicated, this usually precludes vacuum-forming. In the above analysis, the thickness is determined by geometry and diffuse necking is neglected. This is often an acceptable approximation in analysing superplastic process; however, it becomes less valid as the strain-rate sensitivity index decreases; more elaborate calculation may then be necessary.

References

[1] Hosford, W.F. & Caddell, R.M., Metal Forming: Mechanics and Metallurgy, Prentice Hall, New Jersey (1983). [2] Hill, R., The Mathematical Theory of Plasticity, Oxford University Press, London (1950), p235. [3] Marciniak, Z. & Kuczynski, K., Int. Journ. Mech. Sci., 9 (1967), p609. [4] Marciniak, Z. & Duncan, J.L., Mechanics of Sheet Metal Forming, Edward Arnold, London (1992).



Chapter 2

Thermoplastic Composite Sheet Form&g: Materials and Manufactur&g Techniques B. T o m a s , ~ S T R O M

Department of Aeronautics, Division of Lightweight Structures, Royal Institute of Technology, S-IO0 44 Stockholm, Sweden

Contents Abstract 28 2.1. Introduction 28 2.2. Constituents 29 2.2.1. Matrices 29 2.2.1.1. Polymer morphology 30 2.2.1.2. Structural aspects influencing properties 31 2.2.1.3. Thermoplastic polymer matrices 34 2.2.2. Reinforcements 38 2.2.2.1. Glass fibers 39 2.2.2.2. Carbon fibers 40 2.2.2.3. Organic fibers 41 2.2.2.4. Other fibers 42 2.2.2.5. Reinforcement-matrix interaction 42 2.2.3. Preimpregnated reinforcements 43 2.2.3.1. Solvent impregnation 44 2.2.3.2. Melt impregnation 45 2.2.3.3. Powder impregnation 46 2.2.3.4. Commingling 47 2.2.3.5. Comparison of preimpregnated reinforcement types 47 2.2.3.6. Molding compounds 48 2.3. Properties 48 2.3.1. Matrices 48 2.3.1.1. Thermal and rheological properties 49 2.3.1.2. Mechanical properties 52 2.3.2. Reinforcements 54 2.3.2.1. Thermal properties 54 2.3.2.2. Mechanical properties 54 2.3.3. Composites 55 2.3.3.1. Prediction of thermal properties 55 2.3.3.2. Prediction of mechanical properties 56 2.3.3.3. Experimentally determined thermal properties 57 2.3.3.4. Experimentally determined mechanical properties 58 27

28

B.T. flstrd'm

2.4. Manufacturing techniques 60 2.4.1. Prepreg lay-up 61 2.4.2. Prepreg consolidation 61 2.4.2.1. Vacuum-bagconsolidation 61 2.4.2.2. Matched-die consolidation 62 2.4.2.3. Double-belt-press consolidation 63 2.4.2.4. Tape laying 64 2.4.2.5. Intermittent matched-die consolidation 65 2.4.3. Sheet forming 65 2.4.3.1. Matched-die molding 66 2.4.3.2. Rubber-die molding 67 2.4.3.3. Hydroforming 68 2.4.3.4. Deep drawing 68 2.4.3.5. Diaphragm forming 69 2.4.3.6. Folding 70 2.4.3.7. Roll forming 70 2.4.3.8. Matched-die molding of GMT 71 Acknowledgement 72 References 72

Abstract

This chapter provides an introduction to thermoplastic composite sheet forming and the raw materials commonly used. First the relevant basics of polymer physics are introduced in order to provide a rudimentary background to the matrices' macroscopic properties and processing requirements, whereupon different reinforcement types and preimpregnated reinforcement forms are introduced. Second the thermal, rheological, and mechanical properties of common sheet forming raw materials and their composites are discussed and representative properties given. Finally a comprehensive yet brief overview of different composite sheet forming techniques, including blank consolidation processes, is presented. 2.1. Introduction

On the face of it, many structurally capable composites are shell-like components that one way or another ought to be manufacturable through conformation of a flat raw material blank into a complex-shaped final component. It should therefore come as no surprise that the topic of thermoplastic composite sheet forming is one of intense research, which has resulted in a number of forming techniques. Since the concept of thermoplastic composite sheet forming forming of a flat piece of material into an arbitrarily curved c o m p o n e n t - is identical to sheet metal forming, a few of the techniques investigated have been borrowed from this relatively mature manufacturing field, while others emanate from thermoset composites manufacture. Only a minority of the techniques discussed herein have genuinely been invented or developed exclusively for sheet forming of thermoplastic composites. While all forming techniques discussed in this chapter have proven technically feasible, widespread commercial success is rare. However, given the significant research and development

Thermoplastic composite sheetforming

29

efforts thermoplastic composite sheet forming is seeing, there should be little doubt that all this work gradually will lead to commercial successes in the near future. This chapter aims to give the novice to the topic of thermoplastic composite sheet forming an introduction to the raw materials used, their properties, and common forming techniques. The first two sections of the chapter introduce the constituents most commonly used and then go on to discuss the thermal and rheological properties so relevant to manufacturing. Since sheet-formed components are most likely to be used in structural applications, the mechanical properties of both constituents and their composites are also briefly treated. The final section of the chapter presents a comprehensive overview of sheet consolidation and sheet forming techniques, but since several of these techniques will be more thoroughly treated in other chapters of this volume this treatment is brief.

2.2. Constituents

The constituent materials that make up, or constitute, a composite are normally considered to include at least the matrix and the reinforcement. Oftentimes the matrix is not homogeneous but rather mixed with some performance-enhancing additive. Likewise, the reinforcement is normally surface treated or coated with some performance-enhancing substance. These substances may or may not be considered constituents on their own right. This section of the chapter covers the constituents most relevant to thermoplastic sheet forming and describes available types and family characteristics.

2.2.1. Matrices

The matrix of a composite has several functions: it is a binder that holds the reinforcement in place, it transfers external loads to the reinforcement, and it protects the reinforcement from environmental exposure. Moreover, the matrix redistributes the load to surrounding fibers when a fiber fractures and supports the fibers to prevent buckling in compression. Polymer matrices clearly dominate in composites applications, although other matrices are used to a limited degree in specialized applications; these other matrix types are not covered in this chapter. To fully appreciate differences between candidate polymer matrices in terms of properties and processing requirements, it is essential to at least have a conceptual understanding of polymer physics and chemistry. However, this treatment is primarily intended for readers with little chemistry background and the following sections therefore refrain from delving too far into the field of polymer science; the interested reader is referred to the literature specializing in this topic. The following treatment thus merely aims to provide a basic understanding of the polymerscience aspects most relevant to composites properties and their manufacturing requirements, and in particular matrices and issues pertaining to thermoplastic sheet forming.

B.T. ~lstrO'm

30

2.2.1.1. Polymer morphology A polymer is a high-molecular-weight compound that is composed of a multitude (poly) of repeated small segments (mers). Polymers are organic compounds primarily based on carbon and hydrogen atoms bound to each other by primary, or covalent, bonds. Carbon is capable of forming four covalent bonds located tetrahedrally around the atom. Carbon atoms may form covalent bonds to each other both through single and double bonds, the former being referred to as saturated and the latter unsaturated. (Carbon atoms can also bond to each other through triple bonds, but such bonds are seldom encountered in polymer science.) In contrast, hydrogen can form one covalent bond only. The least complex polymers are the hydrocarbon polymers which contain carbon and hydrogen only. The simplest hydrocarbon polymer is polyethylene (PE), the repeating unit of which is illustrated in fig. 2.1, where "n" indicates a large number (103-106) of repeating mers to form a practically useful polymer and " - - " indicates covalent bonds. It is important to note that the two-dimensional rendition of the structure in the figure in reality is three-dimensional due to the tetrahedrally arranged bonds of the carbon atoms. Another important and common hydrocarbon polymer is polypropylene (PP); see fig. 2.2. Several other hydrocarbon polymers besides PE and PP exist, although they are rarely of interest in composites applications. However, if one includes other elements than carbon and hydrogen, virtually endless combination possibilities arise. Apart from carbon and hydrogen, the most common elements are oxygen, nitrogen, sulfur, fluorine, chlorine, and silicon. As long as only carbon makes up the polymer backbone, one talks of carbon-chain polymers, whereas polymers having some non-carbon backbone atoms are referred to as heterochain polymers.

H

H

I

I

-(- C-- C-)-n I

H

I

H

Fig. 2.1. Repeating unit of PE. H

H

H

H

I

I

I

I

-(-- C - C-)-n I

H H-C-H

-(.- C-- C-)- n I

H

I

CH 3

I

H Fig. 2.2. Two ways of illustrating the repeating unit of PP.


31

2.2.1.2. Structural aspects influencing properties There are strong relationships between the molecular structure, or configuration, of a polymer and its macroscopic properties in both solid and liquid form. These relationships may be hierarchically divided into intramer, intramolecular, and intermolecular structure. The next three subsections describe some molecular aspects of relevance and their influence on the polymer's macroscopic properties. Intramer structure. The properties of the polymer are to a large degree influenced by the structure of the mer, i.e. what elements are present and how they are bound to one another. Single bonds allow rotation around the bond axis (torsion), while double bonds do not. Double bonds and cyclic structures, such as the common aromatic ring (see fig. 2.3), in the backbone and large side groups leave the molecule inflexible and bulky, thus impeding molecular motion which significantly influences macroscopic properties. Polyisoprene is a good example to illustrate the strong influence of apparently subtle differences in mer configuration (see fig. 2.4); cis-polyisoprene (natural rubber) is soft whereas trans-polyisoprene (gutta percha) is a hard plastic. Note that these two mer configurations are different since the double bond does not allow rotation. The cis-prefix denotes that the backbone continues on the same side of the double bond and the trans-prefix that the backbone extends on different sides, cisPolyisoprene and trans-polyisoprene are said to be geometric isomers. Intramolecular structure. While the mer may be fully defined, there are still many combinations in which it may form a polymer. Taking PP as an example, the methyl (CH3) group may be located in different positions; see fig. 2.5. Isotactic PP has all methyl groups on the same side, syndiotactic on alternating sides, and atactic in a random manner. Even though single bonds permit rotation, these three forms of PP are different (recall the tetrahedral arrangement of the four bonds of the carbon atom). The regular structures of isotactic and syndiotactic PP, which are referred to

_ cIC'~c -C

I

II

O#

C-

I

Fig. 2.3. Two ways of illustrating the repeating unit of an aromatic group.

H I

H-C-H I

C I

-C-H I

H

H H I

C I

H-C-

I

H

I

H-G-H I

H I

H-GI

C

C

-C-H

H

I

I

I

H

Fig. 2.4. Repeating unit of c/s-polyisoprene (left) and trans-polyisoprene (right).

B.T. ~tstrO'm

32 H I

-CI

H

H I

H I

H I

H I

H I

C -C - C -C-

C-

CH3H

CH3

I

I

I

I

CH3H

I

H

CH3H

H

-C-

H

C -C-

C -C-

C-

H

CH3H

H

CH 3

I I

H I I

I

I

I

I

I

I

H

I

I

H

CH3H

H

-C-

C -C-

C -C-

H

CH3H

I

I

H

I

I

I

I

H

I I

H I

I

H I CI

CH3

Fig. 2.5. Isotactic (left), syndiotactic (center), and atactic PP (right).

as stereoisomers, translate into quite different macroscopic properties from those of atactic PP. Of great significance to the macroscopic properties of a polymer is the number of repeat units or, alternatively, the molecular weight. However, there is no way of producing polymers of a single molecular weight and in reality it may vary by three to four orders of magnitude within the same sample. While all polymer examples so far discussed have been linear with small side groups only, branching may occur. Further, no attention has been paid to the ends of the molecules, which obviously must deviate from the idealized polymer structure, but since the number of repeating units is so large possible effects of the end groups are most often ignored. The molecules may also contain impurities, i.e. some flaw inconsistent with the idealized polymer structure. To improve certain properties of a polymer it is possible to polymerize it from more than one type of monomer. Two different repeating units (here denoted A and B) thus may be polymerized into alternating (ABABABABABA), block (AAABBBBBBAA), random (ABBABAABBBA), or graft fashions, where the latter has a backbone made up entirely of one mer with branches made up entirely of the other one attached. Intermolecular structure. The interaction between molecules is a function of intramer and intramolecular structure. It was earlier pointed out that the intramolecular bonds are covalent. There are also secondary bonds, e.g. van der Waals, hydrogen, and dipole-dipole bonds, which act between molecules. The reason for referring to them as secondary bonds is that they are an order of magnitude weaker than the covalent bonds and therefore are of secondary albeit s i g n i f i c a n t - importance. At a sufficiently high temperature a polymer sample melts; the individual molecules of the melt are randomly arranged, interlaced, and undergoing constant rearrangement. The covalent bonds ensure the integrity of the molecules while the molecular movement caused by the heating dwarfs the secondary bond forces. If the polymer sample then very quickly is cooled, or quenched, into a solid the random molecular arrangement is essentially frozen in place by secondary bonds. However, if the polymer sample is instead cooled slowly, the individual molecules may, under certain conditions, attempt to align themselves into a regular crystal formation. The crystal conformation is preferred since it represents the lowest possible energy state for the molecules. Due to the precise close-packing of the molecules in the crystal state, the crystal structure has higher density than the random molecule arrangement, which is usually referred to as amorphous or glassy. Further, since the crystal conformation is preferred due to the lower energy state, energy is released upon crystallization, i.e. it is an exothermal process.


33

In reality it is not possible to achieve complete crystallinity and amorphous areas therefore partly surround the crystals; polymers possessing the ability to crystallize are consequently referred to as semicrystalline. The degree to which a polymer may crystallize is to a large degree dependent on the molecule being regular in structure and flexible. This is the reason why isotactic and syndiotactic PP may form crystals whereas atactic PP may not, and why PE, due to its extremely simple, regular, and flexible structure, may achieve the highest degree of crystallinity of any polymer. Likewise, molecules that do not contain double bonds and cyclic structures in the backbone or bulky side groups are more likely to achieve a greater degree of crystallinity than if they had these features. Although many polymers of relevance for use as composite matrices are semicrystalline, most polymers are unable to achieve any appreciable degree of crystallinity under any circumstances. The resulting degree of crystallinity in a semicrystalline polymer is enhanced by higher temperature and pressure during crystallization as well as by lower molecular weight. From a manufacturing point of view, especially the former two dependencies are highly relevant. The temperature dependency of the degree of crystallinity is usually assessed in terms of cooling rate; see fig. 2.6. As the figure shows, it is possible to obtain either a more or less entirely amorphous structure through quenching of the melt or a highly crystalline structure through very slow cooling. Upon gradual heating of a semicrystalline polymer the amorphous regions melt before the crystalline regions and a melt with the random molecular arrangement is regained. The melting of the crystalline phase consumes energy in order to dislodge the molecules from their preferred low-energy state and the process is therefore endothermal. The reason why it is possible to reversibly go from solid to melt to solid etc. is that only secondary bonds act between molecules. A polymer with such a reversible behavior is called thermoplastic. In theory the melting and solidification cycles can be repeated an infinite number of times without affecting the polymer. In reality parts of some molecules will react chemically, i.e. covalent bonds will be destroyed or

50 40-

._r m m

L)

3020 10 0

~ 10 o

~ 101

~ 102

~ .... 103

C o o l i n g Rate [~

Fig. 2.6. Crystallinity of polyetheretherketone (PEEK) matrix in carbon/PEEK composite as function of cooling rate. Note the logarithmic cooling rate scale. Redrawn from reference [1].

34

B.T. flstr6"m

created, and the polymer and thus its properties will eventually degrade through oxidation, chain scission, etc. Under certain conditions covalent bonds may form between molecules. One of the more notable locations that readily become sites of such crosslinks is the unsaturated carbon-carbon double bond in the polymer backbone, which through a chemical reaction may open up, leaving a (saturated) single covalent bond within the molecule and creating new covalent bonds to other molecules. Starting from a polymer liquid consisting of molecules capable of forming crosslinks, any of a number of means may be employed to set off a chemical reaction which creates covalent crosslinks to neighboring molecules, thus creating a gigantic three-dimensional molecule. As crosslinks are formed the polymer liquid gradually loses its ability to flow since the molecules no longer can slip past one another as in the thermoplastic melt. The three-dimensional network translates into a lower energy state than the random molecular orientation of the liquid state, so the crosslinking process is (just like crystallization) exothermal. Since the three-dimensional network created is bound together by covalent bonds (in contrast to the previously mentioned intermolecular secondary bonds) it may not be melted through reheating. The type of polymer having the ability to crosslink is called thermoset. In conclusion there are two very different polymer f a m i l i e s - thermoplastics and thermosets. Thermoplastics consist of long molecules with only secondary bonds in between molecules and therefore may be melted. If irregular in structure and stiff, the molecules of a thermoplastic are randomly arranged both in the melt and in the solid; the polymer is amorphous. On the other hand, if the molecules are regular in structure and flexible, the molecules, while randomly arranged in the melt, may form crystals as the thermoplastic solidifies; the polymer is semicrystalline. However, the degree of crystallinity of a semicrystalline polymer is dependent on cooling rate; with a high cooling rate the solid polymer ends up more or less amorphous, whereas with a low rate it will be partly crystalline and partly amorphous, i.e. semicrystalline. Initially thermosets also consist of long molecules with only secondary bonds between them. However, under certain conditions, such as the presence of carboncarbon double bonds in the molecular backbone and chemically reactive substances in the bulk resin, covalent bonds may form between molecules, resulting in solidification of the resin. Since the intermolecular covalent bonds cannot be broken without simultaneously breaking the intramolecular covalent bonds, thermosets cannot be melted. As the molecular arrangement in solid thermosets (as well as in the liquid state) is random, thermosets are amorphous. While thermosets may be regarded as a special case in polymer science, it is a very important special case and thermosets clearly dominate over thermoplastics in virtually all composites applications. However, since the main topic of this volume is thermoplastic sheet forming, thermoset polymers will only briefly be mentioned in the remainder of this chapter.

2.2.1.3. Thermoplasticpolymer matrices While there is a vast array of engineering plastics available, only a few are used as composite matrices, since an engineering plastic with excellent properties does not necessarily make an excellent composite matrix. Issues that are of importance when


35

selecting a polymer for use as composite matrix are reinforcement-matrix compatibility in terms of bonding, mechanical properties, thermal properties, cost, etc., though perhaps the most important aspect may be its processability, i.e. how easy is it to deal with it in manufacturing situations. Among the many issues that may be considered part of the processability are viscosity, processing temperature, processing time, and health concerns. The viscosity is important in achieving reinforcement impregnation, where each reinforcing fiber ideally should be surrounded by the matrix without voids present; impregnation is naturally facilitated by a low viscosity. Not-yet-crosslinked thermosets have shear viscosities at processing temperature of the order of 10~ Pa s, while melt viscosities of thermoplastics at processing temperature are of the order of 102 Pa s or higher (for comparison, the shear viscosity of water at room temperature is 10-3 Pa s), meaning that it is much easier to complete impregnation with thermosets than with thermoplastics. Once impregnation is completed, thermoplastics only need to be melted, shaped, and then cooled to achieve dimensional stability in a matter of seconds, although the temperatures required can be quite high by polymer processing standards. In contrast, thermosets need several minutes to several days for crosslinking to be completed, albeit normally at lower processing temperatures than with thermoplastics. The chemical structure of thermoplastics makes them chemically inert if processed correctly, meaning that no hazardous byproducts need to be considered. On the other hand, the molten thermoplastic and the heated machinery may cause severe burns. This relative lack of health worries is a distinct advantage over thermosets which, due to the active chemistry, give rise to considerable health concerns. A thermoplastic is usually fully polymerized when delivered from the supplier, meaning that all chemical reactions are completed and the user can concentrate entirely on physical processes, such as heat transfer and flow. However, there are some rare exceptions to this rule. The user may choose to take care of part of the polymerization starting off with low-molecular-weight prepolymer, thus avoiding the high-viscosity disadvantage during reinforcement impregnation. Courtesy of the low molecular weight, the polymer fluid may have a viscosity comparable to that of a thermoset resin. After the reinforcement is impregnated, the final polymerization process takes place and the molecular weight thus drastically increases. Depending on the type of polymer, the high-molecular-weight polymer may or may not decompose into lower-molecular-weight polymer molecules upon remelting. One of the main features of amorphous thermoplastics is that they are dissolvable in common industrial solvents. This means that the reinforcement can be impregnated with a low-viscosity solution, thus avoiding the problem of high melt viscosity, but it also means that the solidified polymer (and composite) is not solvent-resistant. For solvent-impregnated reinforcement, the residue solvent that was not completely driven off after impregnation is a serious concern since it impairs the quality of the composite. Amorphous thermoplastics do not shrink much when they solidify, which translates into good surface finish. Semicrystalline polymers usually have good solvent-resistance due to the crystallinity which prevents dissolution of the entire molecular structure. The crystallinity also improves high-temperature performance and long-term phenomena, such as

36

B.T. AstrO'm

creep. If the crystallinity is too low, these benefits are not seen and if it is too high the material loses toughness and becomes brittle, although it usually gains in stiffness. Hence, there is an optimum degree of crystallinity. When processing semicrystalline polymers one thus must consider, and preferably control, the cooling rate (see fig. 2.6), which rarely is an issue with amorphous matrices. Useful semicrystalline polymers have 5 to 50 volume percent crystallinity, with an optimum of 20 to 35 percent for composites applications [2]. Semicrystalline polymers shrink more than amorphous ones upon solidification; the higher the final crystallinity, the higher the density change between melt and solid. Due to the difference in shrinkage between the amorphous and the crystalline regions, the surface of semicrystalline thermoplastics is generally not as good as for amorphous ones. Since solvents normally cannot be used to dissolve semicrystalline polymers (there are some rare exceptions), reinforcement impregnation is extremely difficult. The following subsections aim to give a brief overview of some of the more common thermoplastic polymers used as composite matrices; table 2.1 shows their respective repeating units. The characteristics discussed below are merely family characteristics and large variations are the rule. Polyethylenes. PE can be both commodity (not intended for structural applications) and engineering plastic depending on grade, but is rarely used as composite matrix due to low temperature tolerance and low mechanical properties. However, PE fibers may be used as composite reinforcement. PE has the highest degree of crystallinity of any polymer due to its simple, regular, and flexible molecular structure. Polypropylenes. Just like PE, PP is both commodity and engineering plastic depending on grade. PP is the chemically least complex and cheapest polymer commonly used as composite matrix. In structural composites applications PP is usually reinforced with glass fibers. In recent years PP has become the most common thermoplastic matrix in mass-produced structural composites applications, including automobile components, such as various engine-room parts and seatback frames. Polyamides. One of the best-known thermoplastic polymer families is the polyamides (PA). While Nylon originally was the (Du Pont) trade name for PA fibers, "nylon" (not capitalized) gradually has become an accepted designation for PAs regardless of manufacturer. In contrast to PE and PP, PAs may be used at moderately increased temperatures thus greatly improving its usefulness as matrix. PAs are categorized by the presence of amine groups (--CONHm). A number of different PA grades, e.g. PA 6, PA 6,6, PA 6,10, and PA 12, are available, where the numbers indicate the number of carbon atoms in the repeating unit (see table 2.1); the properties naturally vary accordingly. The biggest drawback of PAs is that they are hygroscopic, i.e. absorb water. In composites applications PAs are normally reinforced with glass fibers and used in applications similar to glass/PP, but where higher temperature tolerance and improved mechanical properties are required. Thermoplastic polyesters. Although perhaps chiefly recognized as thermoset resins, polyesters also are available in thermoplastic forms, e.g. poly(ethylene terephthalate) (PET) and poly(butylene terephthalate) (PBT). The properties of

Thermoplastic composite sheet forming

TABLE

37

2.1

Comparison

of thermoplastic

Polymer

candidates for composites

Mer Structure H

Polyethylene, PE

H

I I~ ~CmC I HI H H

Polypropylene, PP

H

I I mC~C~ I I H

CH 3

0 Polyamide 6, PA 6

H

II C

Polyamide 12, PA 12

(CH2) 5~

~

H

II

I

H

H

0

I

I

II

~N~

Poly(phenylene sulfide), PPS

I

N

0

Polyamide 6,6, PA 6,6

Poly(ethylene terephthalate), PET

applications

(CH2)6~N~

O~

(CH2)2~ O~

C~

0 (CH2)4~

II

C~

O

O

[C[

C

-~s_

_~~_~o_~o_ o

Poly(ether ether ketone) PEEK

o Poly(ether sulfone), PES

II

o

o

o

II

/c~~.~

Poly(ether imide), PEI

CH,

_N,~~.~o_~ i~_~ o_~ :~_~ ,,

O

O O

II

Poly(amide imide), PAI

II

c

_~ ~_~o_~ II

o

38

B.T. ~lstr6"m

PET and PBT are similar to those of PAs, but lacking the hygroscopic disadvantage. In composites applications thermoplastic polyesters are reinforced with glass fibers and used in applications similar to glass/PP and glass/PA. Poly(phenylene sulfides). The most common member of the poly(arylene sulfide) family is poly(phenylene sulfide) (PPS), which has good tolerance to most chemicals and fire. PPS exhibits intermediate mechanical properties and temperature-tolerance. In composites applications PPS is reinforced with glass or carbon fibers and used in high-performance applications. Polyketones. While there are numerous aromatic polyketones, such as poly(ether ketone) (PEK), poly(ether ketone ketone) (PEKK), etc., the most common is poly(ether ether ketone) (PEEK). The polyketones possess high mechanical properties, high temperature-tolerance, good solvent resistance, and a high price. In composites applications PEEK is reinforced with glass or carbon fibers and used in critical high-performance applications. Polysulfones. Polysulfone (PSU), poly(ether sulfone) (PES), and poly(aryl sulfone) (PAS) are high-performance amorphous polymers with good tolerance to high temperatures and fire. These properties naturally come at a high cost and the melt viscosities are very high. Since polysulfones are amorphous, they are not resistant to all solvents although their resistance to many chemicals nevertheless is very good. In composites applications polysulfones are reinforced with glass or carbon fibers and used in critical high-performance applications. Thermoplastic polyimides. The polyimide family includes poly(ether imide) (PEI), polyimide (PI), and poly(amide imide) (PAI), which are all amorphous. Polyimides have the highest temperature-tolerance of the thermoplastics mentioned herein. Despite being amorphous they are very tolerant to solvents and environmental exposure and offer very good mechanical properties with the disadvantages of very high viscosities and high cost. In composites applications the members of the polyimide family are reinforced with glass or carbon fibers and used in critical highperformance applications.

2.2.2. Reinforcements The reinforcement is the constituent that is primarily intended to carry the structural loads the composite is subjected to. The reinforcement therefore to a significant degree determines stiffness and strength of the composite as well as several other properties. Composite reinforcement may be of different forms, but only fibrous reinforcement is relevant to thermoplastic sheet forming. A fiber, or filament, has a length-to-diameter ratio that approaches infinity and a diameter of the order of 10-5 m. All common fibers are manufactured in a drawing process, where the liquid raw material is drawn from an orifice. The drawing process ensures that the molecules of fibers organic in origin are aligned and parallel to the drawing direction, translating into significantly higher strength and stiffness in the axial direction than transverse to it. The most common types of fibrous reinforcement used in composites applications are glass, carbon, and aramid. However, it is not only the fiber type that


39

is of significance; equally important is its configuration or form, e.g. the fibers may be discontinuous or continuous, randomly arranged or oriented, all aligned or in fabric form, etc.

2.2.2.1. Glass fibers The major ingredient of glass fibers is silica (SiO2), which is mixed with varying degrees of other oxides. The mixture is melted and extruded through minute holes in a platinum-alloy plate, or bushing. The glass filaments (fibers) vertically emerging from the bushing are drawn at high speed and are then quenched by air or water spray to achieve an amorphous structure. A protective coating is applied to the filaments before they are gathered together and wound onto forming packages. The wet glass is then dried. A group of collimated glass fibers is called a tow, strand, or yarn and an assembly of collimated tows is called a roving. When the tows are wound onto forming packages, as well as when tows are joined into rovings, they are usually rotated to provide a so-called twist, which promotes integrity and thus simplifies subsequent handling, while at the same time making impregnation more difficult since it becomes more difficult to spread the fibers prior to impregnation. The diameter of the individual filaments varies between 5 and 24 ~tm and is in composites applications commonly in the range 10-20 ~tm. The size of glass tows and rovings is given by tex number (weight in grams of 1,000 m) or yield in yd/lb (in North America). Common tex numbers are 600, 1,200, 2,400, etc., while common yields are 900, 450, 225, etc. (1 yd/lb ~ 500,000/tex). Several different glass compositions are available, the most common being E and S glass, where "E" denotes electrical and "S" high strength. E glass offers excellent electrical properties and durability and is considered a general-purpose grade that heavily dominates consumption. S glass and R glass are similar and offer improved stiffness and strength as well as high-temperature tolerance. Not surprisingly, the latter glass types are considerably more expensive than E glass. ECR glass (_c.orrosion resistant) and C glass are similar and, while having properties similar to E glass, offer improved corrosion-resistance. Since there are several different glass compositions, there is naturally a large variation in properties. Nevertheless, characteristics that tend to be shared by all glass fiber types are: 9 Good mechanical properties 9 High temperature-tolerance 9 Positive coefficient of thermal expansion (CTE) 9 Good electrical properties 9 Good corrosion-resistance 9 Moisture-sensitive 9 Abrasive 9 Inexpensive A characteristic that sets glasses apart from other reinforcements used in composites applications is that they are amorphous (i.e. glassy) and therefore are isotropic.

40

B.T. ~lstr6"m

2.2.2.2. Carbon fibers

Carbon fibers are commercially manufactured from three different precursors: rayon, polyacrylonitrile (PAN), and petroleum pitch. In the first two cases, the starting point of the carbon-fiber manufacturing process is textile fibers, whereas fibers are spun directly from the melt when pitch is the starting point. The fibers are initially drawn and oxidized at temperatures below 400~ to crosslink them to ensure that they do not melt during subsequent processing steps; drawing and oxidizing may occur concurrently. The fibers are then carbonized above 800~ in a process called pyrolysis, i.e. in the absence of oxygen, to remove noncarbon elements and create fibers virtually consisting of carbon only. Graphitization is then carried out at temperatures above 1,000~ to further eliminate impurities and enhance crystallinity. During both carbonization and graphitization further drawing may be employed to enhance orientation within the fibers. After graphitization fibers are surface treated and size is applied. The carbon atoms are covalently bonded together in so-called graphene layers which are held together by secondary bonds. The properties of carbon fibers are the result of the strong covalent carbon-carbon bonds within the graphene layers and it is therefore mainly the degree of orientation of these layers that determines the properties of the fiber. A higher temperature during graphitization promotes orientation of the graphene layers in the fiber direction, thus resulting in a higher tensile modulus. Carbon fibers are supplied in tows denoted 3K, 6K, 12K, etc., depending on the number of individual filaments they contain, where for example 3K stands for 3,000 filaments. Carbon fiber tows receive little or no twist. Filament diameters vary between 4 and 11 ~tm and is commonly around 7 ~m. Carbon fibers are often quantitatively referred to as "ultra-high modulus", "high modulus", "intermediate-modulus", "high strength", etc., where the borders between categories gradually change due to the rapid development of new fiber types. Properties significantly depend on precursor type and heat treatments used. While carbon fibers have the highest strength and stiffness of any compositereinforcement candidate, they generally only provide high strength or high modulus (in the same fiber). The span in properties of different carbon fiber types is vast, but among the properties they tend to share (at temperatures relevant to polymer composites) are: 9 Outstanding mechanical properties 9 High temperature-tolerance 9 Negative longitudinal CTE, positive transverse CTE 9 Electrically conductive 9 Excellent environmental resistance 9 Insensitive to moisture 9 Brittle 9 Expensive to very expensive The negative longitudinal CTE is due to bending of the predominantly longitudinally aligned graphene layers, for which reason the negative CTE increases in numerical value as the modulus (and graphene layer orientation) increases. Whereas the con-


41

ductivity of carbon may be advantageous in some cases it is often a disadvantage. Carbon fibers thus may cause galvanic corrosion of metallic inserts and loose carbon particles suspended in the air may easily short out electrical and electronic equipment. In manufacturing operations dealing with unimpregnated carbon fibers which may be abraded, it is therefore necessary to provide costly shielding of electrical and electronic equipment.

2.2.2.3. Organicfibers While several different organic fiber types have been used as composites reinforcement, the category is dominated by aramid fibers. Kevlar is often assumed synonymous with aramid, but is in fact just the (Du Pont) trade name of the most common of a few commercially available aramid fiber types. Aramids, short for aromatic polyamides, are members of the PA family; fig. 2.7 illustrates the repeating unit of Kevlar (cf. PAs, table 2.1). Aramid fibers are manufactured in a process called solution spinning. The polymer powder is dissolved in sulfuric acid and is extruded through small holes, or spinnerets, into a narrow air gap. The fibers are quenched in a water bath to solidify the fibers and wash off most of the acid. The fibers are further washed, dried under tension, and then wound onto spools. Since aramid fibers are not brittle a protective size is not necessary. When the polymer solution is extruded through the spinneret, the molecules align with the direction of shear and the subsequent quenching ensures that the orientation remains in the final fiber. The degree of orientation may be further enhanced by heat treatment under tension resulting in improvements in longitudinal modulus. Due to its high degree of crystallinity and rigid molecular structure the temperaturetolerance of aromatic polyamide is very good for an organic material. The fiber diameter is typically 12 lam and tows, which are not twisted, consist of anything from a couple of dozen to several thousand fibers per tow. Tows are normally designated either by the number of fibers or the denier count (weight in grams of 9,000 m). Characteristics of aramid fibers when used as composites reinforcement include: 9 Very good mechanical properties, especially toughness and damage tolerance 9 Moderate temperature-tolerance 9 Negative longitudinal CTE, positive transverse CTE 9 Good electrical properties 9 Fair corrosion-resistance 9 Very moisture-sensitive 9 Tough 9 Expensive

-C

0 I1_0~_

0 H II I _.0~_ C-N

Fig. 2.7. Repeating unit of Kevlar.

H I N-

42

B.T. ~lstrO'm

While possessing several attractive properties, aramid also gives rise to a few notable difficulties. From a design point of view it is important to realize that the strength in compression is only a fraction of that in tension and that the fiber-matrix compatibility generally is poor. The outstanding toughness of aramid creates a problem in that fibers are very difficult to cut and machining of aramid-reinforced composites therefore requires special tools and techniques. Polyethylene fibers. High-modulus PE fibers may be manufactured through a process called gel spinning, which is a variant of the solution spinning process used for aramids. Since the tensile properties of both PE and aramid fibers are dictated by the properties of the covalent bonds of the molecular backbones, their mechanical properties are similar, but due to the lower density of PE fibers their specific strength and modulus are higher and comparable to carbon-fiber properties. The main drawbacks of PE fibers are poor matrix compatibility and poor temperature-tolerance, which likely makes PE fibers impossible to use with thermoplastic matrices.

2.2.2.4. Other fibers Several specialty fibers are used in different applications, for example offering extra-high temperature-tolerance, radar transparency, etc. Fibrous reinforcements used in polymer-matrix composites applications include boron and ceramic fibers, metal wires, and natural fibers, such as jute and wood. None of these fiber types is common in sheet forming applications.

2.2.2.5. Reinforcement-matrix interaction Conceptually a fiber-reinforced composite consists of transversely isotropic fibers and isotropic matrix with a perfect bond in between. Reality, however, is significantly more complicated. For a composite to be able to support external loads, fibers and matrix must cooperate.'It is often assumed that the fiber-matrix bond should be perfect, i.e. have the same properties as the matrix, and as strong a bond as possible is indeed often desirable to improve, for example, interlaminar shear strength, delamination resistance, fatigue properties, corrosion-resistance, etc. However, in some load cases a weak bond actually may be preferable; damage tolerance of a composite with a brittle matrix is usually enhanced by a weak fiber-matrix bond [3]. Whatever the load case, the fiber-matrix interface is of crucial importance to the properties of a composite. Manufacturers of brittle fibers, such as glass and carbon, apply a size, or finish, to the fibers to protect them from damage during subsequent handling, such as spinning, weaving, etc. Since a single reinforcement roving may contain tens of thousands of fibers and thus may be difficult to handle, the size also may be intended to promote tow integrity during such handling. However, since a fiber coating may interfere with the creation of a strong interface, and promotion of tow integrity is detrimental to reinforcement impregnation, the size may be seen as a necessary evil. Consequently the size in some instances is removed, e.g. burned off, when subsequent handling has been completed. To enable application of the size to every fiber, it is in glass manufacture applied before the fibers have been gathered into a tow,

Thermoplastic compositesheetforming

43

whereas a carbon-fiber tow must be spread out as widely as possible before application. A good bond between fiber and matrix may be formed through several mechanisms that all require wetting of the fibers by the resin. The preferred bonding mechanism is chemical (covalent) bonding, whereas mechanical interlocking may work well if the fiber surface is irregular, which is the case with some carbon and organic fiber types. Assuming that the fiber is porous, interdiffusion of polymer molecules into the fibers offers another possibility, whereas electrostatic attraction (secondary bonds) probably does not offer a strong enough bond to alone be responsible for satisfactory bonding [4]. However, despite over thirty years of intense research, the true mechanisms behind most successful fiber-matrix bonds are not well understood. Moreover, successful recipes are jealously guarded trade secrets. For glass fibers a coupling agent is applied to the fiber surface to enhance fibermatrix compatibility. Well-functioning coupling agents are available for thermosets such as unsaturated polyesters and epoxies, whereas coupling agents for high-temperature thermosets and all thermoplastics are not as efficient or even nonexistent. However, much work is underway to develop coupling agents for thermoplastic matrices. For carbon fibers the situation is rather different in terms of achieving fiber-matrix compatibility. Instead of applying a coupling agent the fiber is treated so as to promote its reactivity and compatibility with the matrix. Most commonly the fiber surface is oxidized to create surface oxygen groups that can form covalent bonds with the matrix. It appears that mechanical interlocking also is important with carbon fibers, since bonding generally is less good for high modulus fibers which have a higher degree of orientation of the graphene layers and thus smoother surfaces. For organic fibers the situation is further different in that no size is needed to protect the tough fibers and that no successful coupling agent has been developed. A common misconception is that the properties of the matrix are uniform throughout the composite, but various studies have proved the existence of a matrix property gradient from the fiber surface into the matrix bulk, a so-called interphase region (not to be confused with the interface). Without such an interphase there would be a huge discontinuity in modulus at the fiber-matrix interface. It has proven to be advantageous to some properties to have an intermediate modulus or ductile interphase [4]. With some semicrystalline matrices the fibers act as nuclei for crystallization, meaning that the interphase may become highly crystalline and hence stiffer than the bulk matrix.

2.2.3. Preimpregnated reinforcements One of the most complex, difficult, and not least important aspects of composites manufacturing is the impregnation of the reinforcement, particularly if the matrix is highly viscous. Consider a carbon-fiber-reinforced composite with a fiber volume fraction of 0.6, an average fiber diameter of 7 ~tm, and a volume of 1 ml (a cube with 10-ram sides). This volume contains 16 km of fiber, 0.4 ml of matrix, and 0.34 m 2 of interface. If the matrix is a high-viscosity molten thermoplastic it is

44

B. T. ,4str6m

not difficult to imagine that it is extremely difficult to evenly spread 0.4 ml of matrix onto a fiber surface area equivalent to five and a half pages of normal writing paper. Invariably, the impregnation will be imperfect and result in some dry fibers and entrapped gas as well as nonuniform fiber distribution. This is the background to the widespread use of preimpregnated reinforcement (prepregs) in manufacturing of high-cost and high-performance composites. Commercial prepregs are manufactured with dedicated machinery under well-controlled conditions and the result is low void content and reasonably uniform fiber distribution, and the prepregs often contain matrices that are not for sale except in prepreg form. The significant convenience of prepregs naturally comes with a significant disadvantage in terms of high cost. Prepregs are available in several forms depending on reinforcement and matrix as well as intended use. With continuous and aligned reinforcement the major impregnation forms are solvent impregnation, melt impregnation, powder impregnation, and commingling. Preimpregnated discontinuous and randomly arranged reinforcement is common in compression and injection molding processes. Such molding compounds, which may be melt or powder impregnated, are not referred to as prepregs although they conceptually belong to the same category; they are further discussed in section 2.2.3.6.

2.2.3.1. Solvent impregnation

Recalling earlier sections of this chapter, amorphous thermoplastics are not resistant to all solvents and thus may be dissolved and used in solvent impregnation. The polymer is dissolved to significantly lower its viscosity and thus facilitate reinforcement wetting and impregnation. The reinforcement is led into a solvent bath where the combined efforts of surface tension and the fact that the reinforcement is guided over rollers or bars ensures impregnation. Emerging from the bath, the impregnated reinforcement goes through nip rollers that carefully meter the reinforcement-tosolution ratio, whereupon the impregnated reinforcement goes into a drying oven, where the solvent is driven off and recovered (see fig. 2.8). Thermoplastic prepregs are not sticky and no backing paper is used; rolled-up prepregs are stored at room temperature. Correctly performed solvent impregnation produces intimately impregnated reinforcement (see fig. 2.9a). Both rovings and fabrics may be impregnated in

Fig. 2.8. Schematic of solvent impregnation.


45

Fig. 2.9. Cross-sections of different prepreg types. (a) Solvent- or melt-impregnated. (b) Powderimpregnated with polymer sleeve. (c) Commingled. Reinforcing fibers are black and matrix is gray. Matrix powder particles and fibers typicallyhave significantlylarger diameter than reinforcing fibers.

this fashion. Regardless of resin type, residue solvent in the matrix presents a problem since it may be seriously detrimental to the properties of the composite. 2.2.3.2. Melt impregnation Ideally, melt impregnation is the preferred impregnation process, since it completes the ultimately desired intimate fiber wetting without introduction of a solvent (see fig. 2.9a). Unfortunately it is also the most difficult impregnation technique due to the high viscosities involved; with thermoplastics the resin has the consistency of chewing gum. In this case surface tension is of little help, and the first impulse may be to somehow increase the transverse pressure to force the matrix into the reinforcement. However, an increased pressure also compacts the fiber bed further and thus makes it even less permeable, so this tactic has the opposite effect. Some melt-impregnation techniques for thermoplastics involve the application of molten matrix onto the reinforcement right before the nip between the spread-out reinforcement and a rotating roller. With this approach the pressure forces the matrix through the reinforcement towards the lower pressure on the other side of the reinforcement, i.e. along the direction of the negative pressure gradient. Following several rollers like these the process is finished off with nip rollers to ensure that the reinforcement-matrix ratio is correct. The newly fabricated prepregs are cooled by calendering rolls and the matrix solidified. Melt-impregnation techniques of this type, which are carefully guarded by patents, are probably only used to impregnate parallel-fiber tows or yarns, since attempts at impregnating fabrics likely would prove extremely difficult due to the restrictions of tow cross-overs. An alternative melt-impregnation technique capable of impregnating fabrics employs a double-belt press (DBP) (see fig. 2.10). A DBP essentially consists of

46

B.T. ~IstrO'm

Fig. 2.10. Schematic of double-belt-press prepregging of continuous fabric with thermoplastic matrix. two steel belts that feed the material through the machine while applying lateral pressure to the material. In the first section of the machine the steel belts are heated, while in the latter section the belts are cooled. A reinforcement fabric sandwiched between two polymer films is fed into the machine. The heat within the press melts the polymer films and a pressure gradient applied by the belts causes the molten polymer to impregnate the fabric, which finally is cooled before exiting the press. Since the residence time within the double-belt press is long, even highly viscous thermoplastics are capable of percolating the reinforcement structure. An interesting concept is offered by the thermoplastic long discontinuous-fiberreinforced (LDF) material. In this melt-impregnated prepreg product, the fibers are aligned as in an ordinary melt-impregnated prepreg, but the fibers are discontinuous, allowing forming not possible with continuous-fiberreinforced prepregs.

2.2.3.3. Powder impregnation By grinding the solid matrix into a fine powder, the reinforcement can be impregnated using a slurry or a fluidized powder bed. A slurry employs a liquid, often water, to disperse the powder and impregnate the reinforcement with the lowviscosity aqueous solution, whereupon the water is driven off. The slurry may contain some kind of agent to promote adhesion between matrix powder and fibers, or the powder-impregnated reinforcement may be pulled through an oven to slightly melt the powder onto to the fibers. A fluidized powder bed contains a powder cloud that is kept fluidized by circulating air. Correctly performed, electrostatic attraction and/or friction ensures that the reinforcement passing through the powder cloud is properly filled with resin particles. The use of an oven to fuse the matrix onto the fibers is common. Another option to prevent the powder from being shaken out of the reinforcement during subsequent handling involves enclosure of the powder-filled yarn in an extruded polymer sleeve of the matrix material (see fig. 2.9b). The main advantages of powder-impregnated reinforcements is that they are flexible (unless subsequently excessively melted) and that they are cheaper than solventand melt-impregnated prepregs. The main drawbacks are that the reinforcement is


47

not completely melt-impregnated, which thus has to be undertaken during composite component manufacturing, and that the powder rarely is evenly dispersed within the reinforcement. The final melt impregnation is often difficult to satisfactorily achieve and the results are liable to be less good than if melt-impregnated prepregs had been used. Another drawback specific to slurry-impregnated materials is that they may suffer from residue adhesion agent translating into problems similar to those encountered with solvent-impregnated prepregs. Powder-impregnated reinforcement, which tends to be unidirectional, is rarely referred to as prepreg, but rather powder-impregnated tow or yarn. However, not only yarns but also fabrics may be powder-impregnated; resin powder is first distributed onto one side of the horizontal fabric and the powder thermally fused in place, whereupon the other side of the fabric receives the same treatment. Such a powder-impregnation process may be followed by a DBP to produce a fully melt-impregnated fabric.

2.2.3.4. Commingling Commingled reinforcement consists of mechanically commingled (combined) reinforcing fibers and fibers spun from a thermoplastic resin (see fig. 2.9c). The advantages and limitations of commingled prepregs are the same as for powderimpregnated yarns (with the difference that no worry of residues from a slurry impregnation is warranted). Commingled reinforcement is unidirectional and is usually referred to as commingled tow or yarn.

2.2.3.5. Comparison of preimpregnated reinforcement types A qualitative comparison of the products of the aforementioned impregnation methods would consider flexibility, quality of impregnation, and cost. Flexibility is highly desirable to allow conformation to curved shapes and to allow for use in textile processes. High quality of impregnation is of course always desirable and likewise cost should be kept as low as possible. In general solvent- and melt-impregnated prepregs possess limited flexibility. Not surprisingly, high quality of impregnation goes hand in hand with high cost in solvent- and melt-impregnated prepregs. The main advantages of powder-impregnated and commingled reinforcements is that they are flexible enough to be used in textile manufacturing processes such as weaving, braiding, etc. and that they are, on a relative scale, inexpensive. Their main drawback is that the reinforcement is not melt-impregnated, which creates processing difficulties at a later stage. (It deserves to be pointed out that also narrow tapes of solvent- and melt-impregnated prepregs may be used in very specialized weaving processes.) There are relatively few thermoplastic prepregs on the market; available combinations include glass-fiber-reinforced PP, PAs, thermoplastic polyesters, as well as carbon-fiber-reinforced high-performance thermoplastics. Fiber volume fractions of unidirectionally or fabric-reinforced thermoplastic prepregs normally range from 0.35 to 0.6.

48

B.T. flstr6"m

2.2.3.6. Molding compounds Many techniques to manufacture composites with more or less randomly oriented and often discontinuous reinforcement also use some form of preimpregnated reinforcement as raw material. However, when preimpregnated reinforcement does not contain oriented and essentially continuous fibers, it is usually not referred to as prepreg but rather as molding compound. With molding compounds it may be more appropriate to talk about reinforced resin rather than impregnated reinforcement, since the fiber content tends to be considerably lower than in prepregs. Glass-mat-reinforced thermoplastic (GMT) is available in sheet form reinforced with randomly oriented fibers, which may be discontinuous or continuous. The most common technique to manufacture GMT is to use a DBP (see fig. 2.10), where two random-fiber mats and three polymer films or layers of extruded molten polymer are sandwiched before entering the press. Since this type of more or less completely meltimpregnated GMT ends up being a few millimeters thick and thus stiff, it is usually stored fiat instead of being rolled up. In another technique to manufacture GMT, which is similar to paper-making, chopped fibers, resin powder, and additives are dispersed in a slurry, which is deposited onto a moving belt where the water is driven off. This type of GMT thus consists of a porous fiber structure containing matrix powder, which, if desired, may be more or less completely melt-impregnated in a DBP. GMT is also available with part of the reinforcement continuous and oriented; alternatively, randomly reinforced GMT may be combined with continuous-fiberreinforced prepregs right before molding. Fiber volume fractions are normally 0.1-0.3 and fiber lengths in the range 10-30 mm unless the reinforcement is continuous. The commercial incarnation of GMT is massively dominated by glass-reinforced PP. 2.3. Properties The emphasis of this section 2.3 is on properties relevant to manufacturing and basic mechanical properties and intentionally refrains from delving into the quagmire of mechanical properties such as impact, fracture, fatigue, creep, etc. The intention of this section is merely to give the reader a feeling for typical properties of constituent materials on their own and in composite form. The properties quoted herein are from several different sources and thus may be slightly contradictory, which illustrates the significant differences existing between material formulations, processing conditions, test methods, etc. Unless otherwise noted, all properties are for room-temperature (RT) conditions.

2.3.1. Matrices For a matrix to be able to perform its tasks of supporting and protecting the primarily load-bearing reinforcement a number of properties are of relevance. The most pertinent properties usually are moduli and strengths in tension, compression, and shear, while also ultimate strain and fracture toughness may be important. The


49

properties of the matrix usually determines the environmental tolerance of a composite; tolerance to elevated temperature and aggressive environments, such as UV radiation, oxygen, solvents, water, etc., thus are of paramount importance. As with most property comparisons of such broad material families indeed, as with all quantitative information of this section 3 the information should be seen as indicative only.

2.3.1.1. Thermal and rheological properties At sufficiently low temperatures an amorphous polymer is a glassy solid and any macroscopic deformation is likely due to stretching of secondary bonds and angle deformation of covalent bonds and only involves segments consisting of a few atoms. As temperature increases a region of rapid loosening of the secondary bonds is encountered and significantly larger segments of the molecules become free to move through rotation of covalent bonds. The temperature where these changes take place is referred to as the glass-transition temperature, Tg (see fig. 2.11), and is accompanied by a decrease in stiffness of several orders of magnitude. As the temperature increases further, amorphous thermoplastics often have a so-called rubber plateau where the stiffness does not decrease significantly and deformations are due to molecules sliding past one another. Further heating leads to complete melting. Thermosets, on the other hand, which are always amorphous, tend to have an extended rubber plateau, but since covalent bonds hold the polymer network together the polymer never melts. (However, if the temperature increases enough, the polymer will start to degrade, i.e. covalent bonds will be broken or formed.) Semicrystalline thermoplastics also show a drop in stiffness at Tg since the amorphous regions lose so much stiffness (see fig. 2.11). However, the crystalline regions remain unaffected and act as physical crosslinks and the polymer keeps much of its macroscopic stiffness. Not until the crystalline melting point, Tin, is reached does the polymer completely melt from a macroscopic viewpoint. Since the transition temperatures (rig and Tin) are functions of the molecular mobility in the bulk polymer it is easy to appreciate that a more rigid molecular

lO,

"--" 102 ~ 101 ,

i

i

alline i ~~morphous

100 10-1

-~ rr 10.2 10-3 , 50

~ o w t T~100

_-~i 9 Cr~

L molecular\ weight \ 150

High i \ molecular \ weight i I --. ; T~ 250 200

Temperature [~

Fig. 2.11. Relaxation modulus of polystyrene (PS) as function of temperature. Note the logarithmic stiffness scale. Approximate positions of Tg and Tm added. Redrawn from reference [5].

B. T. .~str6"m

50

structure and bulky side groups require a higher temperature to permit the same degree of mobility. Consequently, rigid thermoplastics with bulky side groups and strong secondary (intermolecular) bonds have high transition temperatures. Likewise, the very strong (intermolecular) covalent bonds of thermosets cause them to have higher rig s than many thermoplastics. For amorphous thermoplastics the maximum continuous use temperature consequently is slightly below Tg, whereas for thermoplastics with appreciable degree of crystallinity temperatures in excess of Tg and even close to Tm may be permissible for limited periods of time. Table 2.2 illustrates indicative transitions temperatures for some unreinforced, or neat, polymers as well as common or recommended processing temperatures, Tproc. In the unstressed state the molecules of a high-molecular-weight polymer liquid are heavily intertwined. For the liquid to flow requires that molecules move in relation to one another and the resistance to flow in a high-molecular-weight polymer liquid therefore is significant. However, if the liquid is sheared, the molecules are gradually aligned, fewer entanglements remain, and the resistance to flow (i.e. the viscosity) is reduced. On the other hand, if the molecular weight is moderate, i.e. the molecules are not excessively long, the resistance to flow is lower since there are not as many entanglements. In this case shear is unlikely to significantly lessen the degree of entanglement and thus will not affect the viscosity much. Besides temperature, the molecular weight of a polymer is therefore the single most important factor in determining its viscosity. The viscosity and the so-called shear-thinning, or pseudoplastic, tendency (i.e. that the viscosity is reduced by higher shear rates) increase rapidly with molecular weight. Since a higher temperature manifests itself in increased molecular mobility it strongly facilitates flow. A thermoplastic melt, which consists of high-molecular-weight molecules, is usually shear-thinning (see fig. 2.12, which shows the viscosity of PEEK). As further illustrated by the figure there is also a significant temperature-dependency. Table 2.2 gives typical zero-shearrate shear viscosities, r/0, for a few polymers only, since viscosity data usually are quite difficult to come by in the literature. However, the behaviors exhibited in fig. TABLE 2.2 Transition temperatures, processing temperatures, and viscosities of selected neat polymers [6-13]. The shear viscosities quoted are the zero-shear-rate values at the given temperatures

PP PA 6 PA 12 PA 6,6 PET PPS PEEK PEI PES PAI

Tg (~

Tm (~

Tproc (~

rio (Pa s)

-20--5 50-70 45 55-80 80 85 145 215 225 245-275

165-175 225 180 265 245-265 285 345

> 185 225-290 180-270 270-325 260-310 300-355 360-400 350-425 340-380 < 400

101-102 (230~

380 (38ooc) 103 (360~ > 105 (340~


51

A 700 o

600 o.

500 7

.,~

400

o~

300

~

200 e.-

r

100 0 10 0

~ 101

~ 10 2

~.....~ 10 3

Shear Rate [l/s]

Fig. 2.12. Shear viscosity of molten PEEK as function of shear rate and temperature. Note the logarithmic shear-rate scale. Data from reference [10].

2.12 can be assumed indicative for thermoplastics while the magnitudes and degrees of temperature and shear-rate dependencies naturally vary from one polymer to another. In terms of most composites manufacturing operations a low viscosity is desirable, meaning that it may be tempting to increase the processing temperature based on the temperature dependency displayed in fig. 2.12. Although this temperature-dependency indeed is exploited for this purpose, it cannot be done indiscriminately. As previously mentioned, solid polymers eventually degrade through chain scission and crosslinking. This is even more so for molten thermoplastics since the molecular mobility is so much greater than in solid form, as well as the fact that the higher temperature stimulates chemical reactions. Figure 2.13 illustrates the allowable exposure time before onset of degradation for molten PEEK as function of temperature. The tolerance to degradation of PEEK is greater in the absence of oxygen, which is a

120 ~ ' 100 .n E ,80 0

"u E

60-

GI9 40 o 9 20

.E_ I-

0 360

In Air I

380

.....

I

400

,,,

I

420

~-- Temperature [~

Fig. 2.13. Time to surface degradation for PEEK as function of temperature in presence and absence of oxygen. Data from reference [14].

B.T. flstr6m

52

trait shared with most thermoplastics which readily oxidize if given the opportunity. The general trends exhibited in fig. 2.13 can be assumed indicative for thermoplastics. Heat transfer in polymers is due to thermal agitation across intramolecular and intermolecular bonds; the stronger the bond, the higher the conductivity. The coefficient of thermal conductivity (CTC) therefore increases with molecular weight, molecular alignment, and crystallinity. The CTC may increase or decrease with temperature depending on polymer. The specific heat, or heat capacity, arises from the freedom of movement of the molecules and thus decreases with crystallinity and increases with temperature, i.e. molecular mobility, and accordingly increases rapidly as Tg is passed. It was previously mentioned that since the crystalline morphology represents close-packing of the molecules the density of the crystal is higher than in the amorphous phase (see fig. 2.14). The figure further shows that the density dependency on temperature changes considerably as Tg is passed. This behavior may also be assessed in terms of CTE. The CTE of polymers tends to be a linearly increasing function of temperature both below and above Tg, but with a stronger temperaturedependency above Tg. Closely related to the CTE is the total volumetric shrinkage from melt (processing temperature) to solid (service temperature), which if not taken into account may lead to poor dimensional stability and sink marks. Table 2.3 gives thermal conductivity, k, specific heat, Cp, and CTE, c~, of some neat polymers. The table illustrates that the thermal properties do not vary drastically between polymers; this is essentially true also for thermosets. Since the data of table 2.3 apply at room temperature it is important to recall from the discussion above what happens as the temperature increases.

2.3.1.2. Mechanical properties Since crystals are stiffer than amorphous regions, stiffness increases with degree of crystallinity (see fig. 2.11). However, higher stiffness may also be obtained using

E3

I _

i

Liquid

r~

Fig. 2.14. Polymer density as function of temperature.

Temperature


53

TABLE 2.3 Thermal properties of selected neat polymers [6,15,16]

PP PA 6 PA 12 PA 6,6 PPS PEEK PEI PES

k

G

(W/m ~

(kJ/kg ~

10-6 ~ -~

0.11-0.17 0.24 0.21-0.31 0.24 0.29 0.25 0.07 0.26

1.8-2.4 1.67 1.26 1.67 1.09 1.34

80-100 80-83 61-100 80 49 40-47 47-56 55

1.0

polymers featuring increased molecular rigidity, bulky side groups, and to a lesser degree increased molecular weight, although it should be remembered that such configurational traits impede crystal growth. Thus, if both high stiffness and high temperature-tolerance is desirable there will be a tradeoff between high transition temperatures and the degree of crystallinity, i.e. stiffness. Significantly, the thermoplastics with the highest mechanical properties and temperature-tolerance owe these traits to stiff molecular structures, which also deprive them of the ability to form crystals to any significant degree, i.e. they are amorphous. Thermosets typically are stiffer than thermoplastics due to the three-dimensional molecular structure bound together by covalent bonds. The strength of a material may be measured in so many different ways that sweeping statements about strength are difficult to make. However, the strength of polymers is highly dependent on and increases with the strength of intramolecular and intermolecular bonds, with the degree of crystallinity and, to a lesser degree, with molecular weight. Consequently, courtesy of the three-dimensional molecular structure, thermosets tend to have higher strength than thermoplastics. In general the relatively weak intermolecular forces of thermoplastics translate into a ductile material with high strain to failure, toughness, and damage-tolerance, since the molecules to a certain degree can slip relative to each other without rupturing covalent bonds. Since crystalline regions act as physical crosslinks, ductility decreases with increasing degree of crystallinity. Correspondingly, thermosets tend to be brittle and have low strain to failure, toughness, and damage-tolerance since the covalent bonds cannot yield much. Table 2.4 gives indicative mechanical properties of neat polymers. The table significantly illustrates that the differences in mechanical properties between polymers with the exception of the failure strain are not as significant as one might expect. Several properties other than thermal and mechanical may be of importance, depending on the intended application, e.g. electrical properties, optical properties, and tolerance to environmental exposure, but these are considered beyond the scope of this chapter.

54

B.T. ~lstrO'm

TABLE 2.4 Mechanical properties of selected neat polymers [16]. p denotes density, E elastic (Young's) modulus, a strength, and e strain to failure

PP PA PPS PEEK PEI PES PAI

p (kg/m3)

E GPa

cr (MPa)

e (%)

900 1,100 1,360 1,260-1,320 1,270 1,370 1,400

1.1-1.6 2.0 3.3 3.2 3.0 3.2 3.7-4.8

31-42 70-84 84 93 105 84 93-147

100-600 150-300 4.0 50 60 40-80 12-17

2.3.2. R e i n f o r c e m e n t s

While the composite matrix is normally responsible for properties such as temperature and environmental tolerance, the reinforcement primarily determines the composite's mechanical properties. The reinforcement typically has strength and modulus one to two orders of magnitude greater than polymer matrices. 2.3.2.1.

Thermal properties

Table 2.5 gives representative thermal properties of some reinforcement types. The table illustrates a couple of interesting differences in reinforcement properties. First, glass fibers are isotropic for reasons previously discussed. However, perhaps the most relevant property in this context is the negative longitudinal C T E of aramid and carbon fibers; while another is the high longitudinal CTCs of carbon, which for some carbon types even exceed the CTCs of the best metal conductors. The table further gives approximate m a x i m u m use temperatures Tmax. 2.3.2.2. M e c h a n i c a l p r o p e r t i e s

Table 2.6 gives representative mechanical properties of c o m m o n reinforcements, illustrating the vast range of reinforcement properties available. While table 2.4 illustrates that there are no excessively large variations in mechanical properties of TABLE 2.5 Thermal properties of selected reinforcements [16-20]. Indices l and t denote properties in longitudinal and transverse fiber directions, respectively kl

kt

(W/m ~ E glass S-2 glass Kevlar 49 (aramid) Carbon (PAN) Carbon (pitch)

Cp

(kJ/kg ~

0.87

0.87

0.041 7-70 100-520

0.048

0.825 0.737 1.42 0.7-0.9 0.7-0.9

otI

Tmax (~

ott

(10-6 ~ -~) 5.0 2.9 -2.3 -0.5--0.7 -0.9--1.6

5.0 2.9 41 7-10 7.8

350 300 250 600 500


55

TABLE 2.6 Longitudinal tensile properties of selected reinforcement types [16,18,21,22]. The abbreviations for carbon

fiber types stand for high strength/strain, intermediate modulus, high modulus, and ultra-high modulus, respectively

E glass S-2 glass Kevlar 49 (aramid) Kevlar 149 (aramid) Carbon (HS/S) Carbon (IM) Carbon (HM) Carbon (UHM)

P (kg/m 3)

El (GPa)

~l (GPa)

6l (%)

2,520-2,620 2,490 1,440 1,470 1,700-1,900 1,700-1,830 1,750-2,000 1,870-2,000

73 86 131 186 160-250 276-317 338-436 440-827

3.4 4.5 3.6-4.1 3.4 1.4-4.93 2.34-7.07 1.9-5.52 1.86-3.45

4.88 5.7 2.8 2.0 0.8-1.9 0.8-2.2 0.5-1.4 0.4-0.5

matrices (with the exception of failure strain), there are certainly most significant differences in the mechanical properties of different reinforcement types. It is also noteworthy that the stiffer the fiber, the lower the strain to failure; it is thus not possible to have both high strain to failure and high modulus. The qualitative categorization of the multitude of carbon fibers in table 2.6 is obviously somewhat arbitrary and certainly partially contradictory, but it is nevertheless quite common in the composites industry.

2.3.3. Composites All properties discussed above pertain to the constituents on their own. When the constituents are combined into a composite they all lend some degree of their own properties to the composite; this is after all the underlying concept of a composite. Even if one does not take the overall part geometry into account, there are numerous variables in composites design, such as constituent types, fiber contents, fiber orientations, etc. It has therefore proved to be quite convenient to be able to approximately predict composite properties. The following sections will briefly look at basic relationships to predict some thermal and mechanical properties of the simplest possible composite form: the lamina. A lamina consists of a flat (or curved) assembly of unidirectional fibers or a fabric impregnated with a matrix (see fig. 2.15). Although the properties of unidirectionally reinforced composites of any crosssection may be predicted using these relationships, they will likely prove inadequate when trying to predict properties of composites with more complex geometries, as well as laminated composites composed of laminae stacked at different angles. While laminate theory is considered beyond the scope of this chapter the interested reader should encounter little problem locating one of the many textbooks covering this topic.

2.3.3.1. Prediction of thermal properties To enable determination of lamina properties from those of the constituents, several assumptions may be made; among the more common assumptions are that

B.T. /lstrSm

56

Fig. 2.15. Composite lamina.

matrix and fibers are isotropic. While glass fibers really are isotropic, carbon and aramid fibers clearly are not and it may also be questionable whether the matrix really is isotropic. Through micromechanics-based considerations one may derive expressions to determine the thermal properties of laminae. The longitudinal CTEs may be expressed as [23]:

Vfolf Ef @ VmOlmEm =

(2.1)

v j E j + VmEm

where V is volume fraction and indicesfand m refer to fiber and matrix, respectively. The transverse CTEs may similarly be written [23]:

o~, = Vfotf (1 + vf) + Vmotm(1 + Vm) - (Vfvf + Vmvm)O#

(2.2)

where v is Poisson's ratio and c~t is given by eq. (2.1). Equivalent expressions for the CTCs are [24,25]:

kt = Vfkf + Vmkm kfkm

(2.3) (2.4)

= Okm + Vmk

while the heat capacity may be expressed as [25]:

Up=

Vf pffpf -k- VmPmCpm Vfpf + Vmpm

(2.5)

2.3.3.2. Prediction of mechanical properties Micromechanics-based predictions of lamina mechanical properties are significantly more common than the thermal relationships quoted above. Employing the same assumptions as in the previous section, one may estimate the modulus of elasticity (Young's modulus) in the longitudinal direction as: Et = VuET + VmEm

(2.6)


57

Equation (2.6) is sometimes called the parallel model and constitutes an upper bound for the modulus of a composite. The modulus in the transverse direction may be estimated as: Et -

ETEm

(2.7)

V:Em + VmE: Equation (2.7) is sometimes referred to as the serial model and may be regarded as a lower bound for the modulus of a composite. The parallel model may also be used to estimate the major (in-plane) Poisson's ratio and the serial model correspondingly may be employed to estimate the (inplane) shear modulus, although Poisson's ratios and shear moduli of fibers rarely are known. Comparisons with experimental data have shown that the parallel model yields reasonably accurate results, whereas the serial model predicts moduli considerably deviating from experimental data. It is also possible to predict the lamina strengths based on micromechanics considerations although such expressions require extensive assumptions, including that all fibers are perfectly parallel, have exactly the same properties (i.e. fail simultaneously), and are perfectly bonded to an isotropic matrix. In longitudinal tension one may express the strength as: =

+ Zm m

(2.8)

If the fibers are much stiffer than the matrix (which holds true for all common fiber-reinforced polymers) and the fiber volume fraction is significant (which is the case for all structural composites) the latter term in eq. (2.8) may be omitted. Since this strength expression is based on such highly ideal assumptions it is to be regarded as an upper bound for the strength; indeed it predicts strengths significantly higher than experimentally determined ones. A variety of equivalent expressions for transverse, shear, and flexural strengths have been derived and may be found in the pertinent literature, including textbooks on mechanics of composite materials (e.g. references [26] or [27]). Such textbooks also discuss the assumptions and accompanying weaknesses of the micromechanics models above, including other and more refined models, and invariably also describe how to determine the effective properties of laminates. Prediction of laminae and laminate properties using the equations above as well as other and more refined models no doubt is convenient in the early design stages. It cannot be overemphasized, however, that such predicted properties rarely are sufficient to finalize a design and experimentally determined properties are usually a necessity.

2.3.3.3. Experimentally determined thermal properties Since predictions rarely can replace experimentally determined properties entirely, this section and the next therefore attempt to give some examples of experimentally determined properties. Figure 2.16 shows the temperature-dependency of the thermal properties of unidirectionally reinforced carbon/PEEK, which probably is the most well-characterized thermoplastic-based composite to be found in the open

B.T. AstrSm

58

0.8-

8

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0.3

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1620

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1580

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i i i , t i , ..................................i..................................i ...................................i ..............,..................~...............................i..............., ................... i i i ~ i ! J ! i i i i ......................... ~.................................i ................................ l ................i ................................i............J..................

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100

Temperature

200

Tg

300

T,,, 400

0

[~

Fig. 2.16. Thermal properties of unidirectionally reinforced carbon/PEEK as functions of temperature at Vf = 0.61. Values for CTE in excess of 150~ are estimated. Tg and Tm indicated in graphs. Data from reference [21.

literature. Thermal properties of other material systems are difficult to find in the literature and one therefore often has to resort to using eqs. (2.1) through (2.5).

2.3.3.4. Experimentally determined mechanical properties In analogy with the previous section, this section also attempts to provide some representative property data for thermoplastic composites. Table 2.7 gives properties of composites manufactured from E glass/PP, E glass/PA 12, and carbon/PEEK prepreg. The glass/PP and carbon/PEEK composites were molded from unidirec-

59

Thermoplastic composite sheet form&g

TABLE 2.7 Mechanical properties of composites molded from E glass-reinforced PP, E glass-reinforced PA 12, and high-strength carbon-reinforced PEEK prepregs [2,28,29]. r is shear strength, G shear modulus, and I L S S interlaminar shear strength, while index l denotes longitudinal, t transverse and tensile, c compressive,f flexural, and 2. out of plane Matrix: Reinforcement type:

PP E glass

PA 12 E glass

PA 12 E glass

Reinforcement form:

UD

UD weave

Balancedweave

0.35 1,480 620

0.55 1,900 710 90

0.52 1,850 350 350

570

800 160

500 500

D

p

flit ott

rrtc rrtc

rrtf rrtf rt• rlt

"t't_l_ Ett Ell

Etf Etf Glt Gt! Gt_I_ ~31t Vl_l_ Vtl

(kg/m3) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) (GPa) (GPa) (GPa) (GPa) (GPa) (GPa) (GPa)

27.5 22

44 7.2 38 8

26 26 22 22

(%)

ett ILSS

(%)

(MPa)

0.61 2,130 80 1,100 220

120 175 80 137 9.4

5.1 5.1 3.2 0.33 0.32 0.04 0.40 0.40

21t_l_ V_l_t

e,

PEEK High-strength carbon UD

2.1

1.5 2.2 47

1.6 1.6 42

tionally reinforced m e l t - i m p r e g n a t e d prepregs, while the glass/PA 12 composites were m o l d e d f r o m p o w d e r - i m p r e g n a t e d fabric prepregs of two different types. The prepreg d e n o t e d U D weave was a c r o w f o o t weave with 90 percent of the fibers in the warp direction and 10 percent in the weft direction, whereas the prepreg d e n o t e d balanced weave was a satin weave (with equal a m o u n t s of fibers in the two orthogonal directions). Table 2.8 illustrates how the increased handleability of c o m m i n g l e d materials is also likely to lead to composite properties inferior to those achievable with melti m p r e g n a t e d prepregs. The d r a w b a c k of c o m m i n g l e d feedstock is that it m u s t be m e l t - i m p r e g n a t e d during processing, which is a non-trivial p r o c e d u r e with such a high-viscosity p o l y m e r as P E E K . Similar tendencies should be expected with powd e r - i m p r e g n a t e d reinforcement.

B.T. AstrO'm

60

TABLE 2.8 Properties of composites molded from melt-impregnated and commingled carbon/PEEK feedstock [2] Product form

O'lt (MPa)

Elt (GPa)

Olc (MPa)

Elc (GPa)

o'tt (MPa)

Ett (GPa)

Melt-impregnated Commingled

> 1,172 > 782

132 127

1,175 865

113 115

91 64

8.9 8.9

Table 2.9 provides properties for components compression molded from glass/PP GMT. For all product forms listed, with the exception of the last one which has half the reinforcement longitudinally oriented, the properties should be reasonably isotropic in the plane.

2.4. Manufacturing techniques The term sheet forming may generously be thought of as including both sheet formation, or rather consolidation of the raw material into a so-called blank, and forming of this blank, or sheet, into a curved component. To date virtually all types of sheet forming have employed prepregs and with this raw material form one may think of the route from prepreg to final component as consisting of three basic steps: prepreg lay-up, prepreg consolidation, and sheet forming. In some cases two or even all three of these steps may be combined into one operation, but it is more common that all three steps are separate. The remainder of this chapter introduces the most common routes to achieve these steps, but the order of the techniques described in no way implies any preference in terms of technical or economical feasibility. It deserves to be pointed out that most of the techniques discussed below are known by more than one name and the designations used herein are not necessarily the most common ones. TABLE 2.9 Properties of composites molded from glass/PP GMT [30]. For the last GMT type (Wf --- 0.43) half of the reinforcement is longitudinally oriented. W denotes weight fraction. GMT type

Wf

Fiber length (mm)

p

O'lt Elt (kg/m 3) (MPa) (GPa)

Elt (%)

O'lf Elf (MPa) (GPa)

Powder-impregnated

0.25 0.30 0.35 0.40

12 12 12 12

1,070 1,120 1,160 1,220

75 86 96 105

4.0 4.5 5.2 5.9

3.3 3.0 2.8 2.7

130 140 150 165

4.8 5.5 5.9 6.4

Melt-impregnated

0.20 0.30 0.40 0.43

continuous continuous continuous continuous

1,020 1,130 1,190 1,210

55 85 105 250

3.5 4.5 6.0 10.5

1.8 1.8 1.7 1.7

90 110 140 160

3.5 4.5 5.5 8.5


61

2.4.1. Prepreg lay-up The most straightforward way of laying up the prepreg plies to form a composite no doubt is to cut the prepreg by hand and likewise to lay it up by hand, ply by ply. Due to the research and development status of most sheet forming operations, this fully manual procedure is indeed the most common, although semiautomated or fully automated machinery used in the aerospace industry when dealing with thermoset prepregs certainly could be used with thermoplastic prepregs as well. With such machinery wide prepreg sheets would be automatically cut to size and then robotically stacked in the desired fashion. However, for such procedures to make financial sense, relatively large productions volumes would be necessary. In contrast, with continuous and quasi-continuous consolidation processes the prepreg lay-up becomes an integral part of the consolidation process. In such continuous processes the prepreg plies are continuously uncoiled from rolls and gradually consolidated, as further discussed in the following sections.

2.4.2. Prepreg consolidation Once the prepreg plies have been laid up the stack may be consolidated in several different fashions. The basic requirement on any consolidation technique for thermoplastic prepregs is to apply sufficient pressure to maintain the molten reinforcementmatrix mass in the desired shape for the time required to allow itJto become dimensionally stable. With thermoplastic prepregs this time is of the order of tens of seconds to a couple of minutes, since the part only needs to be cooled for the matrix to solidify. It has been shown that full consolidation of two thermoplastic layers may be achieved in a fraction of a second provided the layers are at sufficiently high temperature and instantaneously are brought into intimate contact. With thermoplastic resins the strength between two layers brought into intimate contact at a temperature in excess of Tg is governed by diffusion of polymer molecules across the interface between the two layers. Given sufficient time this diffusion process will lead to an interfacial strength equal to that of the virgin resin. The time to reach the virgin strength is strongly dependent on temperature, since higher temperatures promote diffusion. This healing process is referred to as autohesion, i.e. self-adhesion between two layers of the same thermoplastic resin. While autohesion has been achieved in very short time frames in laboratory composites consolidation experiments, it is rare that similarly short time frames are achieved in real processing operations. In most manufacturing situations it is not the time required to achieve virgin material strength over an interface that limits the processing rate; the limits are usually set by the time required to heat and cool the material.

2.4.2.1. Vacuum-bag consolidation Following established procedures for thermoset composites manufacture, it is naturally possible to vacuum-bag consolidate a prepreg stack, possibly using an autoclave. Figure 2.17 illustrates how the prepregs have been laid up onto a mold and then covered by a vacuum bag. Vacuum is then drawn under the bag to compact

62

B.T. flstr6m

Fig. 2.17. Schematic of vacuum-bag consolidation.

the prepreg stack with (the external) atmospheric pressure. The vacuum is maintained throughout a complete heating and cooling cycle and results in a fully consolidated laminate. Heating is likely achieved through placing the entire vacuumbag assembly, including mold, in an oven and - - following complete melting of the prepreg matrix - - subsequent removal of the assembly from the oven and back into open air to cool off. If an autoclave is used, higher compaction pressures may be achieved through pressurization of the internal atmosphere of the autoclave; heating would likely be achieved through heating of the same internal atmosphere. Whether an autoclave is used or not, the mold naturally may incorporate provisions for independent heating and cooling to increase process efficiency. Although vacuumbag consolidation is certainly technically feasible, it likely does not make economical sense in anything but laboratory-scale experiments due to the large degree of timeconsuming manual labor and - - if an autoclave is used - - the expensive equipment involved. However, hand layup of thermoset-based prepregs onto a contoured mold followed by vacuum bagging and autoclave consolidation is an established technique to manufacture shell-like composites that also has proven feasible with thermoplastic prepregs. In this case prepreg lay-up and conformation to the mold are combined into one step that is followed by vacuum-bag consolidation (with or without autoclave) without further forming. 2.4.2.2. Matched-die consolidation

A much more common and economically more sensible consolidation technique is to employ one or more hydraulic presses and consolidate the prepreg stack between parallel platens, possibly using a picture-frame mold to prevent resin bleeding from the edges of the laminate. One incarnation of this consolidation technique employs an oven to heat the prepreg to a temperature in excess of the softening point of the matrix, whereupon the prepreg stack is quickly transferred to a press equipped with a mold having a temperature below the softening point of the matrix. The press then very rapidly closes to apply sufficient consolidation pressure during cooling (see fig. 2.18). This consolidation technique is best suited for fully melt-impregnated prepregs and cycle times of less than a minute may be achieved assuming that the matrix is completely melted. The reason for the short cycle times is that with fully meltimpregnated prepregs consolidation is only a matter of squeezing the prepreg plies together to eliminate inter-ply gaps and then to allow for autohesion to occur before the matrix resolidifies.


63

Fig. 2.18. Schematic of matched-die consolidation. For material forms that are not already fully melt-impregnated, e.g. powderimpregnated and commingled prepregs as well as unimpregnated reinforcement layers interleaved with resin films (called film stacking), the processing requirements are quite different. With such materials matrix flow relative to the fibers must be permitted to achieve full fiber wetting and a completely consolidated laminate. Due to the very high matrix viscosities involved this required time frame is significantly longer than that needed for consolidation of melt-impregnated prepregs. To provide such extended time for flow, either two presses and two sets of molds - - one heated and one cooled or a mold which allows both heating and cooling are required. With two presses the prepreg stack is placed in the heated mold, which then is closed to apply slight pressure until the desired equilibrium temperature (in excess of the softening point of the matrix) is reached within the material. When the specified molding temperature has been reached, molding pressure is applied for a given length of time. The heated mold is then opened and the molten material is rapidly transferred to the cooled mold where it is consolidated under pressure. With one mold having both heating and cooling capabilities the prepreg stack is placed in the unheated mold in the press which is then closed. As in the previously described technique the material is gradually heated under slight pressure until the desired temperature is reached when full molding pressure is applied; the mold is then cooled to consolidate the material. (These two techniques may be combined employing one mold and two presses. In this case the material remains in the mold which is moved from the heated to the cooled press.) Neither of these two techniques appear to have much potential for mass production of flat laminates due to the expensive machinery (two presses) and long cycle times; the former technique may possibly achieve cycle times of the order of ten minutes, whereas the latter has cycle times of the order of an hour.

2.4.2.3. Double-belt-press consolidation A DBP offers the only realistic means of continuously consolidating prepregs into wide laminates (see fig. 2.19). The prepregs enter the press and are heated under pressure until the matrix is molten, whereupon the laminate is cooled under pressure so as to exit the DBP fully consolidated. In this case prepreg lay-up and consolidation are essentially performed simultaneously since the incoming prepregs are

64

B.T. flstr6m

Fig. 2.19. Schematic of double-belt-press consolidation.

uncoiled from rolls of material through the forward motion of the bands of the DBP. On-line consolidation is a term that is sometimes used to describe such simultaneous lay-up and consolidation. This consolidation method is the only technique that appears to be economically feasible for large-scale blank manufacture. Linear consolidation speeds are of the order of a few millimeters per second. Any prepreg form may be continuously consolidated into a laminate with a DBP, but processing rates are likely to be lower with not yet melt-impregnated material forms.

2.4.2.4. Tape laying A significantly less common but nevertheless technically feasible technique to online consolidate flat laminates is tape laying. In this case prepreg in tape form is unrolled from a spool and continuously laid up onto the mold (see fig. 2.20). Both the mating surfaces are locally heated and joined under pressure so as to achieve continuous consolidation, or welding. If both the previously laid ply and the incoming prepreg tape have completely melted surfaces when they are joined, no separate consolidation step may be needed and the laminate thus is ready for demolding as soon as lay-up is completed. However, one may instead aim only for partial consolidation to ensure that the prepregs stay in place in relation to one another and then achieve full consolidation in a separate processing step, such as through any of

Fig. 2.20. Schematic of tape laying.

Thermoplastic compositesheetforming

65

the aforementioned consolidation techniques or concurrently with one of the forming techniques described later in this chapter. If only partial consolidation is the aim, the lay-up can proceed much more rapidly with the same amount of heating, thus increasing the processing rate. Tape laying may also be used to produce curved components, thus enabling one-step layup--consolidation-forming. However, due to the localized and highly nonuniform heating history of such a component most attempts at such one-step manufacture have resulted in considerable residual stresses causing component warpage. It is therefore common to combine tape lay-up with subsequent consolidation whether the component in question is a blank or a final component. 2.4.2.5. Intermittent matched-die consolidation The final consolidation technique described herein is intermittent matched-die consolidation as illustrated in fig. 2.21. In this technique the incoming prepregs are heated in an oven so as to melt the matrix (the oven may possibly be replaced by a press with a heated mold to mimic the two-press consolidation procedure described above). The molten material is then indexed to enter a press with a cooled open-sided mold, where it is consolidated. The mold then opens, the material is indexed, and the consolidation repeated. Since this consolidation technique is quasi-continuous it may hold a promise of being economically feasible for large-scale blank manufacture. 2.4.3. Sheet forming Once a fully consolidated blank manufactured through any of the aforementioned lay-up and consolidation techniques is available, there is a range of possible means to form it into an arbitrarily shaped component. Virtually all prepregs contain continuous and oriented fibers, which from a manufacturing point of view are inextensible and embedded in a lubricating liquid resin. The issue of conforming and subsequently reconsolidating a previously consolidated blank (or possibly an unconsolidated prepreg stack) is a non-trivial exercise. Figure 2.22 illustrates possible deformation modes of the plies that make up the blank (or the unconsolidated stack) and the minimum requirements in terms of flow mechanisms to achieve this mode of deformation. Since the blank predominantly is made to conform to the mold and the inextensible fibers allow very little flow, the blank is normally almost the

Fig. 2.21. Schematic of intermittent matched-die consolidation.

66

B.T. AstrO'm

Fig. 2.22. Hierarchy of deformation modes for stacked reinforcement plies and corresponding required flow mechanisms. Redrawn from reference [2].

same size as the final component (often larger) and the thickness change between blank and final component is small. In shaping of doubly curved components there is a pronounced risk of wrinkling of the plies during conformation. The wrinkling tendency is significantly reduced if the plies to be formed have shape and size resulting in as little excess material around the edges (that needs to be trimmed off in a secondary operation following molding) as possible. Another important means of reducing the risk of wrinkling is to keep the plies under slight tension during molding. In most of the following technique descriptions such tensioning devices are neither explicitly mentioned nor shown in the figures, but would nevertheless likely improve results in all techniques when forming doubly curved components. Correctly optimized most of the sheet forming techniques discussed below ought to be able to both form the final component and consolidate a previously unconsolidated prepreg stack in the same step. In practice this has proven difficult to achieve in many (but not all) techniques and it appears as if most work on sheet forming utilizes preconsolidated blanks as raw material. Use of preconsolidated blanks is clearly economically disadvantageous, but generally simplifies and speeds up processing and results in improved consolidation in the formed component. For reasons of overall process economy, one-step forming and consolidation ought to be an area most worthy of research.

2.4.3.1. Matched-die molding Matched-die compression molding, also known as stamping due to its close similarity with sheet metal stamping, employs matching metal dies, or molds, mounted in


67

a press (see fig. 2.23). The general processing steps are similar to those in matched-die consolidation described above. An oven is used to heat the blank to a temperature in excess of the softening point of the matrix, whereupon it is quickly transferred to a mold having a temperature below the softening point of the resin. The press then very rapidly closes to force the blank to conform to the mold and then maintains sufficient pressure during component cooling to ensure that the material is reconsolidated in its new shape. Due to its short cycle times and similarity with compression molding of both sheet metal and thermoset composites, matched-die compression molding is seeing quite some interest, particularly from the automotive industry. Significant drawbacks of this technique are very expensive molds and that forming is so rapid that it is likely that only moderately curved components are manufacturable when the feedstock contains continuous and aligned fibers.

2.4.3.2. Rubber-die molding Rubber-die molding is closely related to matched-die molding; fig. 2.24 illustrates the concept. Rubber-die molding reduces the risk of wrinkles in the part through more evenly applied pressure. Due to the poor heat transfer characteristics of rubber the matrix solidifies less rapidly upon die contact than with metal dies and more deeply drawn components are thus manufacturable. To facilitate molding of more complex geometries the rubber block may be contoured to more or less match the shape of the solid lower mold half. The technique employs significantly cheaper molds than matched-die molding.

Fig. 2.23. Schematic of matched-die molding.

Fig. 2.24. Schematic of rubber-die molding.

68

B.T. ~lstrO'm

2.4.3.3. Hydroforming Another quite similar molding technique is hydroforming. In this process a liquid is contained by a flexible membrane that is capable of conforming to the shape of the other mold half (see fig. 2.25). Following mold closure the liquid is pressurized to force the blank to conform to the other mold half. For the same reasons as with rubber-die molding the cooling is relatively slow, thus allowing for longer forming times and consequently more complex contouring. Also hydroforming reduces the risk of wrinkles in the part through the hydrostatically applied pressure, which may be significantly higher than in rubber-die molding. Hydroforming employs cheaper molds than both the aforementioned techniques.

2.4.3.4. Deep drawing In deep drawing the material to be formed is mounted in a frame that keeps the material under slight tension until forming is completed (see fig. 2.26). As the molten material leaves the preheater it is placed over a female "mold", essentially consisting of a hole the shape of the projected area of the final product. A male mold then rapidly punches the pliable material through the hole of the female mold. This crude forming technique likely produces components with poor external surface finish and allows limited control of material movement during forming. Nevertheless, it is a low-cost method with lower tooling costs than the aforementioned techniques and has proven its commercial feasibility in, for example, manufacturing of hinge covers for civilian aircraft cargo areas.

Fig. 2.25. Schematicof hydroforming.

Fig. 2.26. Schematicof deep drawing.


69

2.4.3.5. Diaphragmforming The only technique that has been developed exclusively for thermoplastic composites manufacturing is diaphragm forming, which may be seen as a refined version of conventional autoclave consolidation. The process has been investigated by numerous different organizations and the results are encouraging. Since diaphragm forming has been investigated by many, the technical solutions vary significantly; two of the more common versions are described in the following. The blank to be formed is placed between two flexible diaphragms. The diaphragms, but not the blank which remains free-floating, are clamped around the entire perimeter using a clamping frame and the air is evacuated between the diaphragms. Thus far in the description most versions of diaphragm forming remain the same; the main differences are in heating and forming techniques. In one diaphragm forming version the diaphragm-blank sandwich is placed in an oven and heated to a temperature in excess of the softening point of the matrix. The diaphragm-blank sandwich is then rapidly placed onto a one-sided female mold and vacuum is drawn in the space between the lower diaphragm and the mold and pressure is applied above the upper diaphragm to force the blank to conform to the mold (see fig. 2.27). Either vacuum and pressure or just one of them may be used in forming. Since the mold is normally unheated the component solidifies as it gradually comes in contact with the mold. In another incarnation of diaphragm forming the diaphragm-blank sandwich is placed on top of the mold and then this entire assembly is placed in an autoclave, which often is purpose-built. The internal atmosphere of the autoclave is then heated to melt the matrix whereupon the combined forces of vacuum below the lower diaphragm and pressure above the upper diaphragm make the blank conform to the mold. When forming is completed the heated gas surrounding the mold and the diaphragms is replaced with cool (ambient) air to solidify the component. More rapid processing may be achieved if the mold incorporates heating and cooling options. The first diaphragm material was superplastic aluminum, but most later work has employed polymer films, particularly PI, and sheet rubber. Rubber diaphragms have an advantage in that they may be reused a few times, whereas aluminum and polymer films may not be reused since they become permanently deformed. It is important that the processing temperature is such that the diaphragms allow large plastic deformations, which for polymer diaphragms translates into temperatures between

Fig. 2.27. Schematic of diaphragm forming.

70

B.T. ~lstrO'm

Tg and Tm. PEEK-based prepregs are thus very well compatible with PI diaphragms, whereas at the processing temperatures common with PP they do not allow sufficient deformation. With rubber diaphragms this is not a concern since they are pliable at all realistic forming temperatures, but instead the processing temperature must be below the upper use temperature of the diaphragms. Since low pressures are involved, simple tooling may be used. Materials include sheet metal which allows rapid temperature changes and, for experimental work, plaster and wood molds, which have their predominant advantage in the low cost. The main characteristic of diaphragm formed components is that they may be deeply drawn and quite complex, especially when forming in an autoclave. This is partly due to the diaphragms keeping the material both under tension and under slight lateral compression and partly due to the matrix being pliable for a long time (basically until it comes into contact with the mold in the first technique and for any desired time in the latter technique). Due to its versatility the scope for commercial applications of diaphragm formed components should be great, but the commercial acceptance of the technique remains to be seen. Components that appear to be nearing commercial reality are glass/PP blister fairings and leading edges for jet engines to replace hand-laid-up and autoclave-consolidated carbon/epoxy components. 2.4.3.6. Folding Folding is a sheet forming technique different from the previously discussed ones in that it only involves localized heating and forming. Blanks may be folded through heating along a line and subsequent bending along this line (see fig. 2.28). Despite the fact that continuous fibers are likely to buckle or fracture, folding even of honeycomb sandwich panels, where the core ends up being crumpled has proven commercially viable in manufacturing of for example parts for aircraft interiors. 2.4.3.7. Roll forming Roll forming, which just like matched-die molding has been borrowed from sheet metal forming, is the only potentially continuous sheet forming technique. In roll forming several consecutive pairs of contoured rollers, normally four or more, gradually deform the molten blank to the desired shape (see fig. 2.29). The rollers, which are driven, are normally unheated and they consequently gradually cool the component. Roll forming is potentially capable of manufacturing any constant cross-section geometry and the products may be curved if desired. Nevertheless, so far thermoplastic roll forming has been used to manufacture hat and Z shapes only. Compared to most of the previously mentioned manufacturing techniques, little

Fig. 2.28. Schematicof folding.


71

Fig. 2.29. Schematic of roll forming.

work on roll forming of thermoplastic composites appears to be ongoing despite the feasibility of the technique having been proven.

2.4.3.8. Matched-die molding of GMT In composites applications the term sheet forming is usually used to refer to conformation of a flat blank reinforced with aligned and continuous reinforcing fibers to a mold. In contrast, in matched-die molding using GMT as raw material the materialflows (rather than conforms) to fill the mold, since there are normally no aligned and continuous fibers to effectively prevent flow and also due to the fact that the fiber content is lower than in prepregs. While matched-die molding of GMT therefore may be slightly beyond the scope of this chapter, it is the only technique to manufacture shell-shaped structural thermoplastic composites that is currently in widespread commercial use and it has therefore been included for reference. The technique employs presses and molds similar to the previously described technique of matched-die molding. The main difference from fig. 2.23 is that in this case the heated raw material does not already cover most of the mold; instead the so-called charge covers only about half the mold area and the closing mold forces the charge to flow to fill the mold (see fig. 2.30). Since the GMT flows to fill the mold a component molded from GMT may have varying thickness and, for example, bosses and ribs, which are features difficult to obtain with matched-die molding of continuous-fiber-reinforced blanks. Since the material flow is notable the reinforcement is oriented in the direction of the flow and properties therefore may vary significantly within a component. In applications where increased stiffness is required GMT with varying degrees of oriented and possibly continuous reinforcement or interleaved unidirectionally reinforced prepregs may be used, thus partially bridging

Fig. 2.30. Schematic of matched-die molding of GMT.

72

B.T. ~lstrO'm

the gap between matched-die molding of GMT and matched-die molding of continuous-fiber-reinforced blanks. The biggest users of GMT are automobile manufacturers, particularly European ones. GMT-based composites are notorious for their poor surface finish and are consequently often hidden from direct view in under-hood applications and in for example seat frames.

Acknowledgement The author gratefully acknowledges that the bulk of this chapter was written when he was a Visiting Senior Lecturer at the Department of Mechanical Engineering at the University of Auckland, New Zealand.

References [1] Thermoplastic Composites Materials Handbook, ICI Composites, Inc., USA, 1991. [2] Cogswell, F.N., Thermoplastic Aromatic Polymer Composites, Butterworth-Heinemann, Oxford, UK, 1992. [3] Jang, B.Z., Advanced Polymer Composites: Principles and Applications, ASM International, Materials Park, OH, USA, 1994. [4] Caldwell, D.L., Interfacial Analysis, in Handbook of Composite Reinforcements, Ed. S. M. Lee, VCH Publishers, New York, NY, USA, 1993. [5] Tobolsky, A.V., Properties and Structure of Polymers, John Wiley & Sons, New York, NY, USA, 1960. [6] Shalaby, S.W. & Moy, P., Thermal and Related Properties of Engineering Thermoplastics, in Engineered Materials Handbook, Volume 2, Engineering Plastics, ASM International, Metals Park, OH, USA, 445-459, 1988. [7] Galanty, P.G., and Richardson, J.J., Polyethylene Terephthalates (PET), in Engineered Materials Handbook, Volume 2, Engineering Plastics, ASM International, Metals Park, OH, USA, 172-176, 1988. [8] Brady, D.G., Polyphenylene Sulfides (PPS), in Engineered Materials Handbook, Volume 2, Engineering Plastics, ASM International, Metals Park, OH, USA, 186-191, 1988. [9] Data Sheet 2: Making Consolidated Sheet from Aromatic Polymer Composite, APC-2, ICI Fiberite Corporation, 1987. [10] Taske II, L.E., Personal communication, BASF, Charlotte, NC, USA, 1990. [11] Fines, R.E. & Bartolomucci, J.P., Polyether-imides (PEI), in Engineered Materials Handbook, Volume 2, Engineering Plastics, ASM International, Metals Park, OH, USA, 156-158, 1988. [12] Watterson, E.C., Polyether Sulfones (PES, PESV), in Engineered Materials Handbook, Volume 2, Engineering Plastics, ASM International, Metals Park, OH, USA, 159-162, 1988. [13] Fitzpatrick, J.E., Polyamide-imides (PAl), in Engineered Materials Handbook, Volume 2, Engineering Plastics, ASM International, Metals Park, OH, USA, 128-137, 1988. [14] The Thermal and Oxidative Thermal Degradation of APC-2, ICI Composites, Inc. [15] Modern Plastics Encyclopedia '95, McGraw-Hill, New York, NY, USA, 1995. [16] Hancox, N.L. & Mayer, R.M., Design Data for Reinforced Plastics- A Guideline for Engineers and Designers, Chapman & Hall, London, UK, 1994. [17] Anon., Fibers, in Engineered Materials Handbook, Volume 1, Composites, ASM International, Metals Park, OH, USA, 360-362, 1987. [18] Bunsell, A.R., Fiber Reinforcement, in Handbook of Composite Reinforcements, Ed. S. M. Lee, VCH Publishers, New York, NY, USA, 199-217, 1993. [19] Morgan, R.J. & Allred, R.E., Aramid Fiber Composites, in Handbook of Composite Reinforcements, Ed. S. M. Lee, VCH Publishers, New York, NY, USA, 5-24, 1993.


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[20] Diefendorf, R.J., Carbon/Graphite Fibers, in Engineered Materials Handbook, Volume 1, Composites, ASM International, Metals Park, OH, USA, 1987. [21] Pigliacampi, J.J., Organic Fibers, in Engineered Materials Handbook, Volume 1, Composites, ASM International, Metals Park, OH, USA, 54-57, 1987. [22] Miller, D.M., Glass Fibers, in Engineered Materials Handbook, Volume 1, Composites, ASM International, Metals Park, OH, USA, 45-48, 1987. [23] Shapery, R.A., Thermal Expansion Coefficients of Composite Materials Based on Energy Principles, Journal of Composite Materials, 2 (1968) pp. 380-404. [24] Rosen, B.W., Thermomechanical Properties of Fibrous Composites, Proceeding of the Royal Society of London, A319 (1970) pp. 79-94. [25] Taylor, R., Thermophysical Properties, in International Encyclopedia of Composites, Ed. S. M. Lee, VCH Publishers, New York, NY, USA, 5, 1-7, 1991. [26] Eckold, G., Design and Manufacture of Composite Structures, Woodhead Publishing, Cambridge, UK, 1994. [27] Daniel, I.M. & Ishai, O., Engineering Mechanics of Composite Materials, Oxford University Press, New York, NY, USA, 1994. [28] Plytron GN 638 T, Unidirectional Glass-Fibre/Polypropylene Composite, Borealis, Stathelle, Norway, 1995. [29] Product Information Vestopreg, HOls AG, Marl, Germany, 1994. [30] Berglund, L.A. & Ericson, M.L., Glass Mat Reinforced Polypropylene, in Polypropylene: Structure, Blends and Composites, Volume 3, Composites, Ed. J. Karger-Kocsis, Chapman & Hall, London, UK, 202-227, 1995.



Chapter 3

Computer Simulation of Thermoforming B.L. K O Z I E Y and M.O. G H A F U R Polydynamics Inc., 1685 Main St. West, Suite 305, Hamilton, Ontario, Canada L8S 1G5

J. V L A C H O P O U L O S and F.A. M I R Z A Faculty of Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7

Contents Abstract 75 3.1. Introduction 76 3.2. Sheet production 77 3.3. Thermoforming simulation 78 3.3.1. Finite element formulations 80 3.3.1.1. Membrane formulations 80 3.3.1.2. Thick sheet formulations 82 3.3.2. Material behaviour 83 3.3.2.1. Non-linear elastic models 83 3.3.2.2. Visco-elasticmodels 85 3.3.3. Thermoforming simulation examples 86 3.4. Concluding remarks 88 References 88 Abstract This chapter provides a description of the application of the finite element method to the simulation of the thermoforming process. The objective of thermoforming simulation is the provision of a rational means of mold design and to also allow for the design of "optimal" final parts using the minimum amount of material. This can be achieved by comparing the simulated behavior using various materials and mold configurations with varying process conditions. This eliminates the need to perform inefficient and expensive "trial-and-error" procedures. A "state-of-the-art" review of the finite element method in the simulation of thermoforming is given. The review covers the details of the membrane and thick sheet finite element formulations as well as non-linear elastic (Ogden, Mooney-Rivlin) and visco-elastic (K-BKZ) material constitutive relationships. Some examples, giving comparisons between simulation results and experimental values are also included. Good agreement was obtained between the predicted and measured thickness distributions. The results 75

B.L. Koziey et al.

76

also indicate that the choice of material model (non-linear elastic versus visco-elastic) must be done carefully if reliable predictions of the thickness distribution are to be achieved. For straight thermoforming into shallow molds a non-linear elastic model is suitable. However, when deep drawn forming, complex mold geometry or plugassistance is involved, a visco-elastic model is required to obtain accurate predictions. 3.1. Introduction

The term "thermoforming" describes a number of related polymer processing techniques, in which thermoplastic sheets are softened by heat and subsequently formed by the application of vacuum, pressure, or a moving plug. The sheet may be stretched over a male mold (positive forming) or into a female mold (negative forming). On contact with the mold heat is lost and the material regains stiffness as it cools. The vacuum and plug-assisted forming processes are depicted in figs. 3.1 and 3.2, respectively. For a detailed description of thermoforming operations, equipment design as well as heating and cooling issues refer to Throne [1]. Geometries of thermoformed products are usually simple (boxes, food trays, various containers, refrigerator liners, but lately also computer casings). Thermoforming competes with blow molding and injection molding. The main advantages of this process are (i) the relatively low cost of thermoforming machines and the very low cost for the molds, and (ii) it is easy to form large area thin section parts. The disadvantages are (i) limited product shapes, (ii) difficulties in obtaining the required thickness distribution, (iii) it is difficult to control molecular orientation, and (iv) limitations in service temperature which may induce strain recovery or shrinkage. In thermoforming the final part thickness is typically controlled by employing differential heating of the plastic sheet and plug assistance. The critical parameters associated with these techniques for controlling the final part thickness have generally been determined by trial and error. Unfortunately this has meant that the A

plastic sheet

B

!

.... Clamp

.

Vacuum holes

// . .l

.

.

.

.

.

.

V

Vacuum

Fig. 3.1. Vacuum forming: (A) preheated clamped sheet over female mold prior to forming; (B) vacuum applied.

Computer simulation of thermoforming A

..................

Clamp

N~

Air

B

77 Air

C

"/" "

Plastic Sheet

T Vent

I Vent

Fig. 3.2. Plug-assist thermoforming: (A) preheated clamped sheet; (B) sheet stretched with plug advance; (C) pressure applied to complete forming.

development of new mold designs and evaluation of thermal process parameters has been inefficient and expensive. Furthermore, a "trial-and-error" process does not allow a quick comparison to be made between competing mold designs and different materials. The objective of computer simulation of thermoforming is the provision of a rational means of mold design and to also allow for the design of "optimal" final parts using the minimum amount of material. This can be achieved by comparing the simulated behavior using various materials and mold configurations with varying process conditions. In this chapter a review of the use of the finite element method in the simulation of the thermoforming process is presented. Because thermoplastic sheet is essential to the thermoforming process a brief description of the primary sheet production methods is given. This is followed by a description of the problems facing the thermoforming industry and what can be hoped to be gained through mathematical modeling of the thermoforming process. A "state-of-the-art" review of the finite element method in the simulation of thermoforming is then given. The review covers the details of the various finite element formulations and material constitutive relationships used. Some examples, giving comparisons between simulation results and experimental values are also included.

3.2. Sheet production Thermoplastic sheet is essential to the thermoforming process. Thermoforming sheet is loosely categorized as thin-gauge (sheet thickness less than 0.25 mm) and thick-gauge (medium-weight sheet: 0.25-1.5 mm; heavy-gauge sheet: greater than 1.5 mm). Thin-gauge sheet is usually produced by the process of calendering while thickgauge sheet is usually produced by the process of extrusion [2] using a coathangershaped die or by calendering [2]. Thermoplastic sheets are manufactured in a variety of widths and lengths and usually come in a variety of predetermined thicknesses. In

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general all thermoplastic resins that can be processed into a sheet can be thermoformed. Most of the fully developed thermoforming markets have been with amorphous [3] resins such as PVC, HIPS, PS, ABS, HDPE, PET, PETG, PP, PVDC, EVOH, PMMA. Amorphous plastics are suitable for thermoforming above the glass transition temperature Tg (usually 30~ to 60~ above Tg). These materials can be processed quite successfully over a wide temperature range. For semi-crystalline and reinforced amorphous materials such as PET and HIPS the forming window is very narrow and in general a higher forming pressure is required. For semi-crystalline materials the temperature should be just above the melting point Tm. The most common and versatile sheet manufacturing technique for thermoforming sheet production is extrusion. In extrusion, polymer pellets are drawn from a hopper into the gap between a heated barrel and a rotating screw. The mass of compacted solid pellets is transported forward and melted under the action of friction and heat. The polymer melt is then pumped through a die, usually of coathanger geometry, to produce a flat sheet which is then cooled and sized to proper gauge. The geometry is designed to allow the melt to flow downstream and laterally simultaneously so that a sheet of uniform thickness is produced. The sheet may be pulled mechanically by a roll stack as it exits the die. This not only reduces the gauge of the sheet, it also produces molecular orientation of the sheet in the machine direction. In most cases this imbalance in the orientation causes problems in the thermoforming process. This is especially true when the parts that are thermoformed are extremely deep or complicated. When the orientation is balanced biaxially on a specially configured extrusion line the strength and impact resistance of the sheet can be significantly increased. The other major process is calendering in which the molten polymer is converted into a sheet by a pair of rotating rolls. The melt forms a characteristic melt bank and spreads as it is squeezed between the rolls. Common calender roll arrangements include the L or Z configurations. A fixed gap is set between the initial rollers which is then continuously reduced between subsequent rollers until the desired gauge is achieved. Unlike sheets produced by the extrusion process those produced by the calendering method have no significant molecular orientation. A considerable amount of information is available in the literature on modeling and simulation of plasticating screw extrusion, flow through flat dies and calendering. The reader is referred elsewhere for more details [4-7].

3.3. Thermoforming simulation The current problems facing the thermoforming industry lie mainly with large wall thickness variations throughout the part with corners typically ending up as the thinner regions. Other problems include physical instabilities during inflation mainly rupture of the sheet as well as shrinkage and warpage of the final part. All these problems have an enormous effect on the performance and cost of a part. Non-uniform wall thickness variations and sheet rupture can be thought of arising for two main reasons, namely, mold geometry and process conditions. Other factors

Computer simulation of thermoforming

79

affecting the wall thickness include the initial dimensions of the sheet, temperature distribution on the surface of the sheet, stretch-strain material properties of the resin, inflation dynamics, and the cooling and solidification phenomena that occur in the mold cavity. Mathematical modeling can provide valuable insights into mold design and process improvement by aiding in the selection of new mold designs, by simulating the behavior of plausible mold configurations, and providing rational means for comparing the formability of different polymeric materials in a given thermoforming process. Such capabilities eliminate the need to perform expensive trial-and-error procedures, in order to optimize the resin distribution and minimize the peripheral waste. Advances in computer technology and numerical methods have made it possible to simulate complex forming problems. The advantages of using the finite element method over any other numerical method are twofold: first, the formulation is not restricted to any particular geometry and, second, the highly non-linear behavior can be directly accommodated into the method. Many difficult aspects of finite element modeling must be addressed in the analysis. These include, but are not limited to, large strains, large deformations, non-linear material behavior, incompressibility, contact between polymer and mold wall, physical and numerical instabilities during inflation, and time-dependent material and thermal effects. While some of these issues, such as large strains and large deformations, must be dealt with rigorously in the formulation, others such as contact between the polymer and mold wall can be included in a simplified manner without adversely affecting the accuracy of the model. The determination of what aspects of the thermoforming process should be included, excluded, or simplified in the finite element formulation is largely dependent on the specifics of the problem to be analysed. For example, for shallow pressure or vacuum forming, in which the forming of the sheet often occurs very quickly, the viscous behavior of the material may not be significant. However, in plug-assisted and deep drawn thermoforming, the forming operation usually takes longer, so the inclusion of time-dependent material effects (visco-elastic) may have a significant influence on the final results. Because of the limited amount of data available these decisions have to be based on engineering judgment and practical experience. A survey of the early work on the application of the finite element method to the simulation of the thermoforming process is given by Zamani et al. [8]. Their review covers the period between 1966 and 1988. In general, these early applications were found to be successful for the problems to which they were applied. However, the usefulness of the models developed as design tools, and their applicability to general thermoforming problems was not well established because of the limited range of problems investigated. These works, however, were very important since they established the basis for much of the future research efforts. Since that time the finite element models have increased in complexity, and more rigorous and comprehensive comparisons between simulation results and actual measurements have been made. As a result the currently available finite element models have become useful design tools allowing for optimization of resin distribution and minimization of peripheral waste. Furthermore, they also provide a means

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of comparing the formability of various polymers under different temperature and pressure conditions. A "state-of-the-art" review of the finite element method in the simulation of thermoforming is given in the following sections. The review covers the details of the various finite element formulations and material constitutive relationships used. Some examples, giving comparisons between simulation results and experimental values are also included.

3.3.1. Finite element formulations In the finite element method the body to be analyzed is divided into a number of small subdivisions, or finite elements. The variables to be approximated are interpolated within each element using shape functions. Provided that the governing differential equations or a variational principle exists, finite element equations can be constructed from which an approximate solution for the process to be modelled can be obtained. Many texts are available on the finite element method and its application. For more information refer, for example, to Oden [9], Bathe [10], and Zienkiewicz and Taylor [11,12]. In the simulation of the thermoforming process there are two distinct types of finite element formulations: those which employ the membrane approximation, and those without the membrane assumption, i.e. thick sheet formulations. Each formulation has certain advantages and disadvantages. These will be described below, along with the details of each approach.

3.3.1.1. Membrane formulations In membrane formulations the bending resistance of the hot polymer is neglected and the sheet thickness is assumed to be very much smaller than its other dimensions. This assumption is quite reasonable for the bulk of the structure except possibly near clamping devices where the sheet may experience substantial bending. The majority of the finite element models formulated for the simulation of the thermoforming process employ the membrane approximation. See for example the work of Allard et al. [13], Warby and Whiteman [14], Nied et al. [15], deLorenzi and Nied [16], Taylor et al. [17], and Kouba et al. [18,19]. In general, the motion of the membrane is referred to a fixed Cartesian coordinate system. The position vectors of an arbitrary point P on the membrane surface in the current and reference configurations are denoted by ~ and ~', respectively. They are related through the expression ~ = X + 5, where 5 is the displacement vector. Since the resulting finite element equations will be non-linear they must be solved in an incremental manner. This is done by referring all variables to a previously calculated known equilibrium configuration and then linearizing the equations so that an approximate solution for the new configuration can be obtained. The solution can then be improved by iteration. Typically either the initial configuration at time 0, or the latest equilibrium configuration at time t are used as possible reference configurations. If all static and kinematic variables are referred to the initial configuration the formulation is referred to as a Total Lagrangian (TL) formulation. If all variables are referred to the last equilibrium configuration the formulation is referred to


81

as an Updated Lagrangian (UL) formulation. The choice of which formulation to employ usually depends on the type of constitutive relation used. Since the constitutive relations typically used in thermoforming simulations are of the hyperelastic type, for example Mooney-Rivlin [20], Ogden [21], and the visco-elastic K-BKZ model the TL formulation is frequently employed. In this case the appropriate energy conjugate stress and strain measures are the second Piola-Kirchhoff stress tensor S, and the Green-Lagrange strain tensor E. The Green-Lagrange strain tensor is defined as 1

E-~(C-I)

(3.1)

where C is the right Cauchy-Green deformation tensor and I is the identity tensor. The constitutive relationship is usually expressed in terms of the principal stretches ~'i of the right stretch tensor U, or the invariants of the deformation tensor C. The invariants of the deformation tensor are easily calculated. To determine the principal stretches the eigenvalue problem for the Cauchy-Green deformation tensor, which is related to the right stretch tensor by U = C, must be solved. This yields two of the principal stretches, )~1 and ,~2, the third principal stretch ,k3 normal to the membrane surface, is determined using the incompressibility constraint )~1~,2~. 3 = 1. The incompressibility constraint in terms of the invariants of the deformation tensor is written as 13 = detC = 1. In membrane formulations the incompressibility condition is always satisfied. Typically the finite element equations are derived using the virtual work principle which requires that the rate of internal virtual work is equal to the external virtual work for an arbitrary velocity field satisfying the kinematic boundary conditions [9]. Assuming that the inertia and body force terms can be ignored the virtual work expression for the deformed membrane using a TL description is given by / S "6Eh0 d A 0 A0

dA

(3.2)

A

where A and A0 are the areas of the deformed and undeformed membranes, respectively. The applied pressure is denoted by p while t7 defines the vector normal to the surface of the deformed membrane, h0 is the initial membrane thickness and 6 is the membrane velocity vector. The finite element equations of equilibrium required for the incremental analysis are obtained through variation and linearization of the virtual work expression, eq. (3.2), followed by the introduction of the finite element discretizations. The elements used for discretization of the membrane typically [16,18] employ linear variations of the displacements within the element. In addition, the elements are usually triangular which allows curved edges to be more easily modeled. As mentioned previously the resulting finite element equations are solved using an incremental procedure. Starting from a known equilibrium configuration, usually the initial undeformed state, a small load increment is applied and the displacement increments are found. The solution is improved by applying an iterative method,

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usually the standard Newton-Raphson method. Since the geometry of the membrane can often change drastically even for small load increments the load vector and stiffness matrix are recalculated during the iteration procedure using the updated geometry while keeping the load constant. After several iterations the incremental deformations become less than some prescribed value at which point the solution is considered to have converged. In the presence of a mold, collision calculations are continuously made to determine whether a node has contacted or penetrated the mold surface. When this occurs within a prescribed tolerance the node is permanently fixed to the mold surface at the contact point. This most closely approximates the actual forming conditions in which very little slip between the polymer and mold is observed. The load is incremented and the iterative procedure repeated until the desired pressure has been reached or all nodes have contacted the mold surface. The two most extensive membrane models of the thermoforming process are those developed by deLorenzi and Nied [16] and Kouba et al. [18,19]. Both employ similar finite element formulations; however, the model developed by Kouba et al. includes both non-linear elastic and visco-elastic material models, while that developed by deLorenzi and Nied includes only non-linear elastic material behaviour. In addition, the model of Kouba et al. includes pre-stretching of the sheet in a plug-assisted thermoforming process. This cannot be simulated using the deLorenzi and Nied formulation. A more detailed description of the various material models employed in thermoforming simulation is given in section 3.3.2. 3.3.1.2. Thick sheet formulations In a thick sheet formulation the bending resistance of the sheet is not assumed to be negligible as in a membrane formulation. Consequently, in addition to inplane shearing and extension of the sheet, transverse shearing and bending effects are also included in the model. This means that the strains and stresses will not be constant through the sheet thickness but will vary. While this provides a more accurate model of the sheet deformation the formulation of a thick sheet finite element model is much more complex than a membrane formulation. The added complexity is due to the fact that, (i) the incompressibility condition in a thick sheet formulation cannot usually be satisfied exactly but must be imposed through some type of numerical constraint (e.g. penalty method or Lagrange multipliers), and (ii) a thick sheet finite element model is inherently more complex than a membrane model. Perhaps the earliest thick sheet finite element model was that developed by Oden [9] which was used to simulate the free inflation of a sheet of finite thickness assuming non-linear elastic material behavior. The model was however not extended to include a mold so the thermoforming process could not be simulated. It was not until very recently with the work of Song [22,23] and Igl and Osswald [24] that thick sheet finite element models were applied to thermoforming process simulation. Igl and Osswald used a one-dimensional shell finite element model to study the thermoformability of wood-fiber-filled polyolefin composites. Song developed an axisymmetric thick sheet finite element model which can simulate straight and plug-assisted thermoforming assuming a non-linear elastic material response. While these


83

simulations were found to be successful the added complexity of the thick sheet formulation is only important in some problems. In typical thermoforming problems the membrane approximation was found to predict results very close to those given by the thick sheet model even for relatively thick sheets [18]. The main advantage of the thick sheet models is that localized effects, such as bending and shearing near clamping devices and in corners, and stress concentrations near a plug boundary can be predicted. In typical thermoforming operations these effects will not dominate and thus the added complexity and computational effort required by thick sheet models is difficult to justify.

3.3.2. Material behaviour

For a material model to be applied successfully in a numerical simulation it must be capable of describing the material response under actual processing conditions. Ideally it should give a good representation of the stress-strain behavior of the plastic for both small and large strains, and over a wide range of temperatures and strain rates. During inflation into the mold cavity the sheet is mainly subjected to biaxial stretching. Consequently, the elongational characteristics of the polymer play an important role in the thermoforming process. From industrial experience the strain hardening characteristics of the plastic have been found to significantly affect the final thickness distribution of the finished product. Throne [1] states that the elastic modulus for materials in thermoforming is typically between 0.07 MPa and 1.0 MPa. Strain rates observed in the process normally range from 0.1 s-~ to 10 s-1. It is generally recognized that thermoplastics in a semi-molten state possess a strong viscous component which allows them to flow when sufficient stress is applied. They also possess a significant elastic component that resists flow and imparts integrity and self-supporting properties to the sheet. As a result in finite element simulations of thermoforming the polymer behavior is typically modeled using either a non-linear elastic or a visco-elastic constitutive model.

3.3.2.1. Non-linear elastic models

There is strong experimental evidence [25-27] that when polymers are extended at relatively high strain rates, at temperatures above the glass transition temperature their behavior can be adequately modeled using constitutive equations originally developed for rubber-like materials. It has also been shown experimentally [28] that the mechanical behavior of polymer materials above the glass transition temperature is essentially incompressible. The assumption of non-linear elastic material behavior greatly simplifies the formulation of the finite element equations, but neglects the viscous component of the polymer response. In non-linear elasticity the components of the constitutive tensor are given in terms of certain material constants, and are also functions of the material strains. For more information on non-linear elasticity refer, for example, to Green and Zerna [29], Green and Adkins [30], and Eringen [31].

B.L. Koziey et al.

84

For an isotropic material the stress-strain relationship is frequently defined using a strain energy function, W, given in terms of the Green-Lagrange strains. Such a material is referred to as a hyperelastic material and the stresses are given by OW S = ~ aE

(3.3)

where S is the second Piola-Kirchhoff stress tensor. Once an appropriate form of the function W has been defined the stresses can be evaluated. The determination of W must be done carefully to ensure that the frame indifference requirement is satisfied. Two different definitions of W which have been used almost exclusively in thermoforming simulations are the Mooney-Rivlin model and the Ogden model. Mooney-Rivlin model. In the Mooney-Rivlin [20] model it is assumed that the strain energy density function, W, for an incompressible material can be expressed as a polynomial function of the first two invariants, I1 and 12, of the Cauchy-Green deformation tensor, C. The generalized form of the strain energy function is given by [201 M

W - Z

N

Z

Aij(I1 - 3)i(I2 - 3) j

(3.4)

i=0 j=0 where A O. are experimentally determined constants. When the body is undeformed the strain energy W = 0 and constant A00 = 0. If only the first two terms, A10 and A01, are retained then the standard Mooney-Rivlin expression is obtained which is written as W -- A10(I1 - 3) + A01 (I2 - 3)

(3.5)

When A01 = 0 the model is referred to as the neo-Hookean model. The components of the stress tensor S can be calculated by substituting eq. (3.5) into eq. (3.3) and performing the required differentiation. Note that the stress normal to the membrane surface, $33, is assumed to be negligible. Ogden model. In the Ogden [21] model the strain energy density, W, is assumed to be a function of the principal stretches, instead of the invariants of the deformation tensor, and is given by m

W-

~/z__~n(,k~n + Z2" + Z3n _ 3)

(3.6)

n=l 0r

where Z l, ~'2 and )~3 are the principal stretches. Constants lZn and an are determined by fitting the model to experimental stress-strain data and can be either negative or non-integer values. However, the constants must yield a positive strain energy density function. Note that, because incompressibility is assumed, the third principal stretch, ~3 is expressed in terms of ~'1 and ~'2 using the constraint ~.1~.2~.3 = 1. The summation over n in eq. (3.6) extends over as many terms as are necessary to characterize the behavior of the material. Usually n is equal to 1, 2, or 3. As with the Mooney-Rivlin model the components of the stress tensor are determined by substituting eq. (3.6) into eq. (3.3) and performing the necessary differentiations.

Computer simulation o f thermoforming

85

Again the stress normal to the membrane surface is assumed to be negligible. Because the Ogden model is given in terms of the principal stretches instead of the invariants, 11 and I2, the physical meaning of the resulting stress-strain relations are much easier to determine.

3.3.2.2. Viseo-elastic models While non-linear elastic models effectively describe the material response under certain conditions, they must be applied with caution in actual thermoforming situations since they neglect viscous effects. For example, for relatively slow thermoforming viscoelastic effects have been found to be extremely important [32]. Hylton gives several examples of how the thermoformability of a given resin may be assessed on the basis of several visco-elastic properties. Perhaps the first finite element model to take visco-elastic effects into account is that given by Kouba et al. [19]. In their formulation the stress-strain data at different strain rates is fitted to a K-BKZ [33] constitutive equation modified by the inclusion of a Wagner damping function. The constitutive equation used is of the integral type and is given by t

s-

f

m ( t - t')h(I1,/2)B(t, t') dt'

(3.7)

where t' is the previous time, t is the current time, B(t, t') is the Finger strain tensor (left Cauchy-Green deformation tensor i.e. C -1) and m ( t - t') and h(I1,12) are the memory and damping functions, respectively. The damping function is of the form proposed by Wagner and Demarmels [34], and is written as 1

h(I1, 12) -

1 + av/(I 1 -

(3.8) 3 ) ( / 2 - 3)

where a is a material parameter and 11 and I2 are invariants of the Finger tensor B. The memory function which is related to the relaxation spectrum is given by (t--tt)

m ( t - t ' ) - Z ai e

(3.9)

ri

where ri are the relaxation times and a i are material constants and i is the number of relaxation processes considered. Assuming that pressure is applied and the deformation of the sheet starts at time t - 0 the stress in the two principal directions (i -- 1, 2) tangent to the surface of the sheet is given by t

S(t) - f m(t - t')h(I1, I2)[LZ(t, t')

-

LZ(t, t')] dt'

0

(3.10)

0

4- h(t)[LZ(t) - LZ(t)] f --00

m ( t - t') dt'

86

B.L. Koziey et al.

where Li(t, t') is the stretch ratio in the i th principal direction at time t related to time t', and L3(t, t') is the stretch ratio perpendicular to the sheet surface at time t related to t'. Temperature effects have also been included in the model because the model constants are a function of the temperature. Another approach to the inclusion of viscous effects in thermoforming is that presented by Vantal et al. [35]. They employ an approach similar to that used in metal forming. For deformation of the solid polymer under the glass transition temperature a visco-elasto-plastic constitutive relation of the form

-- kp(T)(g, e)

(3.11)

is used. Quantities 8, g and ~ are the effective stress, effective strain and effective strain rate, respectively, The temperature-dependence of the material response is included through the function kp(T). Beyond the glass transition temperature the rubbery polymer is modeled using a phenomenological visco-elastic constitutive relation. The material parameters were determined by fitting the constitutive model to uniaxial tensile data obtained for a wide range of temperatures and strain rates. In contrast to the other constitutive models described above, an updated Lagrangian finite element formulation is required since the constitutive relation is valid for small strains only.

3.3.3. Thermoforming simulation examples A finite element software package capable of modeling fully 3-D thermoforming, with or without plug assistance, has been developed and tested at McMaster University [18,36-38]. Extensive comparisons between predicted and experimental thickness distributions for both straight and plug-assisted thermoforming have been made which has established the validity of the finite element model. Experimental data on uniaxial or biaxial testing of polymers is scarce, especially at strain rates and temperatures that are within the ranges found in the thermoforming process. Nevertheless successful simulations have been carried out using both simple and complex mold geometries. For simple shallow mold geometries simulations using the non-linear elastic Ogden model are very accurate. A simulation of the vacuum forming of a simple dome-like automotive fuel tank component was performed using both the Ogden model and the visco-elastic K-BKZ model. The thickness distributions along a cut through the dome predicted by both models are plotted along with the actual thickness distribution in fig. 3.3. There is good agreement between the experimental results and both the Ogden and K-BKZ predictions. While the Ogden model is best suited for the simulation of straight thermoforming into shallow simple molds, the K-BKZ model is required when the simulation includes deep-drawn forming, complex mold geometry or plug assistance. The plug-assisted thermoforming simulation of a sheet into a complex mold was performed. The mold has a volume of about 22 liters and is used to form electronic device casings. A finite element mesh consisting of 1,536 elements was used to discretize the sheet which had an initial thickness of 6.35 mm (0.25 in.). The simulation was performed using both the Ogden and K-BKZ models. The K-BKZ model


87

Fig. 3.3. Comparison of predicted and experimental final thickness distribution for automotive fuel tank component.

was fitted to material stress-strain data obtained for strain rates ranging from 0.01 s-1 to 10 s-1. The thickness distribution predicted using both material models is plotted in fig. 3.4, along with the experimental values for the cutting plane shown in the figure.

Fig. 3.4. Comparison of predicted and experimental final thickness distribution for film scanner casing.

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B.L. Koziey et al.

The distribution predicted by the Ogden model is seen to be in poor agreement with the experimental data. However, the thickness distribution predicted by the KBKZ model is in very good agreement with the experimental distribution. This example clearly illustrates that the choice of material model (non-linear elastic versus visco-elastic) must be done very carefully if reliable predictions of the thickness distribution are to be obtained. 3.4. Concluding remarks A "state-of-the-art" review of the application of the finite element method to thermoforming simulation has been given. In general, the currently available models provide a rational means of mold design and can also aid in the optimization of the final resin distribution and the minimization of peripheral waste. While the existing models are capable of providing good predictions of the final part thickness, care must be taken in the selection of the material model used. Non-linear elastic models such as the Ogden model are attractive in their simplicity in comparison to viscoelastic models such as the K-BKZ model, but typically only provide reliable prediction for straight thermoforming (no mechanical assisted sheet stretching) into shallow simple molds. Future work should be targeted towards the development of less complex viscoelastic material models, inclusion of time-dependent thermal effects, and slippage of the sheet along the plug surface. In addition, more experimental data on uniaxial and biaxial stretching of polymers needs to be established at strain rates and temperatures typically experienced in the thermoforming process. References [1] [2] [3] [4]

Throne, J.L., Thermoforming, Hanser Publishers, New York, 1987. Tadmor, Z. & Gogos C.G., Principles of Polymer Processing, John Wiley & Sons, New York, 1979. Birley, A.W., Haworth B. & Batchelor J., Physics of Plastics, Hanser Publishers, Munich, 1991. Vlachopoulos, J. & Mitsoulis E., Fluid Flow and Heat Transfer in Calendering, in Transport Phenomena in Polymeric Systems, Ellis Horwood, Chichester, 1989. [5] Vlachopoulos, J., Calendering, in Concise Encyclopedia of Polymer Processing and Applications, Pergamon Press, Oxford, 1992. [6] Vlachopoulos, J., Silvi N. & Vlcek J., POLYCAD| A Finite Element Package for Molten Polymer Flow, in Applications of Computer Modeling for Extrusion and Other Continuous Polymer Processes, Hanser Publishers, Munich, 1992. [7] Vlcek, J., Perdikoulas J. & Vlachopoulos J., Extrusion Die Flow Simulation and Design with FLATCAD, COEXCAD and SPIRALCAD, in Applications of Computer Modeling for Extrusion and Other Continuous Polymer Processes, Hanser Publishers, Munich, 1992. [8] Zamani, N.G., Watt D.F. & Esteghamatian, M., Status of the Finite Element Method in the Thermoforming Process. Int. J. Num. Meth. Eng., 28 (1989) pp. 2681. [9] Oden, J.T., Finite Elements of Non-linear Continua, McGraw-Hill, New York, 1972. [10] Bathe, K.J., Finite Element Procedures in Engineering Analysis, Prentice Hall, Englewood Cliffs, NJ, 1982. [11] Zienkiewicz, O.C. & Taylor R.L., The Finite Element Method, Volume 1: Basic Formulation and Linear Problems, McGraw-Hill Book Company, London, 1988.


89

[12] Zienkiewicz, O.C. & Taylor R.L., The Finite Element Method, Volume 2: Solid and Fluid Mechanics Dynamics and Non-linearity, McGraw-Hill Book Company, London, 1991. [13] Allard, R., Charrier J.M., Ghosh A., Marangou M., Ryan M. E., Shrivastava S. & Wu R., An Engineering Study of the Thermoforming Process: Experimental and Theoretical Consideration. J. Polym. Eng., 6 (1986) pp. 363. [14] Warby, M.K. & Whiteman J.R., Finite Element Model of Viscoelastic Membrane Deformation. Comput. Meth. Appl. Mech. Eng., 68 (1988) pp. 33. [15] Nied, H.F., Taylor C.A. & deLorenzi H.G., Three-Dimensional Finite Element Simulation of Thermoforming. Polym. Eng. Sci., 30 (1990) pp. 1314. [16] deLorenzi, H.G. & Nied H.F., Finite Element Simulation of Thermoforming and Blowmolding. Modeling of Polymer Processing: Recent Developments, Isayer, A.I. (ed.) Munich, 1991, pp. 117. [17] Taylor, C.A., deLorenzi H.G. & Kazomer D.O., Experimental and Numerical Investigations of Vacuum-Forming Processes. Polym. Eng. Sci., 32 (1992) pp. 1163. [18] Kouba, K., Bartos O. & Vlachopoulos J., Computer Simulation of Thermoforming in Complex Shapes. Polym. Eng. Sci., 32 (1992) pp. 699. [19] Kouba, K., Ghafur M.O., Vlachopoulos J. & Haessly W. P., Some New Results in Modelling of Thermoforming. SPE Tech. Papers, 52 (1994) pp. 850. [20] Mooney, M., A Theory of Large Elastic Deformation. J. Appl. Phys., 11 (1940), pp. 582. [21] Ogden, R.W., Large Deformation Isotropic Elasticity of Theory and Experiments for Incompressible Rubberlike Solids. Proc. R. Soc. Lond., A326 (1972) pp. 565. [22] Song, W.N., Mirza F.A. & Vlachopoulos J., Finite Element Analysis of Inflation of VacuumForming Processes. J. Rheol., 35 (1991) pp. 93. [23] Song, W.N., Mirza F.A. & Vlachopoulos J., Finite Element Simulation of Plug-Assist Forming. Int. Polym. Proc., 3 (1992) pp. 248. [24] Igl, S.A. & Osswald T.A., A Study of the Thermoformability of Wood Fibre Filled Polyolefin Composites. SPE Tech. Papers, 50 (1992) pp. 122. [25] Treloar, L.R.G., The Mechanics of Rubber Elasticity. Proc. R. Soc. Lond., A351 (1976) pp. 301. [26] Schmidt, L.R. & Carley J.F., Biaxial Stretching of Heat-Softened Plastic Sheets Using an Inflation Technique. Int. J. Eng. Sci., 13 (1975a) pp. 563. [27] Schmidt, L.R. & Carley J.F., Biaxial Stretching of Heat-Softened Plastics Sheets: Experiments and Results. Polym. Eng. Sci., 15 (1975b) pp. 51. [28] Ward, I.M., Mechanical Properties of Solid Polymers, John Wiley & Sons, New York, 1983. [29] Green, A.D. & Zema W., Theoretical Elasticity, Oxford University Press, New York, 1954. [30] Green, A.D. & Adkins J.E., Large Elastic Deformations, Oxford University Press, New York, 1960. [31] Eringen, A.C., Nonlinear Theory of Continuous Media, McGraw-Hill, New York, 1962. [32] Hylton, D., Laboratory Techniques for Predicting Material Thermoformability: A Review. SPE Tech. Papers, 49 (1991) pp. 580. [33] Tanner, R.I., Engineering Rheology, Oxford University Press, New York, 1985. [34] Wagner, M.H. & Demarmels A., A Constitutive Analysis of Extensional Flows of Polyisobutylene. J. Rheol., 34 (1990) pp. 943. [35] Vantal, M.H., Bellet M., Monasse B., Jammet J.C. & Andro R., PPS Tech. Papers, l0 (1994) pp. 317. [36] Kouba, K., Ghafur M.O. & Vlachopoulos J., Computer Modelling of Blow Molding. SPE Tech. Papers, 51 (1993)pp. 1861. [37] Kouba, K. & Vlachopoulos J., The Role of Rheology in Thermoforming Process: Experimental and Theoretical Consideration. SPE Tech. Papers, 50 (1992) pp. 114. [38] Vlachopoulos, J., Kouba K. & Ghafur M.O., The Role of Rheology in Thermoforming and Blow Molding, Fourth European Rheology Conference, Seville, Spain, 1994.



Chapter 4

Thermoforming of Continuous Fibre~Thermoplastic Composite Sheets K. F R I E D R I C H 1, M. H O U 2 and J. K R E B S 1 1Institute for Composite Materials Ltd. (IVW), University of Kaiserslautern, 67663 Kaiserslautern, Germany," 2Centrefor Advanced Materials Technology, Department of Mechanical Engineering, University of Sydney, Sydney, NSW 2006, Australia

Contents Abstract 92 4.1. Introduction 92 4.2. Experimental details and procedures 96 4.2.1. Materials employed for stamp and diaphragm forming 96 4.2.2. Preparation of pre-consolidated laminates 97 4.3. 2-D stamp forming 100 4.3.1. General remarks 100 4.3.2. Experimental details 102 4.3.3. Description of stamping process 104 4.3.4. Characterisation methods for thermoformed components 105 4.3.4.1. Microscopy 105 4.3.4.2. Characterisation of in-plane fibre movement 106 4.3.4.3. Thermal analysis 106 4.3.5. Results and discussion 107 4.3.5.1. Determination of preheating time 107 4.3.5.2. The forming temperature 110 4.3.5.3. Correlation between stamping velocity and stamping pressure 4.3.5.4. Effect of forming condition on part geometry 119 4.3.5.5. Thermoanalysis 130 4.3.5.6. Fibre movement studies 133 4.3.6. Optimised processing window for 2-D stamp forming 135 4.4. 3-D stamp forming 137 4.4.1. General remarks 137 4.4.2. Set-up of 3-D stamp forming device 138 4.4.3. Experimental procedure 139 4.4.4. Results and discussion 140 4.4.4.1. Stamp forming mechanisms 140 4.4.4.2. Stamp forming of GF fabric/PEI laminates 141 4.4.4.3. Stamp forming of UD GF/PP laminates 143 4.4.5. Recommendations for 3D stamp forming 145 4.5. 3-D diaphragm forming of GF/PP laminates 146 91

115

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K. Friedrich et al.

4.5.1. General remarks 146 4.5.2. Experimental procedure 147 4.5.3. Assessmentand characterisation of thermoformed parts 148 4.5.3.1. Large strain analysis technique 148 4.5.3.2. Occurrence of defects and thickness variations in diaphragm formed parts 150 4.5.4. Variation of forming parameters and rating of part quality 152 4.5.4.1. The forming temperature 153 4.5.4.2. The forming ratio 154 4.5.4.3. The forming pressure 156 4.5.4.4. The forming velocity 156 4.5.4.5. The laminate thickness and lay-up 157 4.5.5. Conclusions and recommendations 157 4.6. Summary 159 Acknowledgements 160 References 160 Abstract Continuous fibre-reinforced thermoplastic polymers are a relatively young group of engineering materials compared with their thermosetting counterparts. However, due to their outstanding mechanical and thermal properties these materials are becoming increasingly attractive not only for aerospace and automotive applications. In order to produce defect-free components it is essential to gain a fundamental understanding of the effects of processing conditions on the structure and morphology of the resultant composite component. Only if the material's behaviour under the particular processing conditions is fully understood can the processing parameters be set in such a manner, that the desired microstructure and mechanical performance of the resulting component can be achieved. When forming continuous fibre-reinforced materials instabilities, such as wrinkles and buckles, may occur. In the example of the 2-D, 3-D and the diaphragm thermoforming technique it is demonstrated how the processing conditions can be optimised by individually investigating the parameters mainly governing the properties of the finished component ultimately enabling the production of defect-free parts. 4.1. Introduction Continuous fibre-reinforced thermoplastic polymers are still a relatively young group among the engineering materials compared with their thermosetting counterparts. However, due to their advantageous properties such as good thermal stability, high toughness/damage tolerance, infinite shelf-life and ease of processing, these materials are becoming increasingly attractive to various industrial sectors. In particular applications not only in the aerospace and automotive field but also in branches such as the medical, environmental and recreational industry represent potential markets. In order to exploit the advantageous features of continuous fibre-reinforced thermoplastic composites for a large array of industrial applications and products,

Thermoforming of cont&uousfibre~thermoplastic composite sheets

93

several manufacturing methods have been developed over the last decade [1]. Utilising related processes known from thermosetting composites and adapting sheet forming techniques typical of those used with metallic materials, fabrication techniques, such as compression moulding, tape winding, thermoforming, joining and pultrusion have become available (fig. 4.1). However, the introduction of advanced thermoplastic composites has also led to novel requirements being imposed on processing techniques for manufacture of high-quality intermediates. Unlike thermosets, which are usually compounded at the moulding site, fibre-reinforced thermoplastics have to be supplied in a variety of different ready-to-use intermediates in order to match the requirements of the various production techniques [2]. Embedding the reinforcements into high-viscosity thermoplastic matrices is still a demanding task. Many approaches were necessary in order to overcome the difficulties of impregnation enabling the production of intermediate material forms such as film stacked prepregs (pre-impregnated materials), commingled fibres,

Fig. 4.1. Processingwith thermoplasticcomposites.

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K. Friedrich et al.

pultruded bands and powder impregnated bundles which are commonly used in contemporary thermoplastic manufacturing technology (fig. 4.2) [3]. In order to produce good quality parts it is necessary to initially gain a fundamental understanding of the effects of processing conditions on the structure and morphology of the resultant composite component [4--6] (fig. 4.3). Only if the material's behaviour under the particular processing conditions is fully understood, can the processing parameter be set in such a manner that the desired microstructure and mechanical performance of the laminate can be achieved. In this chapter two thermoforming techniques, stamp forming and diaphragm forming, are investigated with regard to their potential for producing defect-free

Commingled Fibers

Film Stacking

I lll

~-~ Reinforcing Fibers

Fiber Woven Fabric

Polymer Fibers ~ ' - u I u i u i u~ Polymer Films

Powder Impregnated Bundles

Pultruded Band

Fiber Bundle

~

Fiber

Polymer Powder

Polymer

olymer Sheath

Fig. 4.2. Intermediate material forms for thermoplastic composites.

Intermediate Material

Form

H

Processing Method

a.) Commingled Yarn

a.) Compression Molding

b.) Powder

b.) Tape

Impregnated

Fibers

c.) Melt Impr, Tapes

Winding

c,) Stamp Forming

H

Processing Parameters

m,.,cro,u.,r,uo,H

Mechanical

of Bulk Composite

Performance of Laminate

a.) Interlaminar a.) Temperature a.) Morphology Fracture of Crystalline b.) Pressure Polymer Matrix Toughness b.) Materials c,) Time b.) Alignment Stiffness of Fibers and Strength d.) Cooling c.) Formation of Voids [

,

.....

I

No

I

I

Fig. 4.3. Methodology for fundamental studies on processing properties of thermoplastic composites.

Thermoforming of conth~uousfibre/thermoplastic composite sheets

95

components from continuous fibre-reinforced thermoplastic prepreg materials. The particular interest in stamp forming stems from its obvious suitability for mass producing single and double curvatured parts at considerable low cycle times. Diaphragm forming on the other hand is very unlikely to match the productivity of stamp forming; however, when it comes to producing very complex-shaped structures, this technique appears to be more suitable due to its capability to accommodate inter-ply shear induced laminate thickening. Here, superplastic aluminium diaphragms like Supral TM* were originally employed for vacuum-bagging hightemperature fibre/matrix systems such as CF/PEEK (APC-2 TMt, AS4) in autoclaves. Due to the pronounced strain-rate sensitivity, consequently resulting in high cycle times, the fairly restricted stretchability and the high temperatures required for achieving maximum elongation, lately most emphasis has been placed on the use of polymeric diaphragms such as Upilex TM* [1,7-9]. Since polyimid diaphragms are not strain-rate sensitive, forming can be completed in a matter of minutes in contrast to approximately 20 minutes that are required for superplastic aluminium diaphragms. It has to be noted, however, that due to the thermal properties of polyimid diaphragms they are only suited for processing composites containing high melting temperature matrices such as PEEK (poly ether ether ketone) and PEKK (poly ether ketone ketone). As a consequence, when looking into industry branches where attributes such as high volume production, cycle times in the order of seconds, low material costs and automation are of decisive significance, these materials, despite their superior properties, will have difficulty in asserting themselves against the traditional engineering materials which are still dominating the market. According to recent trends in the composites industry, structural materials such as glass-fibre-reinforced polypropylene and polyamide do have the best future prospects for substituting metallic materials in markets such as the environmental sector where there are tremendous opportunities for glass-fibre-reinforced thermoplastics sewage pipes, scrubbers and tanks [10]. Also in the automotive industry where polypropylene is already well established as non-reinforced material the number of glass-fibre-reinforced components is continuously growing. Today, parts such as noise shields, bumper carriers, compartment capsulations and seat shells are made from glass-mat-reinforced thermoplastics (GMT) in order to name only a few [11]. An expansion to continuous glass fibre-reinforced polypropylene structures, therefore, appears to be a more than sensible venture. One of the most recent additions in the group of structural composite materials are Plytron TM~ and Tepex TMw Fundamental studies on the formability and the resulting part properties of this material, as well as mechanical properties and environmental resistance have already been conducted by a number of research groups. However, there is still far more work necessary in order to make thermoforming of such *SupralT M is an Alcan Registered Trademark. tAPC_2TMis a ICI Ltd. Registered Trademark. SUpilexT M is a UBE Ind. Registered Trademark. ~PlytronT M is an ICI Ltd. Registered Trademark. w T M is a DuPont Registered Trademark.

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K. Friedrich et al.

materials become a repeatable and cost-effective fabrication technique capable of producing accurately predictable finished part properties at acceptable cycle times. Employing a number of differently reinforced matrices, unidirectional and fabric, and different types of reinforcing fibres, carbon and glass, the intention of this chapter is to outline the durability and limitations of both stamp and diaphragm forming. It addresses aspects such as flow processes occurring during thermoforming, consolidation quality and achievable structural properties of the resulting components. Moreover, the occurrence of instabilities in the finished components such as wrinkling and buckling in both processes is investigated and illustrated with the aim of creating a complete picture of their potentials and limitations.

4.2. Experimental details and procedures 4.2.1. Materials employed for stamp and diaphragm forming This section intends to give an introduction to the structural and physical properties of the materials employed for the investigations into stamp and diaphragm forming. Furthermore, the procedures followed for pre-consolidating laminates for later usage in the forming experiments is described and illustrated since it is felt that this step has a significant influence on the material's behaviour under thermoforming conditions and the resulting component properties. The following section also provides an introduction to all prepreg materials employed for the subsequent series of experiments, outlining their physical and thermal properties. The most important properties are summarised in table 4.1. (a) Continuous glass fibre (GF) reinforced thermoplastic composite called Plytron | with a polypropylene (PP) matrix, by ICI Ltd., UK. The nominal glass fibre content of this material is 60 wt. % and 35 vol. % glass/polypropylene. The material was supplied as a tape with a width of 240 mm and a nominal thickness of 0.47 mm. TABLE 4.1 List of materials employed for thermoforming experiments Advanced thermoplastic composites (abbreviations)

Melt temp. (~ Glass trans, temp. (~ Fibre volume fraction (%) Material form Manufacturer 2-D forming 3-D froming

GF/PP

CF/PP

GF/PP

CF/PA12 CF/PEEK GF/PEI

145-170 -20 35 Prepreg ICI Ltd. UK

163

163

176

334

20 Prepreg ICI Ltd. UK

33 Prepreg BASF Germany

40 60 Plate Enichem Italy

60 Plate Enichem Italy

9

210 50 Prepreg Ten Cate Holland

Thermoforming of continuousfibre~thermoplastic composite sheets

97

(b) Pultruded continuous carbon fibre (CF) polypropylene (PP)-tape, with a nominal thickness of 0.50 mm and a nominal fibre content of 33 vol. % carbon/ polypropylene, manufactured by ICI Ltd., UK. (c) Pultruded continuous glass fibre (GF) polypropylene (PP)-tape, with a nominal thickness of 0.50 mm and a nominal fibre content of 20 vol. % glass/polypropylene, manufactured by BASF AG, Germany. (d) Continuous carbon-fibre-reinforced pre-consolidated laminates with a polyamide (PA-12) and a polyetheretherketone (PEEK) matrix manufactured by Enichem, Italy. The nominal fibre content of these materials is 40 vol. % and 60 vol. % carbon/polyamide 12 and carbon/polyetheretherketone respectively. The uni-directional (UD) laminates with a nominal thickness of 3.2 mm were made from powder-impregnated fibre bundles. (e) Glass fibre fabric (GF) reinforced amorphous polyetherimide (PEI) manufactured by Ten Cate, The Netherlands. Here, the fibre content is 50 vol. % glass/ polyetherimide with a nominal tape thickness of 0.80 mm. The weave style of the glass fabric was 8 H satin and is illustrated in fig. 4.4. 4.2.2. Preparation of pre-consolidated laminates

An integral part of all forming processes is the consolidation of flat laminates which is either accomplished during forming (in-situ processing) or carried out prior to the actual thermoforming process. Since the properties of the moulding are essentially dependent upon the quality of the lamination, it is important to thoroughly define and control the conditions under which well consolidated material may be obtained. In principle, lamination involves two processes: (a) obtaining autoadhesion between the plies and (b) removing that which lies between them (air or water vapour) [12]. This can be achieved by using either pressure in order to dissolve the air into the melt or vacuum to extract it. For the 2-D and 3-D stamp forming experiments pre-consolidated sheets (100 x 160 mm and 128 x 128 mm) were prepared by pressurising a loose stack of plies with a predetermined stacking sequence in between two heated platens. The unidirectional and quasi-isotropic sheets with a [0~ [0~176176 and [0~176 s [13] stacking sequence were made from CF/PP and GF/PP (BASF) prepregs according to the

Fig. 4.4. Woven structure of 8-H satin glass fabric in GF/PEI composite.

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K. Friedrich et al.

following procedure. First, a steel mould filled with several layers of prepreg material is placed in a heatable press. The stacked pile of plies is then preheated in the absence of pressure until the matrix has reached its molten state. Consolidation is achieved by applying external pressure for about 5-10 min. Finally, the mould is cooled below the melt temperature of the matrix whilst maintaining the applied pressure in order to prevent the occurrence of voids within the laminate. The consolidation temperature and pressure have to be carefully monitored throughout this process since too high a temperature and/or pressure can lead to undesired fibre misalignment caused by excessive matrix flow and fibre migration. However, on the other hand, if the temperature and pressure are set too low the resulting laminates are likely to contain high void content and poor inter-ply bonding. The resulting sheets employed within this study exhibited a thickness of 2.8-3.0 mm. A simple but effective method for characterising the movement of the reinforcements during forming is to embed tracer wires made from material that is not transparent to X-rays into the surfaces layer of a pre-consolidated laminate (e.g. copper wires). The motion of the wires during stamp forming can then be detected by X-ray analysis techniques or usage of powerful light sources for composites with transparent or opaque matrices. The technique utilised for fabricating pre-consolidated laminates with embedded copper tracer wires is illustrated in fig. 4.5. First, the copper wires are mounted onto a metal frame with a uniform lateral distance between them. Then the copper wires are pressed onto the surface of a prepreg ply using a hot press set to the melting temperature of the individual matrix in the ply. The plies with integrated copper wires thus obtained are then used for preparing sheets for subsequent fibre motion measurements. For the stamp forming experiments described here, blanks were cut to size, as shown in fig. 4.6, where L denotes the length, B the width and do the original thickness of the laminate. In order to measure the temperature profile of the heated pre-consolidated sheets during stamp forming, NiCr-Ni thermocouples were embedded into the centre layer of several laminates. An alternative method that may be employed for the production of pre-consolidated laminates is depicted in fig. 4.7. For implementing the diaphragm forming

Fig. 4.5. Schematic diagram of manufacturing pre-consolidated laminate with embraced Cu trace wires.

Thermoforming of continuousfibre/thermoplastic composite sheets

99

Fig. 4.6. Definition of sample cut from GF fabric/PEI laminate.

Metal Frame with Gasket u,apnra~m Top Plate

~(Alumini

;

j

/

~g~'~

m)

, ~ ~ O v e n Bag #2 , Stacked ~Prepreg Plies ~ M e t a l Strip ~ O v e n Bag #1 Vacuum Table (Aluminium) Outlet to Vacuum Pump

Fig. 4.7. Preconsolidation device for diaphragm forming experiments.

experiments it was decided to use vacuum rather than pressure for pre-consolidating rectangular flat sheets with different lay-ups and thicknesses. In order to consolidate a multi-ply sheet a completely uncompacted stack of plies is placed on a vacuum table. Oven bags (Melinex Type S [14]) covering the plies prevent the material from sticking to the aluminium platens and metal strips surrounding the plies during consolidation. Applying a vacuum pressure of about - 2 0 kPa the stack of plies is heated up in an oven to the matrix's melt temperature where it dwells for about 15 minutes. In the case of Plytron, the cooling rate which basically determines the

1O0

K. Friedrich et al.

extend of crystal growth in the semi-crystalline polypropylene matrix should be greater than 1~ since otherwise too high a level of crystallinity is achieved, resulting in a low fracture toughness [12].

4.3. 2-D stamp forming 4.3.1. General remarks

Thermoplastic polymers can undergo a reversible phase change from solid to liquid, thereby enabling the development of shaping and joining methods analogous to those for conventional metallic materials. When transferring a flat, continuousfibre-reinforced laminate into a 3-D shaped component a number of different deformation mechanism governing the forming behaviour of this material have to be taken into account. Unlike the monolithic metallic sheet, continuous fibre-reinforced thermoplastic (CFRT) materials are virtually inextensible in the direction of the reinforcement. For these material systems, the dominant mode of deformation, parallel to the fibres, during sheet forming is therefore shearing within the individual plies and between them, namely intra- and inter-ply shear. Additional mechanisms that occur when transferring a flat multi-ply sheet into a double curvature formed component are resin percolation through and along the layers of the reinforcing fibres, resin flow transverse to the fibres and rotation of adjacent plies relative to one another [15-19]. A schematic diagram of the deformation modes in the increasing order of shape complexity and correlated flow mechanisms shown in fig. 4.8 can be described as follows. (a) Resin percolation is fundamental to all flow processes and occurs to some extent in all types of fabrications. It is the flow of polymer matrix through and along the layers of the reinforcing fibres. This process allows layers of prepreg to be bonded together to form one sheet. Fritzer and J~iger studied the flow behaviour of matrix materials in order to optimise the processing parameters such as pressure and temperature leading to a homogeneous distribution of the matrix in the composite [20-22]. (b) Transverse flow is the process by which a prepreg spreads out to accommodate local pressure variations during forming processes. It is responsible for apparent stretching that can occur in a unidirectional laminate in perpendicular direction of the reinforcements [23]. A small amount of transverse flow is observed during any forming process at elevated forming temperatures caused by local pressure gradients that arise from small variations in the laminate thickness and mould clearances [13,24]. Transverse flow can also result from shear stresses developing between the thermoplastic material and the forming tool surface. (c) Inter-ply slip is a relative shear movement of two adjacent laminate layers. In this case the polymer matrix acts as a lubricant between neighbouring plies. When a laminate is formed onto a curved surface it has to deform in such a manner that inter-ply slip can account for the gradual change in shape. If this process is inhibited fibre wrinkling and buckling are normally the result [25-27].

Thermoforming of continuous fibre/thermoplastic composite sheets

101

Fig. 4.8. Deformation modes and flow mechanisms of continuous fibre-reinforced thermoplastic materials. [1].

(d) Intra-ply shear is needed when a shearing strain occurs in the plane of the laminate, thus allowing part conformity to complex curvature geometry. Theoretically, there is no limit to the amount of shear deformation in unidirectional laminates. Fabrics, by contrast, are usually interlocked at fibre crossover points, limiting the shear strain to the locking angle of the unit cell (trellis angle) [281. (e) Inter-laminar rotation is required for forming multi-ply laminates into double curvatured shapes. This shear action occurs in a thin "resin-rich layer" that forms at each laminate surface during consolidation due to resin migration. Most complex curvature parts require a change of initial fibre orientation between adjacent plies. For the production of 2-D and 3-D components the occurrence of inter- and intraply shearing processes is of particular interest. Only if the reinforcements can alter their orientation by shearing and rotating relative to one another during forming instabilities such as wrinkles and buckles can be prevented from occurring. Therefore, particular attention has to be devoted to these flow mechanisms in any thermoforming procedure for continuous fibre-reinforced thermoplastic composites.

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K. Friedrich e t al.

4.3.2. Experimental details

In the series of 2-D stamp forming experiments described in the following subsections, the quality of the finished components made from fiat pre-consolidated laminates is evaluated by investigating the effect of the processing parameters such as pressure, temperature, cycle time, velocity, mould geometry and laminate architecture on the microscopic and macroscopic properties of the formed parts. For this series of experiments blanks made from CF/PP, GF/PP (BASF), CF/PA12, CF/PEEK and GF fabric/PEI were employed. The 2-D stamp forming experiments were conducted employing the matched metal die forming process as it is commonly known from sheet metal forming. For simplicity, the forming set-up was mounted into an universal testing machine that allowed closing velocities ranging from 1 to 1,000 mm/min. Forming was carried out under non-isothermal conditions, which means that the pre-consolidated laminates had to be pre-heated to processing temperature in a laboratory hand press prior to forming. Once the desired temperature was reached the laminates were then transferred into the press and formed immediately. In order to record the load conditions occurring during forming, an x - y recorder was connected to the press's pressure transducer. The alignment of the male and female moulds was realised by two pillars ensuring that both mould parts were kept aligned (fig. 4.9). The male mould was supported by two coil springs surrounding the pillars. The springs not only prevented possible damage to the pressure transducer that can occur at high

Fig. 4.9. Schematic diagram of angle mould for 2-D stamp forming.

Thermoforming of continuousfibre/thermoplastic composite sheets

103

loads but also allowed the moulds to open up automatically after each processing cycle, easing de-moulding and handling of the formed samples. In the forming series discussed in this section three pairs of right-angle vee-shaped moulds with three different bend-radii (2.5, 5.0 and 10.0 mm) were employed with a uniform clearance between male and female mould of 2.5 mm (fig. 4.10). The universal testing machine was operated as a load-controlled mechanical press under compression mode. The maximum applicable stamping pressure was controlled by pre-setting switch-off pressures. Figure 4.11 depicts the correlation of stamping pressure and stamping stroke versus time. Here, the solid line represents the load and the tinted line the stroke of the stamper. In order to form a part, the stamper was driven at a constant speed. Once it physically touches the pre-heated laminate forcing it into the cavity of the female mould, the load increased until the pre-set switchoff load was reached which immediately terminated the forming stroke. The forming

Fig. 4.11. Definition of processing parameters.

104

K. Friedrich et al.

durations thus obtained ranged from 4 to 20 s dependent on the stamping velocity (fig. 4.12). Due to inaccuracies in the press's control unit, reaching the switch-off load did not immediately lead to a halt of the stamper, but resulted in a swing-over effect which increased with increasing stamping speed. After the peak value was reached the compression pressure began to drop to an equilibrium pressure level which can be related to processes such as matrix flow, fibre migration and shrinkage of the laminate that occur upon cooling. An additional finding of this series of forming experiments was that the stacking sequence of the laminate also significantly affects the final stamping pressure. The effects of this phenomenon will be discussed in more detail in section 4.3.5.3.1. 4.3.3. Description o f stamping process

Generally, the deformation behaviour of thermoplastic composites are directly linked to their processing temperature. Amorphous polymers can be deformed when in their rubber-plastic state (above glass transition temperature Tg), whereas semi-crystalline polymers can only be deformed near or above their melting temperature. Therefore, pre-consolidated laminates produced as described in section 4.2.2 generally have to be subjected to some pre-heating procedure before deformation can take place. There are three different principles that may be utilised for preheating thermoplastic laminates: (i) conduction heating between two heated platens, (ii) infrared heating and (iii) forced convection in air or inert gas circulation ovens. In this part of the study contact heating plate were employed for heating pre-consolidated sheets because this method was found to relatively efficient on a laboratory scale [29]. The major drawback of this method, however, was found to be that the laminate may de-consolidate during heat-up, and the tendency of the molten matrix to stick to the contact surface of the heated platens. Therefore, in order to ease the 25 o 20 2: o,-~ ~9 ,__.~ 15

H

= O

E I-

\

g

10

.,-.,

5 0

200

400

600

Stamping velocity v [ mm/min ]

/

H ts~

Fig. 4.12. Closing time in relationship to stamping velocity.

h

v

800

Thermoforming of cont&uousfibre~thermoplastic compositesheets

105

handling of the heated sheets it is advisable to sandwich them between two polymeric diaphragms, i.e. polyimide films such as Kapton 200 HN. An advantageous side effect of this measure is that it normally enhances the quality of the surface finish of the finished components and it also reduces the cooling rate of the heated sheets during forming. This way the total duration at which the laminate can be deformed is significantly extended. In order to form a part, the sheets were pre-heated to processing temperature, then transferred into the stamping device and formed. Transferring should not exceed a few seconds so that the laminate retains its formability. During stamping the laminate is cooled below its glass transition temperature or melting temperature through the direct contact with the cold metal moulds. This means that de-moulding can normally take place directly after forming is accomplished. The geometry of a fiat laminate and a stamped bend is depicted in fig. 4.13, where L denotes the length, B the width, 0 the final angle of the stamped bend, d the final laminate thickness, and Ad the reduction in thickness relative to the original thickness do. Two different types of blanks (a) B = 15, L = 80 and (b) B = 60, L = 80 were used for these experiments, where the latter had copper wires embedded for subsequent X-ray analysis procedures.

4.3.4. Character&athgn methods for thermoformed components 4.3.4.1. Microscopy Optical microscopy is a suitable and inexpensive method for examining the fibre arrangement and impregnation quality of polished cross-sections of stamped samples. For this purpose, specimens cut from stamped vee-bend components L o

_-o

l

"

!

(a)

Length Direction

(b) ~

90

~ -

Fig. 4.13. Sample geometry and its definition.

/

106

K. Friedrich et al.

were embedded in epoxy resin and polished with 180, 500, 800 and 1200 sand paper, followed by polishing with 1 ~tm AL203 paste. Photographs were taken from three sections in one specimen, i.e. at both ends and the bend region. 4.3.4.2. Characterisation o f in-plane fibre movement

A qualitative study investigating the in-plane fibre movement in stamp-formed components was implemented by using X-ray analysis techniques on specimens with embedded copper tracer wires. X-rays (produced by RBVII/TYK9B, Rich, Seiteut & Co.) travel through the formed sample sensitising a film (AGFAGEVAERT D4) placed behind the sample (fig. 4.14). Due to the higher absorption of X-rays of the copper wires, these wires appear as dark lines on the film. In order to evaluate the distortion of copper wires, the lateral distance between adjacent wires has to be measured. The histogram of copper wires at different distances compared with the corresponding original alignment (standardised distance between adjacent copper wires in this experiment: 2.5 mm) indirectly indicates the magnitude of fibre migration. 4.3.4.3. Thermal analysis

The crystallinity of thermoplastic polymers mainly depends on their thermal history experienced during forming. In order to study the effect of processing conditions on the morphological properties of the matrix materials, DSC (Differential Scanning Calorimetry) is a suitable method for determining the degree of crystallinity of polymeric matrices before and after forming. For this reason, test samples (weight ~ 10 g) were cut from the stamp formed parts and heated at a rate of 10~ Principally, the crystallinity of a polymer is determined by integration of its DSC curve. The measured enthalpy AH is directly proportional to the degree of crystallinity of the matrix but also proportional to the matrix fraction in the sample. Therefore, after each DSC measurement the tested sample needs to be subjected to a TG-analysis (Thermal Gravimetry) in order to determine the pure matrix weight (WT~). With AHc as the degree of enthalpy for 100% crystallinity, the

X-ray

Film

Outer Surface

Inner Surface

Fig. 4.14. Schematicdiagram of X-ray equipment.

Thermoforming of continuousfibre~thermoplastic composite sheets

107

following equation can be applied for the calculation of the crystallinity of a polymer: C=

AH WDS C

Anc WTo

• 100 [%]

(4.3.1)

where C = crystallinity of a sample [%], W D S C - - sample weight for DSC-analysis [g], AH = enthalpy measured by DSC-analysis [J/g], WXG = matrix weight of the same measured by TG-analysis [g], and AHc =theoretical enthalpy for 100% crystallinity [J/g]. In order to acquire data for a theoretical calculation of the final angle reduction of vee-bent parts (section 4.3.5.4.3), the thermal expansion coefficients of pre-consolidated laminates along and perpendicular to the fibre direction have to be determined by TMA (Thermal Mechanical Analysis). The samples (5 • 6 • 6 mm 3) were cut from pre-consolidated plates with a diamond saw. It has to be noted that during the preparation of TMA samples the surfaces between detector and sample table has to be kept parallel. The heating rate in this study was set to 2~ with a load of 0.1 N applied to the detector which was equivalent to a pressure of 5.6 kPa. The measuring temperature range for the individual fibre/matrix system was determined by the melting temperature of the corresponding polymeric matrix.

4.3.5. Results and discussion 4.3.5.1. Determination of preheating time The contact heating method employed is a one-dimensional unsteady-state conduction procedure. Thermal conduction is an energy transportation through atomic and molecular interactions resulting from unequal temperature distributions. A simple heat transfer analysis can be used to obtain an estimate of the pre-heating time. Equation (4.3.2) describes the general three-dimensional thermal conduction problem, regarding the temperature as a function of position in space and time [30]: 8t = P-~e \~2x + ~

+ ~2z }

(4.3.2)

where T = plate temperature [~ t =time [s], X = thermal conductivity [Cal/ cm s ~ Cp = specific heat [Cal/g ~ and p = density [g/cm3]. Since the length and width of the pre-consolidated plates were much bigger than the thickness, it was assumed that the heat can only be conducted in the laminate's thickness direction. The heating process can therefore be reduced to an one-dimensional heating problem. The one-dimensional unsteady-state heat conduction model is illustrated schematically in fig. 4.15. Assuming that (a) the thickness of the two polymeric films is almost zero and therefore negligible and (b) the surfaces of the plates reached the pre-set heating temperature (Zheating) as soon as heating is initiated and retain this temperature throughout the process. The plate which had to be heated was of a thickness of 2x0 and an initial temperature of To. Then the differential equation for unsteady-state heat conduction in one direction is:

108

K. Friedrich et al.

Fig. 4.15. One-dimensional unsteady-state heat conduction model. ST_ 6t

k~ ( 8 2 T ~

-pc.

\-r

(4.3.3)

t > o, o < ~ < ~o

with the following initial and boundary conditions: dT ~=0, dt T -- Theating

x-0,

t>0

(4.3.4)

X - X0,

t> 0

T -- T o

O

100000

>

r

0.00 50000 f 0

B l

10

20

30

,

l

40

J

l

50

'

-0.01

'

60

Time (rain) Fig. 5.9. Transverse flow and apparent viscosity variation with time for (0)16 APC-2.

initiated) at point A. The initial flow viscosity around point B is approximately 60,000 Pa s, which slowly increases up to point C to a value of 300,000 Pa s as transverse flow occurs. This point at C represents the transverse flow "locking" effect when slight twisting in the fibres interferes with any further flow. When the consolidation pressure is increased at point C to 1 MPa, the higher pressure causes flow

172

A.M. Murtagh and P.J. Mallon

to re-start and the viscosity decreases once more to 60,000 Pa s at point D. After this, the sample was cooled and transverse flow ceased. The value of 60,000 Pa s observed for the initial flow viscosity is an order of magnitude higher than that recorded by Barnes and Cogswell [6]. However, lower consolidation pressures were used in their work. The effect of lay-up on consolidation quality was also investigated and fig. 5.10 shows three sample C-scans. Sample A ((90)8 lay-up) was constrained in the longitudinal direction but allowed to flow transversely. The B sample, (0,90,0,90)s lay-up, was unrestricted on all sides. Sample C ((0)8 lay-up) was arranged to prevent transverse flow parallel to the fibres, but allowed resin squeeze-out at the ends of the fibres. The C-scan for Sample A again shows the band of poor consolidation quality across the centre as seen previously. Sample B shows good consolidation quality and it was observed that there was minimal transverse flow in this specimen. Sample C shows that the resin squeezed out at the edges of the sample increases the void content substantially, indicated by the white regions along the top and bottom of the sample. Further evaluation of this work involved ultrasonic scanning of samples both with and without transverse flow having occurred. The effect of consolidation pressure can be seen in fig. 5.11 for eight (0)8 APC-2 samples. Scans (a,b,c,d) are for samples that had unrestricted transverse flow. Samples (e,f,g,h) were placed in a picture frame during consolidation and so squeeze flow was minimised. White areas on the scans indicate the presence of voids, and grey areas indicate better consolidation quality. The unrestricted samples show an increase in porosity as the consolidation pressure was increased. Most interesting is the white band that appears across the centre of each sample which grows thicker as the pressure is increased. A possible explanation for this would be the migration of resin from the centre of the laminate towards the edges where the squeeze flow was taking place, resulting in the creation of voids in the central region where the pressure was released. The other four samples (e,f,g,h)

Fig. 5.10. Ultrasonic scans for 8-ply APC-2 laminates.

Shear&g and frictional behaviour during sheet forming

173

Fig. 5.11. Ultrasonic scans for 8-ply APC-2 laminates consolidated at 0.41 MPa.

show the expected pattern, i.e. better consolidation quality as the pressure is increased.

5.3. Intra-ply shear A number of experimental and theoretical studies have been carried out to characterise axial and transverse intra-ply shear in unidirectional continuous fibrereinforced composite materials, specifically APC-2. For small deformations, experiments have been carried out using oscillatory flow techniques to quantify axial and transverse shear viscosities. Conventional rheometers operating in a torsional mode impose both axial and transverse shearing modes in a composite sample as shown in fig. 5.12. Ideal fibre reinforced fluid theory, first developed by Spencer [8], and adapted by Rogers [9], allowed both axial and transverse components to be separated out from experimental results on a number of samples. Work carried out by Groves [10] on APC-2 estimated the value for the axial intra-ply shear viscosity of 7,400 Pa s and for the transverse intra-ply shear viscosity of 6,100 Pa s, a ratio between the two viscosities of approximately 1.2. Cogswell [1] recorded slightly lower values, 6,000 Pa s in the axial and 3,500 Pa s in the transverse mode. At a higher angular velocity of 100 rad/s, Scobbo [11] measured an axial viscosity of 6,000 Pa s and a transverse viscosity of 3,500 Pa s. The average ratio of axial to transverse viscosity is approximately 1.5.

174


Oscillating

" Axial shear

shear Fig. 5.12. Intra-ply shearing modes in oscillatory torsion.

All the studies performed indicate a highly non-linear response, with a yield stress of about 1,000 Pa. Comparison of the composite viscosity with the measured viscosity for the neat resin indicate a large increase in viscosity for the composite [11]. This would seem in part to be due to fibre twist and interference within the laminate. The temperature-dependence of melt viscosity for the composite material is the same as that for the resin. A 10~ increase in temperature reduces the viscosity by approximately 17% [5]. In fabrics, intra-ply shear in the 1-2 plane, which gives rise to the trellis effect as shown in fig. 5.13, can be investigated in purely kinematic terms to predict the trellis angle for a particular fabric strain. The effects of the resin are negligible on this

Instron

|

1. lnstron frame

5. Extension rod

2. Crosshead

6. Sample clamp

3. Load cell

7. Fabric sample

4. Top cooler

8. Environmental chamber

connection

i

_

/ \ /"" / \ /"I \ / \ /AN / \. 4

,, \ J O

:,,.',,I \ .('

"\.,

o(t)l Ic;;• / X /

"

\ /

..-I

Ix.,, \/I

- - - - - - - 1 . ~ ,,. / \ / .,, fl ["4 \ / \ /

Fig. 5.13. Trellis-angle measurement on deforming fabric specimen.

\q

I I0

Shearing and frictional behaviour during sheet forming

157

effect. For a bi-directionally reinforced fabric orientated at 45 ~ to the shearing direction, the trellis angle can be predicted from the simple kinematic expression: cos 0 -- cos 00 exp(,kt)

(5.3)

where 00 is the initial fibre angle (45 ~ in this case), at time t = 0. This shows that movement is symmetric about the X-axis and that the fibre angle decreases as a function of applied strain rate ~ and is independent of the material constitutive law, i.e. is purely kinematic. The true axial strain (not to be confused with the engineering strain) in the sheet is equal to e l l - ln(~0t)) -- )~t

(5.4)

and we can see that the angle change is simply dependent on the axial strain. Experiments were carried out to verify this model. This involved shearing an appropriate fabric specimen (glass-fibre-reinforced polyamide, 7-H satin weave, Vestopreg G101 | at processing temperature inside an environmental chamber [12]. The fabric was gripped using special jaws which were in turn connected to an Instron straining frame, as shown in fig. 5.13. A cross marked in ink at the centre of the specimen was observed as the specimen was strained vertically. The change in angle was recorded and fig. 5.14 is a plot of true strain against predicted trellis angle (from eq. (5.3)) and the observed trellis angle. The experiment shows relatively good agreement with the theory. Differences may be attributed to uneven shearing at the ends of the specimen, which was caused by the presence of the grips which 50 Model 40

D

Specimen

30 Trellis angle (e)

20

10

'Locking'

,=,,,=

angle

0.0

0.1

0.2 True strain

0.3 I; ! 1

Fig. 5.14. Comparison of model and test values for trellis angle.

0.4

176


constrained the sample from reducing in width. The shaded region indicates the spread of values for which the trellis locking angle was observed, i.e. the strain at which out-of-plane buckling was first observed visually on the specimen. Thus for G 101 fabric, the locking angle lies between 25 ~ and 30 ~ This value is in accordance with that observed by other researchers [13,14]. The ideal fibre-reinforced fluid constitutive model for one family of fibres has been extended to include two families of fibres by Johnson [15]. The original model [8] defines stress in terms of strain rate and two viscosity terms/71 and/Tt, the axial and transverse viscosities. For a fabric, a third viscosity term must be included: 1

O'11 -- ~, [4/71 -- (3/71 -- 2/72) sin 2 20 -- ~/73 sin2 40]/sin 4 0

(5.5)

all is the stress in the 1-1 direction, Z is the shear rate and 0 is the trellis angle. The three viscosity terms are denoted by/71,/72 and/73. They may not be related to simple shearing modes in any particular plane in the fabric, unlike/Tz and/Tt which can be related to shear in the 1-3 and 2-3 planes for unidirectional materials. Instead, they may be consider as "mixed-mode" parameters. Using the same experimental set-up that was used to verify the kinematic model for trellis angle prediction, it was possible to obtain an estimate for these three viscosities for the G101 specimen. Three samples were sheared at a constant shear rate at three different temperatures. Tensile stress in the 1-1 direction was calculated as a function of tensile force and the instantaneous cross-sectional area of the sample across the centre. A plot of true strain against tensile stress is shown in fig. 5.15, for 225~ 245~ and 265~ 5.00e+6

al

-

,,

4.00e+6

n_

I

"9 3.00e+6

,,,

,,,

a

Exp 225~

e

Exp 245~

,&

Exp 265~

. .1

Model225~

2

Model 245~

,e,-

t:)

J

.e

3

Model 265~

2.00e+6

m

m r

o I-

1.00e+6

A

0.00e+0

0.00

-

0.05

0.10 True strain

0.15 ~

Fig. 5.15. G101 fabric stretch test modelled using eq. (5.5).

11

0.20

0.25


177

Equation (5.5) was used to model the stress response as shown. Note that the initial elastic-viscous stretching of the specimen (around region A) is not modelled as the model assumes steady flow. The value of the three viscosity parameters r/l, 02 and 03 are given in table 5.1. Values for r/1 decrease as temperature increases, while conversely values for r/2 increase with temperature. This would not be expected for "real" viscosity components but may be possible for these "mixed-mode" parameters. The ratio between 01 and 02 decreases from 13.33 to 1.71 as temperature is raised from 225~ to 265~ At lower temperatures, an adequate curve fit was achieved by setting ~2 = 0, which simplifies the model considerably. The optimum value for 773 was found to be approximately zero for all conditions.

5.4. Inter-ply slip Inter-ply slip in unidirectional materials occurs due to the fact that the reinforcing fibres in a composite laminate may be considered to be inextensible. When forming single or double curvature shapes, where the stack of plies making up the laminate may be considered as a number of inextensible, yet flexible, plates, then a relative displacement must occur between the layers to accommodate the different path lengths of each ply around the bend. Micrographs taken at the edge of formed parts with initially ground and square edges serve to illustrate this phenomenon [12]. The total slip deformation, d, can be shown to be a function of the bend angle, 0, number of plies, N, and the thickness of each ply, t (see fig. 5.16), and is given by Ot

d - ( N - 1)~-

(5.6)

T A B L E 5.1 P a r a m e t e r s for fabric m o d e l T e m p e r a t u r e (~

O~ (Pa s)

7"]2 (Pa s)

773 (Pa s)

265 ~ 245 ~ 225 ~

1.2 e 7 3.0 e 7 4.0 e 7

7.0 e 6 3.5 e 6 3.0 e 6

0 0 0

t

0

Fig. 5.16. Ply slip a r o u n d b e n d angle 0.

178


Figure 5.17 is taken from a (0,90,0,90,)s APC-2 laminate formed over a 90~ The slip occurs in the resin layer between each ply and intra-ply shear within each ply is negligible. The step-like slip effect can be seen along the edge of the laminate (for example at point A, the interface of a 0 ~ and 90 ~ ply). The only point at which no slip can be seen is at the central axis of the laminate, at the interface between two 90 ~ plies (point B). Other cross-ply laminates show similar degrees of slip fig. 5.18 shows the deformed edges of a quasi-isotropic (0/+ 45/90/-45)s 90~ part. Resin layers can be seen as dark lines between the plies. Some intra-ply shearing is evident on the top 0 ~ and adjoining +45 ~ ply, possibly due to friction against the tool during forming. The slip behaviour of unidirectional (i.e. all plies oriented at 0 ~ laminates contrasts greatly with that for cross-ply parts. In most cases, for pre-consolidated unidirectional parts, the dominant flow behaviour was intra-laminar, with no obvious resin layers existing and with the entire thickness of the laminate behaving in many respects as a single ply. This is shown in fig. 5.19 for a (0)8 90~ part where the

Fig. 5.17. Inter-ply slip for (0,90,0,90)slaminate.

Fig. 5.18. Inter-ply slip for (0/+45/90/-45)s laminate.


179

Fig. 5.19. (0)8 l a m i n a t e - intra-ply shearing.

flow is even across the thickness, and there is no distinction between plies. One exception to this rule was observed with laminates pre-consolidated at low pressure (100 kPa) before forming. Figure 5.20 shows a distinct step-like behaviour (no apparent resin layers) with each ply seeming to act independently. This may be caused by the low consolidation pressure not causing sufficient fibre/fibre interaction between plies to, in effect, "fuse" the plies together. In fabrics, the inter-ply slip behaviour can differ markedly from that seen in unidirectional materials. The existence of a crimp in the fabric due to the woven nature of the tows means that the assumption of inextensibility does not hold. When a tensile force is placed across the plies during forming, the crimp allows fibres to straighten to a certain degree. The amount of possible stretch varies depending on the weave style [17]. This is shown in fig. 5.21 - - the fibre straightening factor (FSF) is the possible percentage change in length of a ply segment along its length. It is a maximum for the most highly crimped style, i.e. plain weave. To measure this elongation in a ply under tension, specifically for Cetex fabric, rectangular samples were tested in an environmental chamber and their load response to an applied displacement was measured [16]. Figure 5.22 is a plot of

Fig. 5.20. (0)8 laminate - - step-like behaviour.

180


Fig. 5.21. Possible tow straightening in fabrics.

0. =E

Cetex fabrics:

-

B

Temperature 320~ Speed 0.5 mm/min I a

5-H weave 9

.

Plain weave .Model 5,.H

m. r

I-

m

0

. - ~ -

|

1

....

2 Strain

|

3

(%)

Fig. 5.22. Stretch testing of Cetex fabric specimens.

strain in the longitudinal direction against tensile stress, showing the response for both a plain weave and a 5-H satin weave sample. The behaviour shows that there is an initial strain in the samples before the stress begins to increase exponentially, i.e. a "strain-hardening" phenomenon. The plain weave allows for more tow stretching compared to the 5-H satin weave sample. The stress/strain behaviour of the 5-H satin weave sample was modelled using a curve-fitting technique as follows: r~ - 0.03061 e 2"1003(e)

(5.7)

where a = tensile stress and e = strain in specimen. This model is useful in predicting internal tensile stresses in a deforming fabric ply and can be used in conjunction with an understanding of the inter-ply slip behaviour of the material to form part a numerical model for sheet forming of Cetex fabric. As stated previously, inter-ply slip occurs in the thin resin interlayer between plies. In order to obtain a thorough and quantitative understanding of the nature of the shear stresses to be encountered in this layer during forming, a number of analyses

Shear&g and frictional behaviour during sheet form&g

181

by different researchers have been carried out. Cogswell [1] was the first to identify the mechanism for unidirectional tapes, specifically APC-2, and carried out some initial slip characterisation studies. Scherer [18] obtained experimental results from an inter-ply slip apparatus taking into account the effects of shearing velocity, temperature, pressure and lay-up for a carbon-fibre-reinforced polypropylene unidirectional composite. A model obtained using these results was used as input to a finite element analysis on the inter-ply slip process during thermoforming [19]. Xiang Wu [20] also performed pull-out tests on 16-ply uniaxial APC-2 laminates and modelled the forming of 90~ parts as approximating 3-point bending. He calculated the apparent viscosity in the resin-rich interlayer and noted an order of magnitude difference between measured values for a (0)16 laminate and predicted values for the neat resin. Groves [21] observed this viscosity increase in APC-2 using a dynamic spectrometer and one explanation proposed was possible fibre friction and interference between layers. Further investigations by Jones [22] showed that the observed non-Newtonian behaviour of the composite and the assumption of the individual plies behaving as buoyant plates was not due to inertia effects and instead was due to intra-ply shearing. Kaprielian and O'Neill [23] performed pull-out experiments on a steel plate from between stacked plies of APC-2 and were able to correlate results with a model based on the ideal fibre-reinforced fluid constitutive equation [8]. Soll [24] performed tests to optimise the forming conditions when forming simple rightangled bends using a unidirectional material and noted that a tensile force applied across the laminate during forming increased part quality by reducing fibre wrinkling. Tam and Gutowski [25] developed a linear visco-elastic model of the inter-ply slip process, modelling the fibre-rich plies as a linear elastic layer and the resin interlayer as a viscous layer. This model allows prediction of laminate stresses and displacements, and strains in the slip region. Results showed good correlation with isothermal forming experiments. Scobbo [11], using DMA analysis, observed the effects of fibre interaction between adjoining plies with fibre effects beginning to dominate visco-elastic behaviour at higher temperatures. More recently, Morris and Sun [26] have performed inter-ply slip experiments on APC-2 laminates at lower temperatures, approaching and below the melt temperature, Tm, and have modelled this solid-phase forming behaviour. The remaining part of this section will describe and summarise part of another inter-ply slip study performed by the authors [12,16,27]. This work was carried out with the aim of simulating the conditions of slip during forming in a controlled manner and examining the effects of different forming parameters (slip velocity, temperature, normal pressure and fibre orientation) on shear stresses in the interlayer. Experiments were carried out using a consolidation unit [7] together with a custom-built shearing apparatus [28]. The consolidation unit consists of two heatable platens mounted on a 100 kN hydraulic press. The shearing apparatus is made up of a motor driven leadscrew which performs the pull-out motion on the horizontally mounted sample lay-up. A 500 N load cell recorded the shearing load. A schematic of the apparatus is shown in fig. 5.23. Figure 5.24 is an overall view of the shearing apparatus and the consolidation mounted together on the hydraulic press.

182


Consolidation unit

Exterior ply clamp

DC M otor

Load cell

Shearing apparatus

Fig. 5.23. Consolidation unit/shearing apparatus for inter-ply slip testing.

Fig. 5.24 Test set-up for inter-ply slip experiments.

The sample lay-up comprised of a central pull-out ply, two exterior stationary plies and intermediate plies with various fibre orientations. For the APC-2 sample shown in fig. 5.25, the lay-up is (0, 90, 0)s the central and two exterior plies are oriented at 0 ~ to the pullout direction, and the two inner plies are at 90 ~ A narrow shim of material behind the pull-out ply keeps the gap between top and bottom platen constant to avoid "pinching" of the specimen. All APC-2 and Cetex fabric specimens were first consolidated at a pressure of 1 MPa for 5 minutes prior to testing. A specified normal load (usually 100 kPa) was then applied via the hydraulic press for the duration of the pull-out test. The shearing


183

Shim

Fig. 5.25. Specimen geometry for inter-ply slip testing.

force and ply displacement were recorded for a particular shearing velocity. The shear stress was calculated simply by dividing the shear force by the sheared area using Fs

r -

(5.8)

w ( L - d)

where r is the shear stress, Fs is the shearing force, L and w are given by the specimen geometry and d is the displacement of the pull-out ply at a particular time t. Figure 5.26 show the results for a particular test, where the shearing velocity has been increased in increments. Each increase in velocity causes a corresponding increase in the associated "steady" shear load, as shown. This allows the shear

0.4

250 u

(0,90, 0)S APC-2 CP 1 MPa, NP 0.1 MPa

200 A

Z v

SPT 375~

0.3 A

150

E

"o

...o

0.2

3

l_

vE

8

2 .-._,,ml

m

L.

0.1

50

Load

Velocity 0

100

200 Time (sec.)

Fig. 5.26. Velocity increments during inter-ply slip test.

300

] 400

0.0

=

,,r

184


velocity/shear stress relationship to be determined from an average of single sample tests for a particular set of conditions. This technique was used throughout this test programme to obtain all the shear velocity/shear stress plots shown. The effect of processing temperature has a large effect on the shear deformation behaviour of composites. This is due to the resin viscosity, which is strongly dependent on temperature. The reinforcing fibres are unaffected. For APC-2, the melt temperature is 343~ so theoretically a laminate can be formed at any temperature above this. It is recommended that processing should occur in a window between 360~ and 400~ Isothermal conditions, and a constant resin viscosity is readily achievable with diaphragm forming, where the entire laminate is held in a heated chamber. For press forming, temperature may be uniform initially, after being transferred from the heating unit, but decreases rapidly, due to convection cooling in the air. Conduction cooling occurs once contact is made with the tool, which may be around 250~ Indeed, forming may actually occur at temperatures less than 343~ for APC-2 under certain conditions, but in this case, inter-ply shearing may result in a high level of shear stress [26]. Figure 5.27 shows the effect of varying temperature on a (0, 90, 0)s sample. As expected, raising the temperature decreases the shear stresses in the laminate. However, at higher temperatures, problems such as surface oxidation and excessive in-plane fibre wrinkling or "washing" (due to the low viscosity of the resin) may occur. For an anisothermal process such as press forming, a wide variation in temperature is unavoidable. The effect of releasing normal pressure completely during a typical slip test after consolidation is shown in the initial part of fig. 5.28. After reaching a "yield" level of 12

a

,

,,

,,,,

,,=

(0,90,0)S APC-2 CP 1 MPa NP 100 kPa 10

A

J tJ

360~ 3700C

L

l

A v

Ir

380~ 390~ 400~

A

ml|

0.0

|

i

!

0.1 Shear velocity (mmls)

Fig. 5.27. Effect of temperature on inter-ply slip of APC-2.

I

0.2

Shear&g and frictional behaviour during sheet forming

185

2.5

200 a

(0,90,90,0)S APC-2 SPT 385~ CP 1.5 MPa 2.0

150

A A

zv

Shear load

_8 loo | _m

Pressure

1.5

x

i_

1.0 m

m

50

0

0.5

0

200

400

600

800

o Z

0.0

Time (sec.)

Fig. 5.28. Variation of shearing force with normal pressure.

100 N, shear load relaxes to a reduced level of 25 N. However, once pressure begins to increase, to about 100 kPa, shearing forces recover to a higher level than the original maximum (120 N). At a constant pull-out velocity, as pressure is increased further, the shearing force continues to increase, but the magnitude of further increases is much smaller than the initial "jump" when pressure was first reapplied. The initial jump increased stress levels by 500% - - at a pressure of 2 MPa (20 times the original step increase), shear stress has only increased by a further 50%. One possible reason for this is that under no normal force, the plies are free to disengage from intimate contact and can slide semi-freely against one another. However, as soon as a nominal normal pressure is re-applied, the plies come together once again, intimate contact is re-established and viscous slip in the layer between plies resumes. Further increase in pressure does not greatly affect this viscous slip. Theoretically, for an incompressible fluid, viscous forces should be independent of normal pressure, in the absence of a pressure gradient along the direction of flow. In practice, pressure increases do increase the shear stresses, possibly due to increased fibre contact, but not significantly. This effect need not be crucial in terms of diaphragm forming, where there is always a normal pressure present in the form of a vacuum applied between the diaphragms. As the pressure rises and the part begins to form, a hydrostatic pressure across the area of the laminate would cause an increase in shear stress. However, most forming would occur at low pressures, as there would be no reaction force against the back side of the bottom diaphragm until it made contact with the tool, when inter-ply slip would have ceased. For press forming, the situation is more

186


complex. Initially, the laminate is heated to forming temperature and is under no normal pressure, except for the parts of the surface directly beneath those parts of the forming die which first come into contact with the top ply. At a constant pull-out velocity, as pressure is increased further, the shearing force continues to increase, but the magnitude of further increases is much smaller than the initial "jump" when pressure was first reapplied. Thus, some regions may undergo inter-ply slip, under no normal pressure, until the forming die comes into direct contact. The pressure distribution across the laminate is much more difficult to predict than with diaphragm forming. Further tests were carried out to establish the shearing velocity/shear stress relationship as normal pressure was varied from 20 to 400 kPa. This involved preconsolidating (0, 90, 0)s APC-2 specimens at 1 MPa. Pull-out tests were then carried out on each specimen under a particular normal pressure, and the shear stress level was recorded as shearing velocity increased. Temperature during this programme of experiments was kept constant at 385~ Results are shown in fig. 5.29. As expected, shear stress rises as normal pressure is increased. Figure 5.30 shows a plot of normal pressure plotted against shear stress at two typical shearing velocities, 0.075 and 0.22 mm/s. This plot shows further evidence that significant increases in shear stress occur at lower values of pressure, especially so for the higher velocity. Once pressure increases beyond 100 kPa, the increase in shear stress is less pronounced as the pressure rises further. To examine the effect of varying fibre orientation, a series of experiments was carried out under standard conditions of pressure and temperature, for different lay30ee

(0, 90, 0)S APC-2 SPT 385~ CP 1 MPa

Normal

pressure (kPa) " " 20 eL ,=~

:':- -9- . , . e - - - -

v

w

f~

I

t-.

tll @

,=

I

0

0.0

i

0.1

,I

I

0.2

9

I

|

0.3

0.4

Shearing velocity (mmls) Fig. 5.29. Effect of normal pressure on inter-ply slip of APC-2.

9

0.5

40

-'-

100

i

200

----o---10

20

400

187


20

A

cO

A.

Shear stress at velocity"

v

T= lo

.-e-

(4

-e=- 0.22mm/s

t,=

0.075mm/s

@

0

100

200

300

400

Normal pressure (kPa)

Fig. 5.30. Significant increase in shear stress at low normal pressure. up orientations. As it was not possible to change the orientation of the pull-out and exterior plies to any angle other than 0 ~ relative to the pull-out direction, the fibre angle of the free ply between the exterior and pull-out ply was varied. Thus the layup for a particular experiment may be expressed as (0, 0, 0)s, where 0 is any angle between 0 ~ and 90 ~ Figure 5.31 shows a plot of shear velocity versus shear stress for a number of lay-ups. Lay-ups where the fibres in the free ply lay at some angle other than 0 ~ to the pull-out direction gave similar results, showing that the resin layer in each case was fully existent and of similar proportions for all orientations. Some 30 (0, 0,0)S APC-2

01010

SPT 385~ =

013010

n_ 20

-=

0/60/0

m

=

0/90/0

CP 1 MPa NP 0.1 MPa

014510

A

(II

r, L_

Q

,c

10 "

,

0.0

1

i

i

illll

i

|

iii

0.1

i

i|1

i

illl

0.2

Shear velocity (mmls)

Fig. 5.31. Effect of lay-up variation on inter-ply slip of APC-2.

i

i

0.3

i

188


fibre rotation was observed, especially in the 30 ~ and 45 ~ lay-ups. Fibres in the free ply tended to re-orientate themselves to become aligned with the fibres in the pull-out ply and the more grossly displaced specimens showed most evidence of this. In the (0, 0, 0)s lay-ups, shear stresses were much higher than that for angled layups: in this case, it might well be assumed that a distinct resin layer was not formed during consolidation, and shearing actually occurred through the thickness of the middle ply. Micrographs taken through a section of a (0)8 laminate indicate the absence of any distinct resin layer [12]. Further evidence of this inhibited form of shearing in (0, 0, 0)s lay-ups is shown in fig. 5.32, which illustrates the instability in shear stress as shearing occurred at a steady velocity. This is probably due to fibre interference and entanglement between plies. Observations on tested specimens showed that this was indeed the case, with some fibres being grossly distorted and buckled. As already mentioned, the effects of fibre interaction have also been observed by other researchers [11]. If we now consider a further analysis of the different slippage behaviour between the parallel-plied (0, 0, 0)s and other cross-plied lay-ups ((0, 90, 0)s (0, 45, 0)s, etc.), we can relate the different shearing rates that occur to determine an inter-ply slip viscosity. If we assume the cross-plied lay-ups to behave in the same fashion, i.e. a 6 pm resin layer being sheared between the plies, the associated shearing rate in this layer can be calculated and from this the viscosity can be found. For the parallelplied lay-up, shearing occurs throughout the thickness of the ply between the exterior 500

-

0.5 o

(0,0,0)S APC-2 SPT 385"C C P 1 MPa NP 0.1 M P a

400

z -"9 Io t~ o

0.4

300

0.3 Unstable

1

e=

G

200

0.2

#

l

100

0

0

200

IlL

,=.,.

i....

r @ ,c

I

0.1

--D- Shear load --

Velocity

400

o @ > ==

m

600

800

T i m e (sec.)

Fig. 5.32. Stress instability during (0, 0, I))s pullout.

1000

1200

0.0

r

Shear&g and frictional behaviour dur&g sheet form&g

189

and pull-out ply so the sheared layer thickness is equal to the ply thickness (125 ~tm). The viscosity is this case must be much higher due to the lower shear rates and this is shown in fig. 5.33. The viscosity of the parallel-plied lay-up ( > 20,000 Pa s) is almost two orders of magnitude greater than the viscosity of the cross-plied lay-up ( < 1,000 Pa s). The viscosity seen in the cross-plied lay-up is similar to the viscosity of neat PEEK resin as measured by Cogswell [5]. The slip viscosity for the (0, 0, 0)s lay-up may be related to the longitudinal intra-ply shearing mechanism, as mentioned in the previous section. Inter-ply slip of fabrics is affected by the tow straightening effect, as mentioned previously. Pull-out experiments on fabric samples were further complicated by having two directions of reinforcement tensile force could be applied to fibre tows lying in the pull-out direction, but the transverse tows at 90 ~ to the direction of pull-out tended to remain behind in the sample whenever deformations over a few millimetres occurred. This effect was not so pronounced in unconsolidated specimens and shear results shown here are for samples tested at lower pressures than would be expected during full consolidation. Figure 5.34 illustrates the difference observed in shear behaviour between unidirectional and fabric materials during a typical pull-out test. Both results shown are for a carbon fibre/PEI material (the fabric is 5-H satin weave), tested under similar conditions of heat and pressure. The 0~ pull-out ply in the (0, 90, 0)s allows direct transmission of the traction load to the sample and the measured shear load quickly rises to a steady level. For the fabric material, the shear load

100000

-

10000 A I0 v

s

/

F" : -

Parallel-plied layup

Cross-plied layup

looo

0 O

lOO

10

1000

i

a

i

J

t

a

i

iJ ........

I

I

10000 Shear stress (Pa)

Fig. 5.33. Inter-ply shearing viscosity for parallel-plied, cross-pSed lay-ups.

I

I

I

I I

190


120

i-

lOO

t 7 b~176176 F ......... ,,

, ,,

,

Material:

CF/PEI

,

SPT 320 ~ NP 100 kPa

8O Z o

60

I

r a=

r

Unidirectional"

Transistion 55N

ID

,

A

i. , ..... i

_ L LI __.111 .

slip

(0,90, 0)~ Fabric"

40 Fibre straightening

20 0

([o/9o1, [o.9oi ),

0

50

100

150

Time (sec.)

Fig. 5.34. Direct comparison of unidirectional/fabric materials.

increases in a different f a s h i o n - initially, the load applied to the ply causes the fibre tows to straighten and this continues up to point A. Here, the nature of the load increase changes from an increasing to a decreasing rate. This point, at 55 N, can be regarded as the required load to cause inter-laminar shearing along the full length of the sample at the interface between two plies, rather than cause the tows to straighten any further. The stationary level of shear stress reached thereafter is composed of two parts the tensile force in the stretched fibres plus the viscous traction force required to shear the plies. The transition load is a function of the total amount of fibre stretching, in both the area of the sample under normal pressure and the pull-out ply length between the sample and ply clamp on the shearing apparatus. Any analysis of inter-ply slip in fabrics must take account of initial fibre stretching. Shear velocity/shear stress plots may be generated in a similar fashion to unidirectional materials by determining the steady shear load levels corresponding to various shear velocities. The effect of processing temperature on inter-ply slip of fabrics may be regarded as similar to that for unidirectional materials once fibre stretching has been taken into account. Figure 5.35 shows a plot of shear velocity versus shear stress for a Cetex 5-H satin fabric sample, sheared at temperatures between 300~ and 340~ Normal pressure remained constant at 100 kPa for each test. As with APC-2, an increase in temperature of 40~ reduces the level of shear stress occurring in inter-ply slip substantially, due a decrease in viscosity of the PEI matrix material. Localised inplane wrinkling of surface fibres that can occur at increased processing temperatures


191

50

NP 100 kPa 3 plies 5-H Cetex 40

A t~

30

W

t= i_ tll Q

20 t

tn

300"C

10

,

_=

,

r. 0

I

0.0

|

!

0.1

I

320oc 3400C

,

0.2

I

0.3

Shearing velocity (ram/s)

Fig. 5.35. Effect of processing temperature on Cetex fabric slip. with unidirectional fibre-reinforced composites is not such a large problem with fabrics as the woven nature of the tows constrains any excessive movement of fibres. For variation of normal pressure, tests were performed between applied pressures of 20 kPa and 400 kPa. Figure 5.36 shows the obtained results; load cell limitations reduced the attainable shearing velocity to approximately 0.25 mm/s at higher normal pressures. As with APC-2, a significant increase in shear stress is seen as the pressure is increased. The magnitude of the recorded stresses are much higher compared with the unidirectional material. Even allowing for matrix and viscosity differences, there is a much greater resistance to inter-ply slip for the Cetex material, again probably due to the nature of the interaction between adjoining plies, with much more interference to sliding being caused by the uneven surface of the woven plies. Initial test results showed that inter-ply slip of laminates was not initiated until a certain yield point had been reached. Even at low shearing velocities, pull-out forces required to shear the laminate were substantial. In order to determine this value more accurately, the test set-up was changed. Rather than use the leadscrew to provide the pull-out force, a pulley system using dead-weights was installed at the front of the shearing frame. To measure the very small displacements at loads approaching the yield point, two miniature LVDTs were mounted behind the ply clamp (see fig. 5.37). This allows very small movements of the central ply to be recorded. Care was taken to exclude any movement of the ply clamp and any displacement necessary to take up slack in the pull-out ply. The yield load was defined

192


50

40

Normal

pressure (kPa) lg a,. A

30

20

w

"-='-

20

--e--

50

=

100

--o-

200 400

m @

10 SPT 320~

3 plies 5-H Cetex 0

9 0.0

~ ,, 0.1

,

I 0.2

i

I 0.3

=

I

0.4

"

0.5

Shearing velocity (mm/s)

Fig. 5.36. Effect of normal pressure on Cetex fabric slip.

.

0 LVDT A

3

...

Pulley

Load cell

o I

LVDT B Dead

weights

Fig. 5.37. Positioning of LVDTs for yield measurements.

as the force required to cause an irrecoverable displacement of the pull-out ply. For unidirectional materials, this point was relatively easy to determine as pull-out force is transmitted directly through the straight fibres to the specimen, For fabrics, however, initial fibre straightening meant it was difficult to separate fabric stretching from true slippage displacement in the lay-up. Inter-ply shear tests were carried out under various conditions of temperature, pressure and lay-up to see their effect on the yield point. Figure 5.38 shows a typical yield plot of applied dead-weight loading and recorded displacement against time for a steel foil sheet being sheared from between two plies of APC-2 (i.e. friction of

Shear&g and frictional behaviour dur&g sheet forming

i

'F

40

8

30

6

193

-

20

(g

2

t~ 100 0

0 500

1000

1500

2000

Time(sec.) Fig. 5.38. Yielding situation for APC-2/steel foil.

composite against a smooth surface see section 5.5). This result shows the ideal s i t u a t i o n - no displacement is seen until the critical load is applied, when a definite yielding of the ply is observed, and seen to increase steadily as the load is kept constant. This sudden yield occurs only when there is no interaction between fibres from adjoining layers. Further increases in applied load causes the displacement to occur at a faster rate. In reality, most samples with two plies interacting did not show this behaviour. Instead, initial yielding showed a slight displacement (as in the initial part of fig. 5.39), followed by an almost complete cessation Of movement. This behaviour represents an elastic/plastic effect and cannot be regarded as a true yield in terms of continuous inter-ply slip. Instead, the yield point can be defined as the point at which irrecoverable, steady shear flow commences. A typical response in yielding is shown in fig. 5.39, for a (0, 0)s APC-2 sample. Here, as would be expected, application of an increasing dead-weight force causes movement of the pull-out ply, but without continuous sliding occurring. At point A, when 45 N of load has been applied, displacement of the pull-out ply has reached approximately 0.2 mm. Region B shows the response when the load is taken off; the ply displacement recovers back to practically a zero value, indicating an elastic effect. This effect may be due in some measure to the fact that as loading occurs, fibres from adjacent plies interact and cause an elastic resistance to shearing, and "spring-back" when the load is removed. Although this behaviour was observed in all lay-ups of APC-2, it was most evident in the (0, 0)s sample. This behaviour in the fibre direction may be related to a similar elastic "spring-back" effect observed in the through-

194


100 ' " l Note: Noise in the load cell signal [ causes each dead-weight load to

-I 2.0 ,,--.~

80 I flickerto some degree

n

60 ~- (0,O)sAPC-2 [ SPT 385"C '~k~ 40 P I a CPr 1MPaNP100

I

I

0

A /-d

Load

ne

/

I

ii

]

1.5

/!

/I

fl 1"0 e=eue 0.5

i~

20

o0

250

500

750

1000

io.o

1250

Time (see.) Fig. 5.39. Yielding of a (0, 0)s sample.

thickness direction, in other research by Muzzi [29], where the fibre bundles are assumed to behave like coiled springs. Applying a compressive force to a bundle of stiff, slightly wavy fibres causes them to compress elastically, and when the compressive load is removed they can recover. In shear, adjoining fibre layers m a y impress u p o n one another under pressure and slippage of one layer across the other causes a slight elastic effect where some fibres m a y " s n a g " temporarily. Once shearing is halted, elastic recovery of any " s n a g g e d " fibres m a y occur. Increasing the load to the level shown at C caused complete yielding of the specimen. Table 5.2 summarises the results for various yield stress measurements carried out on unidirectional materials under different conditions. F o r APC-2, the yield stress TABLE 5.2 Yield stress values for APC-2 Material

Lay-up

Conditions

APC-2

(0, 90, 0)s

365-405~ NP 50,100 kPa NP 400 kPa 365-405~ NP 50,100 kPa NP 400 kPa

(0, 0)s

Yield stress (kPa) 1.1• 1.2-t-0.2 2.4• 2.6+0.2


195

more than doubles (1.2 to 2.6 kPa) when the fibres are in an aligned state, i.e. (0, 0) s, compared with a (0,90) arrangement, or for any other lay-up where adjacent plies lie at an angle 0 to one another. To model the inter-ply slip behaviour of APC-2 and Cetex fabric, a modified form of the Herschel-Buckley power model was used as shown (v = shear velocity): (5.9)

Z" = "gyield + k(v) n

This allows a value for a yield s t r e s s (Z'yield) t o be inputted and then a power-law relation can be used to describe the viscous flow in the resin interlayer between plies. The values of the parameters Z'yield, k and n are dependent on the various process conditions (temperature, normal pressure, fibre orientation). Using the experimental data obtained, a curve-fitting technique was used to determine relationships between the process conditions and between ~'yield, k and n. For example, the effect of normal pressure on shear stress for APC-2 can be described by r(P, V) = (0.95 + 1.28 e-3(P)) + (-28.639 +

31.143(logP))(V~176176176 (5.10)

i.e.

"~yield - - 0.95 + 1.28 e-3(P) kPa

k = (-28.639 + 31.143(log P) n = 0.1635 + 0.3079(log P) valid for: velocity 0 < V < 0.5 mm/s, and pressure 20 kPa < P < 400 kPa. The curve-fits for the effect of normal pressure are shown in fig. 5.40. In order to combine these three different models into one master equation to calculate shear stress for any arbitrary combination of temperature, T, relative fibre angle, 0, and normal pressure P, in terms of shearing velocity, V, a factoring technique was applied. Using this method, a standard set of values was used to normalise all other points, which results in three factors fr, fp and fo, which, when multiplied by the original standard value, give the shear stress for any set of parameters. The standard conditions chosen for APC-2 were as follows: 9 Temperature 385~ 9 Normal pressure 100 kPa 9 Fibre orientation 90 ~ This results in the standard model: rs = 1.0 + 28.7083 V 0"8152

(5.11)

Then we can write

Apc-2(v, T, P, O) =iT "Up- Jb-

(5.12)

or "~APC_2(V, T, P, 0) =

r(v, T) r(V, e) r(v, 0) rs

rs

rs

(5.13)


196 35

3O

20 kPa model ---2

40 kPa model

25

-"-= 100 kPa model

tl Q" 20

"-'-8 400 kPa model

__.4 200 kPa model

A

L..

o r

10

0 0.0

0.1

0.2

0.3

0.4

[]

20 kPa exp

0

40 kPa exp

&

100 kPa exp

X

200kPaexp

4-

400 kPa exp

0.5

Shear velocity (mints) Fig. 5.40. Model versus experimental values - - pressure variation.

A similar method was applied to modelling the behaviour of Cetex fabric, the exception being that the possibility of tow stretching has to be taken into account. From fig. 5.34, it is known that the transition between tow stretching and inter-ply slip occurs at a shear stress of 5.5 kPa. By equating shear stress in the interlayer to tensile stress in the ply at this point, we can write: ~'A s - - f i a t

(5.14)

where As is the sheared area and A t is the cross-sectional area of the ply under tension. Assuming constant width, we can than deduce that the tensile stress in a ply, that causes a shear stress of 5.5 kPa, can be represented by a-~

rLf

= 1.667 e7Lf

(5.15)

where r = 5.5 kPa, and tp = ply thickness = 0.33 mm Thus the effective "span" length, Lf, of the structure being formed, i.e. the length of the ply undergoing shear, is critical in determining the tensile stress. If the flange length Lr is sufficient that the total required amount of inter-ply slip (depending on geometry conditions) can be accommodated as pure fabric stretching, then no slippage between the plies need occur. Thus in a numerical simulation of press forming, a check should first be made to calculate the required amount of inter-ply slip from eq. (5.6). Using this value, and by calculating the required amount of longitudinal strain, the associated tensile stress in the deforming ply can be found from eq. (5.7).

Shearingandfrictional behaviourduringsheetforming

197

If the resulting tensile stress is sufficient to cause a shear stress of greater than 5.5 kPa in the interlayer, then inter-ply slip must occur and the power-law part of the model must be introduced. Similarly to APC-2, the effect of temperature and normal pressure on shear stress can be modelled using a curve-fitting/normalisation technique. The effect of fibre angle was ignored for the fabric. The standard set of conditions chosen for Cetex are as follows: 9 Temperature 320~ 9 N o r m a l pressure 100 kPa This results in the standard model: rs = 5.5 + 55.246(V) 0"4902

(5.16)

The master model thus obtained may be described by

r(v, 7") r(v, e)

"~Cetex(V, T, P) = ~

rs

~~'s rs

(5.17)

For both materials, the inter-ply slip model to predict inter-layer shear stresses may be condensed into an alternative general form as

T--(~TY(i)-~-kigni) "~s

(5.18)

The value of rs, yield stress ry(i) and of the power-law parameters k and n are given in tables 5.3 and 5.4. for APC-2 and Cetex respectively.

5.5. Friction during thermoforming In sheet forming of thermoplastic composite sheet, friction must occur due to the motion of the composite against the contacting surface which transmits the forming force. In the case of diaphragm forming, friction occurs between the composite and diaphragm, and between the diaphragm and tool surface. The study of this type of

TABLE 5.3 Inter-ply slip power-law model parameters for APC-2 Material: APC-2 rs = 1.0 + 28.708V~ i

ry

k

n

Conditions

1 2 3

1.0 0.95+(1.28 e-3)(P) 1.0 2.4

28.708 28.639+ 31.143 (log P) 28.708 79.14

-2.01 +(7.33 e-3)(T) 0.1635 + 0.3079 (log P) 0.8152 0.4471

360~ 190~

arrow diagram showing approximately one quarter of it is shown in fig. 6.27. Using a combination of coarse and fine grids in the flange and buckled areas respectively, a plane strain deformation transverse to the surface direction is evident under the punch nose, which indicates thinning and fibre bundle separation. This is not consistent with the deformation of a woven fabric and when such localised strain occurs in metallic sheets, it leads to tensile instability. This is a direct result of strain suppression along the length of the defect [18] and in this case the surface fibres provide an inextensible constraint which permits the defect to develop. For the same dome another interesting feature becomes apparent when out-ofplane sheet buckling is investigated. Figure 6.26 clearly shows that the extent of buckling increases with the forming speed. Furthermore, though the strain magnitudes are not very large compared to other buckle-free specimens studied [17], a large jump in compressive strain is evident where the buckling has occurred. Thus gross buckling can be linked to the strain gradient not the magnitude of strain alone. This is believed to be the case because the stress magnitude is dependent on strain rate which is reflected by the strain gradient. It becomes more obvious from fig. 6.28 where the strain contour map is shown for the same quarter. A similar but more

240

T.A. M a r t i n et al.

Fig. 6.26. 175-mm square Plytron blanks formed at varying speeds: (a) 2.5 mm/min, (b) 12.5 mm/min, (c) 50 mm/min; temperature = 175~ [17].

explicit example is shown by the same researchers while forming a dome in a carbon fibre/PEK laminate with long discontinuous fibres (LDF) of [4-45]4 s fibre architecture [14]. A digitised mesh plot of the surface of a 112.5 x 175 mm LDF sheet after forming is shown in fig. 6.29. The wrinkles in the direction off-axis to the fibres are evident in this diagram and the corresponding arrow diagram is shown in fig. 6.30. As expected, close to the hemispherical indentation large tensile strains directed towards the centre of the punch are accompanied by compressive strains. It is interesting to note that because the 45 ~ fibre direction does not represent a plane of geometric symmetry in this blank, the degree of deformation in short sides exceeds that in the longer side of the blank. Again the buckles coincide with the regions of high strain gradients. Although the strain magnitudes are much smaller near the indentation on the long side, the strain gradients are higher as is evident from the

Grid strain

analysis

241

surface fibre direction ._

Jr

,,,r

~ -~

§ ~

x

§

.+..~

+

~

.-/-..+.

§

'r

.+,

§

o

It

+

'F

!

"1,

!

%

',0,

I

9

'q'. ip

o

9

,

nnunn Fig. 6.27. Arrow diagram for one-quarter of 175-mm square Plytron sheet after forming at a speed of 12.5 mm/min, temperature = 175~ Elmax-- 17%, E 2 m a x - - - 1 6 . 5 % [17].

strain contour map (fig. 6.31). Interestingly the buckling is also reported to take place first in this region. 6.8. Concluding remarks 9 The grid (large) strain analysis technique provides a snapshot of the deformation process, which illustrates the characteristic surface strains generated during the forming of fibre-reinforced composite sheets. 9 Fibres behave as inextensible constraints and dominate the deformation process. A laminate with two directions of fibre reinforcement seems to behave like a bidirectional woven fabric when formed into a die. If this is the case, over the majority of the sheet the principal strain directions must change during forming as the fibres rotate. The knowledge of such deformation paths becomes important for calculating the resulting stress magnitudes but has no effect on the strain results.

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20 kPa < P < 400 kPa 0~ < 0 < 9 0 ~ 0 mm/s < s < 0.5 mm/s where s is the slip velocity, P is the normal pressure, T is the forming temperature, and 0 is the difference in fibre angles between contacting plies. The normal pressure is equivalent to t u . The finite element implementation of the model was evaluated as follows. The model lay-up consisted of two flat plies (see fig. 7.69), the lower one was fully constrained on the bottom, the upper one was subjected to uniform normal and shearing stresses on top. The resulting flows were simple shear flows. The nodal slip velocity along the inter-ply contact interface was compared to the applied shear stress. The slip velocity s was found by subtracting the velocity at the contact nodes on the lower ply from the velocity at the corresponding contact nodes on the upper ply. The cr13 stress distribution was not completely uniform throughout the model because of the tendency of the plies to "bend" slightly, a consequence of the fact that it is not possible to implement perfectly the incompressiblilty and fibre inextensibility constraints. Because of this, the cr33 stress distribution along the inter-ply contact interface resulted in negative values for P. It was necessary to average the normal pressure over the contact interface in order to calculate the contact tangential stress, on account of the log(P) terms in eq. (7.57). This was possible in this case because of the simple geometry of the problem. In a more complex problem eq. (7.57) would have to be recast in order to calculate the contact tangential stress from the normal pressure at each individual contact node. Figure 7.73 shows a comparison between the results from the finite element formulation and the analytical curves given by eq. (7.57). The agreement is excellent.

7.8. Conclusions of plane deformation analysis A plane strain finite element formulation has been developed to model sheet forming of single-curvature composite shapes. Numerical analysis of single-ply and multi-ply forming was demonstrated for the initial time step. Each composite

316

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uniform pressure 12 kPa

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ply was modelled as a transversely isotropic incompressible Newtonian fluid, with a single direction of inextensibility. These restrictive kinematic conditions were implemented correctly using a mixed penalty method. An experimentally determined lubricated friction law, incorporating rate effects and yielding behaviour, was implemented between the plies and used to model the

318

C.M. 0 BrSdaigh et al.

first step in forming a multi-ply laminate. Future work will include development of geometry updating and tool contact algorithms, in order to fully simulate the composite sheet forming process. Acknowledgements

The authors would like to acknowledge the European Commission, who supported much of this work through Brite-EuRam Contract No. BE-93-5092, as well as the collaboration of our industrial and academic partners and the Center for Composite Materials, University of Delaware, USA. Also, our appreciation is due to the staff of the Department of Mechanical Engineering at University College Galway for their assistance with the experimental work, and to Eoin Simon and Gary Fahey for their help with the manuscript. Nomenclature a

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nth time step A r b i t r a r y tension stress Discretized tension stress Velocity vector Discretized velocity vector Virtual velocity vector C o m p o n e n t s o f fixed Cartesian axes Penalty n u m b e r Fibre tension penalty n u m b e r Pressure penalty n u m b e r K r o n e c k e r delta function N o r m a l contact penalty n u m b e r Tangential contact penalty n u m b e r Velocity vector Fibre tension vector Pressure vector Traction boundary Strain rate vector Virtual strain rate vector Isotropic d i a p h r a g m viscosity C o m p o s i t e longitudinal shear viscosity C o m p o s i t e transverse shear viscosity Fibre orientation angle Stress tensor Material p r o p e r t y function Problem domain

References [1] 6 Brfidaigh, C.M., "Sheet Forming of Composite Materials", Chapter 13, Flow and Rheology in Polymer Composites Manufacturing, Volume 10 of Book Series: Composite Materials. Editor: S.G. Advani, Elsevier Science Publishers, Amsterdam, 1994. [2] Cogswell, F.N., Thermoplastic Aromatic Polymer Composites, Butterworth-Heinemann Ltd., Oxford, 1992. [3] Klenner, J. and Brandis, H., "The Production of Non-Developable Composite Aircraft Structures", Proceedings of Third International Conference on Automated Composites, ICAC'91, Amsterdam, October 1991. [4] Gysin, H.J., "Mechanical Parts Made of Thermoplastic Matrix Composites", Proceedings of the 3rd International Conference on "Flow Processes in Composite Materials", University College Galway, July 1994. [5] O Brfidaigh, C.M., Pipes, R.B and Mallon, P.J., "Issues in Diaphragm Forming of Advanced Composites", Polymer Composites, Vol. 12, No. 4, August 1991, pp. 246-256 [6] Pickett, A.K., Queckb6rner, T., De Luca, P., and Hang, E., "An Explicit Finite Element Solution for the Forming Prediction of Continuous Fibre Reinforced Thermoplastic Sheets", Composites Manufacturing, Vol. 6, No. 3-4, pp. 237, 1995. [7] European Commisssion Brite-EuRam Contract BE-5092, 1992, "Industrial Press Forming of Continuous Fibre Reinforced Thermoplastic Sheets and the Development of Numerical Simulation Tools".

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[8] 6 Brfidaigh, C.M. and Pipes, R.B., "A Finite Element Formulation for Highly-Anisotropic Incompressible Elastic Solids", International Journal for Numerical Methods in Engineering, Vol. 33, 1992, pp. 1573-1596. [9] 6 Br/tdaigh, C.M. and Pipes, R.B., "Finite Element Analysis of Composite Sheet-Forming Processes", Composites Manufacturing, Vol. 2, Nos. 3 & 4, 1991, pp. 161-170. [10] 6 Brfidaigh, C.M., McGuinness, G.B. and Pipes, R.B., "Numerical Analysis of Stresses and Deformations in Composite Materials Sheet Forming: Central Indentation of a Circular Sheet", Composites Manufacturing, Vol. 4, No. 2, 1993, pp. 67-83. [11] McGuinness, G.B. and 6 Brfidaigh, C.M., "Effect of Preform Shape on Buckling of Quasi-Isotropic Thermoplastic Composite Laminates during Sheet Forming", Composites Manufacturing, Vol. 6, Nos. 3-4, 1995, pp. 269-280. [12] McEntee, S.P. and 6 Brfidaigh, C.M., "Numerical Modelling of Single-Curvature Composites SheetForming", Proceedings of the ASME Materials Division, MD-Vol. 69-2, IMECE, pp. 1119-1132, 1995. [13] Cattanach, J.B. and Cogswell, F.N., "Processing with Aromatic Polymer Composites", Developments in Reinforced Plastics, Editor: G. Pritchard, Applied Science Publishers, 1986, pp. 1-38. [14] Soil, W.E. and Gutowski, T.G., "Forming Thermoplastic Composite Parts", SAMPE Journal, Vol. 24, No. 3, pp. 15-19, 1988. [15] Cakmak, M. and Dutta, A., "Instrumented Thermoforming of Advanced Thermoplastic Composites. II: Dynamics of Double Curvature Part Formation from PEEK/Carbon Fibre Prepreg Tapes", Polymer Composites, Vol. 12, No. 5, pp. 338-353, 1991. [16] Okine, R.K., "Analysis of Forming Parts from Advanced Thermoplastic Composite Sheet Materials", Journal of Thermoplastic Composite Materials, Vol. 2, No.I, pp. 50-76, 1989. [17] VanWest, B.P., Pipes, R.B., Keefe, M. and Advani, S.G., "The Draping and Consolidation of Commingled Fabrics", Composites Manufacturing, Vol. 2, No. 1, pp. 10-22, 1991. [18] Bergsma, O.K. and Huisman, J., "Deep Drawing of Fabric Reinforced Thermoplastics", Proceedings of CADCOMP '88, Editor: C.A. Brebbia, Computational Mechanics Publications, Springer-Verlag, Berlin, 1988. [19] Gutowski, T.G., Hoult, D., Dillon, G. and Gonzalez-Zugasti, J., "Differential Geometry and the Forming of Aligned Fibre Composites", Composites Manufacturing, Vol. 2, No. 3/4, pp. 147-152, 1991. [20] Gutowski, T.G., Dillon, G., Chey, S. and Li, H., "Laminate Wrinkling Scaling Laws for Ideal Composites", Composites Manufacturing, Vol. 6, Nos. 3/4, pp. 123-135, 1995. [21] Tam, A.S. and Gutowski, T.G., "Ply-Slip during the Forming of Thermoplastic Composite Parts", Journal of Composite Materials, Vol. 23, pp. 587-605, 1989. [22] Talbot, M.F. and Miller, A.K., "A Model for Laminate Bending under Arbitrary Curvature Distribution and Extensive Interlaminar Sliding", Polymer Composites Vol. 11, No. 6, pp. 387397, 1990. [24] Spencer, A.J.M., Deformation of Fibre-Reinforced Materials, Clarendon Press, Oxford, 1972. [25] Rogers, T.G., 1989, "Rheological Characterisation of Anisotropic Materials", Composites, Vol. 20, No. 1, pp. 21-27. [26] Hull, B.D., Rogers, T.G., and Spencer, A.J.M., "Theoretical Analysis of Forming Flows of Continuous-Fibre-Resin Systems", Flow and Rheology in Polymer Composites Manufacturing, Editor: S.G. Advani, Elsevier Science Publishers, Amsterdam, pp. 203-256, 1994. [27] Rogers, T.G. and O'Neill, J.M., "Theoretical Analysis of Forming Flows of Fibre Reinforced Composites", Composites Manufacturing,, Vol. 2, No. 3/4, pp.153-160, 1991. [28] Golden, K., Rogers, T.G. and Spencer, A.J.M., "Forming Kinematics of Continuous Fibre Reinforced Laminates", Composites Manufacturing, Vol. 2, No. 3/4, pp. 267-278, 1991. [29] Tucker, C.L., "Sheet Forming of Composite Materials", Advanced Composites Manufacturing, Editor: T.G. Gutowski, John Wiley, New York, 1997. [30] Thompson, E.G., Wood, R.D., Zienkiewicz O.C. and Samuelsson, A. (Eds), Numerical Methods in Industrial Forming Processes, Numiform 89, Fort Collins, CO, June 1989, A.A. Balkema, Rotterdam, 1989.


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[31] Scherer, R., Zahlan, N., and Friedrich, K., 1990, "Modelling the Interply Slip Process during Thermoforming of Thermoplastic Composites Using Finite Element Analysis", Proceedings of CADCOMP '90, Brussels, Belgium, pp. 39-52 [32] Beaussart, A., Pipes, R.B. and Okine, R.K., "Modeling of Sheet Forming Processes for Thermoplastic Composites", Proceedings of CADCOMP '92, Editor: S.G. Advani et al., Computational Mechanics Publications, Southampton, 1992. [33] Simacek, P., Kaliakin, V.N. and Pipes, R.B., "Pathologies Associated with the Numerical Analysis of Hyper-Anisotropic Materials", International Journal for Numerical Methods in Engineering, Vol. 36, pp. 3487-4508, 1993. [34] Simacek, P., "Numerical Modelling of the Sheet-Forming Process", PhD Dissertation, Department of Mechanical Engineering, University of Delaware, 1994. [35] Pipkin, A.C. and Rogers, T.G.,"Plane Deformations of Incompressible Fiber-Reinforced Materials", Journal of Applied Mechanics, Vol. 38, pp. 634-640, 1971. [36] ICI Fibreite Data Sheet 5, Fabricating with APC-2 Composites. Fiberite Corporation, 1986 [37] Groves, D.J. and Stocks, D.M., "Rheology of Thermoplastic-Carbon Fibre Composites in the Elastic and Viscoelastic States", Composites Manufacturing, Vol. 2, No. 3/4, pp. 179-184, 1991. [38] Scobbo, J.J. and Nakajima, N., "Dynamic Mechanical Analysis of Thermoplastic Composites and Resins", Polymer Composites, Vol. 12, No. 2, pp. 102-107, 1991. [39] Kaprielian, P.V. and Rogers, T.G., "Determination of the Shear Modulii of Fibre-Reinforced Materials by Centred and Off-Centred Torsion", Proceedings of the 34th SAMPE International Symposium,1989. [40] McGuinness, G.B., Canavan, R.A., Nestor, T.A. and 6 Brfidaigh, C.M., "A Picture-Frame Intraply Shearing Test for Sheet-Forming of Composite Materials", Proceedings of the ASME Materials Division, MD-Vol. 69-2, IMECE, pp. 1107-1118, 1995. [41] McGuinness, G.B. and 6 Brfidaigh, C.M., "Characterisation of the Processing Behaviour of Unidirectional Continuous Fibre Reinforced Thermoplastic Sheets", Proceedings of 4th International Conference on "Flow Processes in Composite Materials', University of Wales, Aberystwyth, September 1996. [42] 6 Brfidaigh, C.M. and Pipes, R.B., "A Punch Deformation Experiment for Sheet Forming of Thermoplastic Composites", Proceedings of International Conference on Automated Composites (ICAC '91), The Hague, Netherlands, 1991. [43] Monaghan, M.R. and Mallon, P.J., "Study of the Mechanical Behaviour of Diaphragm Films", Composites Manufacturing, Vol. 2, No. 3/4, pp.197-202, 1991. [44] Tadmor, Z. and Gogos, C.G., Principles of Polymer Processing, John Wiley and Sons, New York, 1979. [45] Zienkiewicz, O.C. and Taylor, R.L., The Finite Element Method, 4th Edition, Vol. 1, McGraw-Hill, London, 1989. [46] 6 Brfidaigh, C.M., "Analysis and Experiments in Diaphragm Forming of Continuous Fibre Reinforced Thermoplastics", PhD Dissertation, Department of Mechanical Engineering, University of Delaware, 1991. [47] McGuinness, G.B. and 6 Brfidaigh, C.M., "Finite Element Analysis of a Thermoplastic Composite Sheet Forming Process", Proceedings of the Irish Materials Forum Conference (IMF-8), University College Dublin, Sept. 1992. [48] Monaghan, M.R., 6 Brfidaigh, C.M., Mallon, P.J. and Pipes, R.B., "The Effect of Diaphragm Stiffness on the Quality of Diaphragm Formed Thermoplastic Composite Components", Journal of Thermoplastic Composite Materials, Vol. 3, July 1990, pp. 202-215. [49] Murtagh, A.M., "Characterisation of Shearing and Frictional Behaviour in Sheetforming of Thermoplastic Composites", Ph.D. Dissertation, Department of Mechanical and Aeronautical Engineering, University of Limerick, Ireland, 1995. [50] Monaghan, M.R. and Mallon, P.J., "Development of a Computer Controlled Autoclave for Forming Thermoplastic Composites", Composites Manufacturing, Vol. 1, No. 1, pp. 8-14. [51] Upilex Product Data Sheet. UBE Industries, Tokyo, Japan, 1987. [52] Martin, T.A., Bhattacharyya, D., and Collins, I.F., 1995, "Bending of Fibre-Reinforced Thermoplastic Sheets", Composites Manufacturing, Vol. 6, No. 3/4, pp. 177-187, 1995.

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[53] Murtagh, A.M., Monaghan, M.R., Mallon, P.J., "Investigation of the Interply Slip Process in Continuous Fibre Thermoplastic Composites", Proceedings of the Ninth International Conference on Composite Materials (ICCM-9), Madrid, July 1993. [54] Kaprielian, P.V., and O'Neill, J.M., "Shearing Flow of Highly Anisotropic Laminated Composites", Composites, Vol. 20, No. l, pp. 43-47, 1989. [55] Rogers, T.G., and Pipkin, A.C., "Small Deflections of Fibre-Reinforced Beams or Slabs", Journal of Applied Mechanics, Vol. 38, pp. 1047-1048, 1971. [56] Laursen, T.A., and Simo, J.C., "A Continuum-Based Finite Element Formulation for the Implicit Solution of Multibody, Large Deformation Frictional Contact Problems", International Journal for Numerical Methods in Engineering, Vol.36, pp. 3451-3485, 1993. [57] Coffin, D. W., "Flange-Wrinkling and the Deep-Drawing of Thermoplastic Composite Sheets", PhD Dissertation, Department of Mechanical Engineering, University of Delaware, 1993.


Chapter 8

Rheology of Long Fiber-Reinforced Composites in Sheet Forming S.G. ADVANI,

T.S. C R E A S Y *

and S.F. S H U L E R t

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA

Contents Abstract 324 8.1. Introduction 324 8.1.1. Sheet forming philosophy 325 8.1.2. Processing methods 327 8.1.3. Materials 327 8.2. Rheological properties 329 8.2.1. Unfilled polymer melts 329 8.2.1.1. Viscosity and relaxation phenomena in shear flows 329 8.2.1.2. Viscosity in elongational flows 336 8.2.2. Filled viscous fluids 338 8.2.2.1. Viscosity and relaxation in shear flows 339 8.2.2.2. Viscosity in elongational flows 343 8.3. Rheological measurement techniques 348 8.3.1. Standard techniques 348 8.3.1.1. Rotational viscometers 348 8.3.1.2. Capillary flow 350 8.3.1.3. Use with filled polymers 351 8.3.2. Non-conventional apparatus 352 8.3.2.1. Shear viscosity 353 8.3.2.2. Elongational viscosity 354 8.4. Why the rheological properties are important and how to use them in sheet forming 8.4.1. Mechanisms 356 8.4.2. Important properties 357 8.4.3. Resin percolation 357 8.4.4. Transverse squeezing flow 358 8.4.5. Axial intra-ply shear deformation 361 8.4.6. Inter-ply shear deformation 362 8.4.7. Extensional flow 364 8.4.8. The importance of rheological parameters to thermoforming 364 8.5. Outlook 366 References 367 * Currently at University of Southern California, Los Angeles, CA, USA. t Currently at General Electric Co., Pittsfield, MA, USA. 323

356

324

S.G. Advani et al.

Abstract

This chapter introduces the reader to sheet forming philosophy, processing methods, and the materials applied to produce thermoformed components. Rheological properties that must be understood are introduced first for unfilled polymer melts by discussing viscosity and relaxation phenomena in shear and elongational flows. With this foundation we present the same properties for filled viscous fluids and we show the sometimes surprising results such as shear thickening. Filler aspect ratio affects shear and elongation phenomena; this presentation shows these effects and lists the theories developed to account for the filler/matrix interactions. Following the background material, the section on rheological measurement techniques discusses standard techniques for unfilled materials (rotational and capillary flow viscometers) and their limited use with filled polymers. The presented nonconventional apparatus (linear, squeeze flow and elongational viscometers) reveal the scale issues involved in measuring rheological properties of thermoforming systems. The chapter concludes by considering why the rheological properties are important and how to use them in sheet forming. Mechanisms that affect forming flows (resin percolation, transverse squeezing flow, axial intra-ply shear deformation, inter-ply shear deformation extensional flow) show the complexity of the process. Finally, we deliberate the outlook for application of thermoforming and improvement of the knowledge base of system behavior. 8.1. Introduction

Although the enhanced performance characteristics of collimated fiber composite materials are widely acclaimed, an obstacle limiting the utilization of advanced composites has been the historic manufacturing difficulty. Traditional composite manufacturing methods are often labor-intensive, slow and difficult to control precisely. One basic strategy in composite processing is to pre-impregnate the fiber tape or tow preform, assemble it into a multiaxial laminate, conform it to a curvilinear tool surface and then subject it to thermal and pressure cycles sufficient for crosslinking cure of the thermoset polymeric matrix. This is typical of thermoset filament winding, matched die molding and autoclave processing techniques. Another composite processing strategy is to impregnate, shape and consolidate the fibers, and cure the resin in one step. This occurs in pultrusion and the liquid composite molding processes of resin transfer molding (RTM) [1] and reaction injection molding (RIM). The processing difficulty and rate-limiting step associated with these processing techniques surrounds the need to control the cross-linking chemistry of the thermoset matrix. The use of high-temperature thermoplastic polymers in the composite preforms presents an opportunity to develop faster, lower-cost manufacturing methods. Heated to forming temperatures, thermoplastic polymers undergo a reversible phase change from solid to liquid allowing them to be formed in ways similar to conventional materials. This offers potential automated manufacturing using processes such as tape laying, pultrusion and sheet forming [2] and eliminates the need

Rheology of longfiber-reinforced composites

325

for expensive autoclaving equipment. The thermoplastic matrix can be rapidly hardened after forming simply by cooling. Reduced forming cycle times are possible due to the absence of a time-consuming cross-linking step. Sheet stamping is a well established and widely used process in the sheet metal forming industry. Its counterpart in composite sheet forming is a promising processing technique for thermoplastic matrix composite part manufacture [3]. The basic material form used in thermoplastic composite sheet forming consists of individual plies of either randomly placed short fibers or long aligned fibers imbedded in a thermoplastic matrix. The individual lamina can be stacked to form multiaxial laminates ranging from uniaxial to quasi-isotropic form. With such material precursors increased forming cycles are possible since the thermoplastic, which controls the forming characteristics, can be heated and cooled rapidly. One obstacle faced in forming these advanced thermoplastic composite material systems is the lack of extendibility of the reinforcing fibers. While random short fiber systems offer excellent formability they lack the superior directional properties desired in advanced composites. The enhanced mechanical properties achieved by using continuous aligned fiber reinforcement comes at the expense of material inextendibility in the fiber direction during forming. Extendibility in the fiber direction can be obtained by introducing breaks along the individual fiber lengths. The resulting aligned long discontinuous fiber reinforcement provides enhanced formability in multiaxial sheets with little loss in final mechanical properties [4]. The objective of this chapter is the description of important non-linear rheological effects associated with the sheet forming of thermoplastic-matrix fiber-reinforced sheets near the melt temperature of the polymer. The particular material forms considered are multiaxial thermoplastic matrix laminates containing high concentrations of aligned, collimated continuous and discontinuous fiber reinforcement. We begin with a summary of properties basic to sheet-formable composites and the various basic sheet forming methods. Next is a review of the rheological properties of both viscous fluids and viscous fluids filled with long fibers. What follows is a review of various standard rheological measurement techniques and the problems encountered when using conventional measurement techniques with these composite materials. Finally, there is a discussion of how the rheological properties are important in fiber-reinforced thermoplastic composite sheet forming. Insight into the forming mechanics and material flow behavior is necessary to predict the geometry and fiber structure of finished parts. Knowledge concerning the material flow behavior will ultimately assist in the prediction of properties and performance of formed parts and facilitate the development of low-cost conventional forming methods vital to increasing the market for advanced composites.

8.1.1. Sheet forming philosophy Composite sheet forming is a process well suited for the forming and shaping of thermoplastic matrix short and long fiber-reinforced composites. The material preform is non-reinforced or reinforced with uni-directional or multiaxial fibers in a sheet and can be either in stacked or pre-consolidated form. Sheet forming starts

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with heating the preform to its forming temperature, defined as the temperature where the viscosity of the resin is low enough to allow the fibers to slide relative to one another and permit easy shaping of the sheet. Then either mechanical or hydraulic pressure forms the sheet over a curvilinear tool surface. The forming step is analogous to several common sheet metal bending and forming operations and includes deformation of the sheet both in and out of the plane. This material flow is highly viscous (the viscosity may be 7 to 12 orders of magnitude greater than that of water) and is characterized by the flow of both resin and fibers together. This chapter will focus on this aspect of the process and discuss methods of measuring some transient rheological properties. After the forming step is complete consolidation pressure remains on the part until it cools. Once sufficiently cooled, the part is removed from the tool surface and, if required, a final edge-trimming step is performed. If needed the reversible solid-liquid phase change characteristic of thermoplastics enables the once formed part to be transferred to another tool surface and repeatedly reformed or incrementally formed until the final desired geometry results. The oldest form of sheet forming, also known as thermoforming, exists with the processing of non-reinforced thermoplastic sheets. Isotropic in nature, the sheets are usually held along their edges over a tool surface and brought up to their material softening temperature. This is usually somewhere slightly below the actual melt temperature to work the material while in a compliant but not liquid state. Common forming methods are "hot stamping" the sheet between matching dies and "vacuum forming" where a vacuum drawn through small holes in the tool face pulls the sheet down and spreads the sheet over the surface. The processing science for long and short fiber-reinforced thermoplastic sheets grew out of a need for large parts with strength and stiffness higher than nonreinforced sheets. Faster processing cycle times than those for thermoset-matrix composites were required also. Besides faster forming cycles, thermoplastics have more flexible processing parameters since the viscosity is a function of temperature not of cross-linking as in thermosets. As previously mentioned, the ability to remold and reshape thermoplastics can be an advantage to using thermoplastic sheet formed parts over similar thermoset parts. Sheet formed parts also have the potential to reduce the total part count in a structure by molding in and incorporating reinforced areas. Common reinforced thermoplastic processing methods are injection molding, pultrusion and tape laying. The sheet forming process holds several unique advantages over each of these methods. The nature of injection molding combined with the high viscosity of the thermoplastic precludes the use of high aspect ratio fibers (> 1,000) that provide the necessary mechanical properties desired in high-performance applications. Also, it is difficult to make large parts by injection molding. Sheet forming provides greater control over and ability to predict the final fiber architecture. Thermoplastic pultrusion solves this by providing continuous fiber reinforcement in one direction. Still, it would be difficult to pultrude parts of any great width or net shape and multiaxial laminates would not be possible. Finally, thermoplastic tape laying permits precise long fiber placement within large multiaxial and even axisymmetric parts, however, the process cycle times are much longer than for sheet formed


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parts. Why has sheet forming not become the manufacturing method of choice? The main hurdle may be the combination of the directional properties and the inextendibility of the fibers that may lead to instabilities in the process. Better understanding of the material deformation behavior during the forming process can help manufacturing engineers design the tool and processing conditions to avoid the instabilities. 8.1.2. Processing methods

The major composite sheet forming processing methods can be broadly classified as hot stamping, diaphragm forming, and incremental processing. Composite sheet stamping or matched-die press forming imitates the stamping methods employed in the field of sheet metal forming as a high-volume, low-cost manufacturing process. The heated composite blank is pressed against the tool surface. A variation on this is rubber tool stamping where the sides of the die are compliant. In the case of tool misalignment this helps maintain an even consolidation pressure across the part. In diaphragm forming two disposable plastically deformable diaphragms of either superplastic aluminum or polyimide polymer hold the blank between them. During the forming cycle the diaphragms have their edges clamped, they heat up with the blank and the sandwich is deformed by air pressure toward the tool surface. The diaphragms serve to hold the blank in tension and prevent fiber buckling that can occur under compressive stresses. When forming parts containing continuous fiber reinforcement the diaphragms are clamped but the blank cannot be. This is due to the inextendibility of the fiber reinforcement. Hydroforming is a process similar to diaphragm forming where hydraulic fluid provides the pressure behind a permanent rubber diaphragm. Incremental processing enables the forming of large structures using smaller, lower-cost fabricating equipment. After the usual heating and forming steps there is an additional part transfer step added to the forming cycle. Incremental forming produces final shapes that would be difficult otherwise. Stock shapes can be produced and later incrementally formed into custom configurations. One promising incremental forming method is stretch forming. Stretch forming makes exclusive use of aligned long discontinuous fiber-reinforcement technology. As the name implies an extensional mode of deformation in the fiber direction is enlisted during the forming. Since the fibers are discontinuous the composite sheets may be locally heated and deformed. This allows certain incremental forming techniques not possible with continuous fiber-reinforced materials. For example, linear beams can be stretch formed into curved sections with favorable mechanical properties since the fibers follow the curvature of the beam [5]. The key to successful stretch forming is precise control over the final fiber placement. This is achieved by clamping both ends of the uniformed part, heating up the portion between the clamps and then carefully forming the stock shape to the desired curvature [6]. 8.1.3. Materials

The basic materials consist of the polymer matrix and the reinforcing fibers, which may be continuous or discontinuous. Thermoplastic matrix polymers are the

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common constituent in all sheet-formable composite structures. The difference between thermoplastic and thermoset polymers is the lack of cross-links in thermoplastics. This results in the ability of thermoplastics to be heated and reshaped repeatedly. Their higher initial viscosity makes thermoplastic polymers more difficult to process than thermosets. But the multistep processing and cross-linking necessary in thermosets can be time-consuming. An additional processing advantage associated with the use of thermoplastic matrix polymers is their infinite shelf life at room temperature. This significantly eases composite preform storage in contrast to thermoset matrix polymers that require constant refrigeration. Thermoplastic polymers also offer the mechanical properties of toughness, good adhesion to the fibers, wear resistance and environmental resistance. The high-temperature thermal properties of thermoplastics are inferior to those of thermosets; however, advanced thermoplastics such as polyetheretherketone (PEEK) and polyetherketoneketone (PEKK) have working temperature ranges than can make them competitive. Other thermoplastic matrix polymers of interest are polyphenylenenesulphide (PPS), polyethersulphone (PES), polyamide (PA), polyetherimide (PEI) and polypropylene (PP) [7]. The reinforcing fibers provide the high strength and stiffness to the composite. The desired fiber properties in a composite are stiffness, strength, low density, environmental resistance and a resistance to temperatures encountered during the processing cycles. The reinforcing fibers utilized in sheet-formable composites include organic fibers (Kevlar), inorganic fibers (glass) and carbon fibers (AS4). Besides determining the final mechanical properties of the composite, the fibers, particularly long fibers, serve to dictate the overall flow of the sheet blank during forming. Although random short fiber-reinforced composites have good forming characteristics they lack the high directional properties of aligned long fiber reinforcement. This tradeoff goes both ways since part complexity is limited by the movement capability of the fiber reinforcement during forming. Aligned long discontinuous fiber reinforcement offers improved forming behavior since it allows for an extensional mode of deformation in the fiber direction. It is important to combine the selected matrix and fiber components into material preforms that are easy to handle and are suitable for forming into structures. The most common preforms exist with the fiber reinforcement preimpregnated with the matrix to form a "prepreg". Any forming process must occur above the melt temperature of the matrix polymer. At these elevated temperatures oxygen may interact with the matrix and fiber surfaces. Oxidation reactions can affect the matrix/fiber surface adhesion and in turn affect the mechanical properties of the composite. By preimpregnating the fiber reinforcement before the actual forming process takes place extended time at high temperature can be avoided. The general classifications of composite sheet preforms are woven fabrics, unidirectional plies or tapes, and random short fiber sheets. Additionally, individual plies may be stacked to form multi-ply and multi-angle laminates. One widely used perform is prepreg uniaxial continuous fiber-reinforced tape. This preform's advantages include simple storage and handling, easy cutting and placement to construct multi-angle laminates with specific fiber orientations, and rapid forming ability. Forming is rapid since the tape only needs to be melted and fused at a low pressure


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to form the final structure. The reinforcing fiber geometry and orientation within the preform determine both the forming behavior of the sheet and its final mechanical properties.

8.2. Rheological properties The deformation behavior or the fluid dynamics of polymeric melts can be described by a set of rheological properties called material functions. These functions describe the manner in which the fluid response changes as a function of the flow conditions imposed upon the melt. These conditions can be the applied strain rate (y for shear, k for elongation) or the applied stress ('gyx for shear, rxx for normal stress causing elongational flow). Material functions can be defined under both steady state conditions and as transient functions with time as an additional parameter. The transient functions should approach the steady functions for large times under steady applied strain rate or stress. Deformation behavior of Newtonian materials can be defined by one material function called the viscosity. For non-Newtonian materials more than one material function is necessary as the melt may be shear thinning and visco-elastic, and may exhibit time-dependent behavior. For more details see chapter 3 of Bird et al. [8]. In this section we present important material functions to describe some steady and transient rheological properties. These functions can then be compared with the flow phenomena of filled melts to show the change from unfilled melt behavior. This will show that, in addition to an expected increase in the viscosity, fillers also can perturb local flows with unexpected results.

8.2.1. Unfilled polymer melts The material functions for unfilled polymer melts or neat fluids provide a good basis for understanding complex melts. The two most important flow fields investigated are shear flow, and elongational flow, as most deformations can be expressed as a combination of these two flow fields.

8.2.1.1. Viscosity and relaxation phenomena in shear flows Steady-state shearing viscosity, ~/s, is the most basic material function used to quantify the flow of a fluid. The flow condition used to define r/s is conceptually simple and called planar Couette flow [9]. Figure 8.1 illustrates the flow velocity profile for a layer of fluid in simple shear between two parallel plates. The top plate moves with a constant velocity, U, while the bottom plate remains fixed. The analysis assumes a "no-slip" boundary condition is at each plate. Thus the fluid elements touching the surface of the plate remain fixed to the plate and keep the same position with respect to the plate always. The resulting velocity profile is linear and is proportional to the height above the fixed lower plate as given by the relation OVx Vx - -~y y

(8.1)

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Fig. 8.1. Simple flow of a fluid layer between two plates. (a) Couette flow geometry. (b) Stress on a fluid element.

where the velocity gradient OVx/Oy - ~)yx, the shear strain rate in the fluid. The shear stress, ryx, is proportional to the applied f/yx as expressed by the relevant relationship "gyx = OSf/yx

(8.2)

Thus the steady shear viscosity relates the shear stress to the shear strain rate. Note that r/s is not necessarily a constant. The nature of dependence of r/s on i/yx classifies the fluid as either Newtonian (no dependence) or non-Newtonian. If nonNewtonian, r/s may be function of strain rate for inelastic fluids and may exhibit time-dependent behavior for a visco-elastic melt. Stress relaxation following shear flow is the decay of the steady ryx that occurs when the applied ~ stops. This material function is noted as ry-~,where the minus sign indicates a decreasing function of time. This function is by definition a transient response of the fluid and it will be discussed with other transients. We will start by describing the Newtonian fluid. For Newtonian fluids the shear stress in the fluid is proportional to the shear strain rate through the relationship [9] -

.;,yx

(8.3)

where/z, defined as the Newtonian viscosity, replaces the more general r/s. For a Newtonian fluid,/z is a single constant value for any ~'yx. Newtonian fluids have a simple molecular structure with interactions between molecules over short distances. The fluids of interest in sheet forming are usually non-Newtonian polymer melts, which may be neat or particle-filled. For these complex fluids the entanglement of the polymer macromolecules produces a rate dependence of the steady viscosity [8]. Figure 8.2 illustrates the steady-state shear viscosity as Yyx increases for Newtonian, shear thinning (viscosity decreases) and shear thickening (viscosity increases) fluids. To differentiate the Newtonian from the non-Newtonian liquids /z is replaced by ~ s - ~s(fJyx) so that "ryx -~ 17S(f/yx)f/yx

(8.4)

As shown by fig. 8.2, polymer melts behave as Newtonian fluids in creeping flows, ~)yx~ 1.Osec -1, but then demonstrate "shear thinning" for large y. At decreasing

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Shear Thickening

J Inll s

Shear Thinning

Fig. 8.2. Steady shear viscosity as a function of shear strain rate.

i/yx, Os

approaches a constant value called rl0. This is the "zero shear rate viscosity" the viscosity of the fluid would have when deformed infinitely slowly. Shear thinning materials are common among polymer solutions and melts [10]. However, these melts also may exhibit visco-elasticity. Visco-elasticity can be characterized by measuring material functions such as first normal stress difference, second normal stress difference and relaxation parameters. Usually Deborah or Weissenberg number characterizes the elasticity effect in the melt [8]. The shear thinning behavior exhibited by polymer melts under steady-state conditions, rls(i/yx), can be modeled by either the power-law [11,12] or Carreau [13] relations as illustrated in fig. 8.3. In many engineering processes e.g., injection molding i/yx is high everywhere and the transition to steady-state flow occurs rapidly. For these conditions the decreasing rls region of fig. 8.2 is the only range of interest. Usually an empirical power-law relation of the form

,('-~) ~?S(~'yx) -- mryx

(8 5)

10 5

"~ _

"................. "'" ......... u ~-,~,~

I 0 Huppler 1967 IE] Dodd 1966 ] ........ Power L a w

InT1 s

_

10 0 10-4

I

I

........

!

I

I

10 2

I.t. Fig. 8.3. Steady shear viscosity as modeled by the empirical power law and Carreau relations.

S.G. Advani et al.

332

is sufficient, where m and n are the parameters used to obtain the best least-squares fit of the data on a ln-ln scale. Note that for shear thinning fluids n < 1 so that the power-law slope is negative. Once m and n are determined for a given fluid rls can be quickly calculated for any i'yx in the power-law range. Note that significant error appears when applying the power-law relation to low strain rates. Should the application need shear viscosity values for a broad range of f/yx the Carreau relation should be used. The Carreau relation provides a good description of the steady viscosity from Newtonian creeping flows to high power-law strain rates. The basic relation is r t s - 00[1 + (~.?'yx)2] (n-l)/2

(8.6)

where the new parameters are rl0 and ~. Again, 00 is the zero shear rate viscosity while ~ (with units of time) is a constant for the material. ~ adjusts the position of the "knee" in the ~s-~ curve. Here n has the same definition as in the power-law relation; it still controls the slope of the curve in the power-law region. When a Newtonian fluid at rest is set into motion in shear the shear stress moves from zero to ryx in a step function as shown in fig. 8.4. Also, as shown in the figure, when the flow stops the stress immediately drops to zero. This immediate response means that Newtonian liquids do not exhibit any memory effects. In contrast, the response of a polymeric liquid does not follow immediately the applied shear rate. This is characteristic of visco-elastic behavior. Such fluids exhibit a retardation or a stress growth phenomenon. Similarly, when the flow stops the stresses do not go back to zero instantaneously. This is relaxation. The relaxation and retardation times are characteristic of the material under consideration and are important material functions to characterize transient response. Another important transient phenomena is shear recovery. If the shear stress is removed after reaching steady state, a Newtonian fluid will not deform any further. A visco-elastic polymer will recoil before coming to a complete stop and the negative deformation is shear recovery. A purely elastic body in these conditions will exhibit a complete recovery. Hence the partial recovery can be used as a characterization transient material function. These

0 Simple Fluid D Linear Viscoelastic 9 Non-linear Viscoelastic

~

+

,

0

!:

FlowStart up -. ~ I ~

Stress R e l a x a t i o n ~

I ~~-"'-"~

Time

Fig. 8.4. Transient effects in simple shear. ?'yx is applied at t = 0. ~'yx= 0 at t = tl.


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transient material functions are important to thermoforming since the forming process involves rapid deformation and short processing times. When polymeric liquid is set into shear flow from rest it takes finite time for the fluid to reach steady state. This is the result of the visco-elasticity of the fluid. Since "gyx and r/s are now functions of both f/yx and time they usually are denoted by + 9 ryx(Yyx, t) and r/~(i/yx, t). The plus sign represents a flow begun from rest at time "zero" with " ryx + or r/s+ increasing into positive time. Given sufficient time ry+~--~ ryx and r/~ ~ r/s. Visco-elastic fluids may be classed as linear or non-linear depending on the way that ry+xrises to ryx. Figure 8.4 demonstrates stress growth for both visco-elastic fluid types. For linear visco-elastic fluids the stress grows up to the steady stress level without rising above it. A time constant relevant to the flow, usually denoted by )~1 and called the "relaxation time", is introduced as a measure of the time required to reach the steady state response of the system. The relaxation time changes the arithmetic equation (8.4) into a differential equation on stress such as the familiar Maxwell [14] equation (constant r/s) or White-Metzner [15] equation r/s(f/yx)

ry+x+ Z, 4:y+x= r/s(f/yx))yx

(8.7)

Note that this equation uses the steady shear thinning viscosity r/s(f/yx). The transient viscosity is defined by the solution to eq. (8.7): r/-~(i/yx, t)= ryx(Yyx, + " t)/i/yx. For a linear viscoelastic fluid each r/~ curve falls below the curves found at lower strain rates. The slowest strain rate curve will have the highest viscosity. The relaxation response of the linear viscoelastic fluid is different from the Newtonian liquid too. Just as ry+xrequires a finite time to reach 72yx, now ryx takes a finite time to decay to zero stress. When the flow stops the stress relaxes to zero with exponential decay of the form [10] "Cyx -- ry x e [-t/~'l]

(8.8)

where ryx represents the decaying stress, rex is the steady-state stress present when the flow stopped and Z l is the same relaxation time defined above. The above discussion has been simplified from the situation of polymer melts with a single-valued relaxation parameter ~1. Actually, the distribution of molecular weights and the variety of molecule to molecule interactions available in a polymer melt make the material respond with a distribution or spectrum of relaxation times. However, ~'1 can be used to designate the largest relaxation value present in the distribution and thereby simplifying the discussion. Some polymers also may exhibit non-linear visco-elastic response. The material functions still carry the same notation, e.g., Tyx(Yyx, + " t), it is the way in which r;+x approaches ryx that characterizes the non-linearity. At small 1) usually for ~'yx < 1/).1 - the non-linear visco-elastic fluid will act just like a linear one [16]. When f/yx grows large enough it stimulates non-linear stress growth. As fig. 8.4 shows, ry+ grows larger than ryx and then falls to reach the steady value. Also, as f/yx rises further the ratio of the peak ry+xto the steady ryx increases. The peak value of ry+xis the yield stress rYx.

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1.0

~

looo~o

0.1

+co

10,000 ;/0

0.01 0.01

Time Fig. 8.5. Transient viscosity function for a non-linear visco-elastic fluid in shear.

A set of r/~ functions for a non-linear visco-elastic fluid is presented in fig. 8.5. The slowest i/yx data forms an envelope curve that is a maximum 0~ function for the fluid. As i/yx grows each r/~ curve falls under this envelope. The steady r/s values reached at each strain rate are equivalent to the steady-state shear thinning property shown in figs. 8.2 and 8.3. The appearance of this non-linear stress growth relates to the change in the conformation of the polymer melt. At rest and without applied stress the long chain molecules reach a random entangled network, which is the preferred rest conformation. This rest conformation is depicted by the characteristic relaxation constant ,kl. When exposed to small i/yx small enough to produce linear viscoelastic response stress growth and relaxation are linear with ,k1 as the relevant parameter. That is, the rate is small enough that the melt can adjust to the flow by the same diffusion processes that allow attainment and maintenance of the rest conformation. Higher i/yx stimulates a rearrangement of the conformation. The fluid cannot accommodate the strain rate with the diffusion processes and it undergoes a conformation adjustment. The stress grows until sufficiently large to change the mechanism by which the molecules adjust to the stress. This creates a catastrophic realignment. Stress falls to ryx and becomes stable [16]. During this conformation change the relaxation constant decreases. That is, )~1 falls from its initial value to a new value called ~.'. Further, ,k' decreases as i/yx and y increase, thus, ~.' = ,k'(~, t). This impacts the stress relaxation of the fluid. Once the flow stops ryx falls initially with a time constant ~'(~, t). However the fluid can regain its original "structure" or conformation as the stress falls. Therefore ~' approaches Z l as the relaxation progresses. Figure 8.4 demonstrates the effect of this change. Initially the stress relaxes faster than that of the linear visco-elastic fluid. As ~' increases the stress relaxation is delayed such that a longer time is needed to remove the stress than taken by the linear fluid. These fluids require the use of nonlinear constitutive relations and the introduction of additional material parameters [17,181.


335

The simplest constitutive equation that has a qualitative description of non-linear fluid response is the corotational Jeffreys fluid. As presented in Bird et al. [8] the from the relation is 1: -'1- ~.1~1 -'~-1/~.1 {71 "'1: .qt_.,1:,71 /

- -

r/0171 +/~'272 +

kzl't1"~'l }]

(8.9a)

where ~ is the stress tensor, 7 is the strain tensor, rl0 is the zero shear rate viscosity, k l is the relaxation time and )'2 is the retardation time. One constraint of the model is that )~2 is always less than k l. The subscripts (1) and (2) on the stress and strain tensors are Bird's notation for the zeroth and first convected derivatives of the tensor respectively. The strain tensor and its derivatives have the following definitions: 71 - ~ / - Vv + (Vv) T 72

D -

72

~-~

-

(8.9b)

{(Vv)T'71 + 71 .(Vv)}

(8.9c)

The derivative of the stress tensor comes from 1:1

~

D ~-~1;

{(Vv)T.~ + ~.(Vv)}

(8.9d)

For situations where k2 "~,k] the model can exhibit reasonable response to simulated flows. However, as k2 approaches k l the stress-time curve begins to oscillate and the model becomes less suitable (see fig. 8.6). In this example the rate of strain tensor is

'~1-

[0,01 l

0

0 0

0 0

~,

(8.9e)

with kl = 7.85, k2 = 0 and y = 0.172 for the solid line. With k2 ~ ~.1 = 11.274 the model peaks at the same time and with the same ratio of peak stress to steady stress for ~ = 0.315. The dashed line shows the excessive oscillations that can occur for large k2. The Giesekus model provides realistic behavior for non-linear visco-elastic fluids. The form of the model used is from Bird et al. [8]:

L"~~

.

' ' ".

.

'll .. . . . .

.

.

.

~ -o .

.

.

.

t (seo) Fig. 8.6. Jeffreys fluid in simple shear.

.

.

~,2 __- ~1

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S.G. Advani et al.

(~,2)2 zl [ 17-+- ~.1171 --O~m{ 17"17}-O~2{71''~-]'17"71} -- 170 71 - ~ - ~ ' 2 7 2 - - C t ~ {]r ~ r/0 )~1

1 (8.9f)

where t~ is the parameter that determines the degree of non-linear behavior, the retardation time is ~'2 ~'~ )vl/l,000 and the other terms are defined in the Jeffreys equation. When done it shows the non-linear behavior shown in figs. 8.4 and 8.5 without the oscillations of the Jeffreys fluid.

8.2.1.2. Viscosity & elongational flows Shear viscosity is the primary material function of use in most fluid flow applications. When one turns to thermoforming, however, the elongational viscosity is also of great importance in analyzing the flow. The volume of the fluid remains constant under the assumption of the incompressibility of a fluid. The incompressibility effect renders elongation a three-dimensional flow. Therefore strain rate is expressed best in tensor notation as

~t~t-

0.5

0

0 )

o

o.5

o

0

0

-1

o oo)

o -o.5 0

~

0

Biaxial elongation

Uniaxial elongation

(8.10)

-0.5

where k is the elongational rate. Note that only the terms along the diagonal are nonzero. Thus these elongational flows are shear-free flows. Figure 8.7 shows a thermoforming sheet clamped at the edges with a greater pressure applied to its lower surface. The sheet has inflated like a bubble. An element of the sheet, also shown in fig. 8.7, deforms in biaxial elongation. The sheet stretches in x and y as it thins in z. Collecting material functions in biaxial flow is difficult.

(a) (b) Fig. 8.7. Thermoforming of fluid sheets with clamped edges in a biaxial elongation flow. (a) Inflated sheet. (b) Fluid element.

337


Most elongational tests are conducted in uni-directional elongation to simplify the procedure. Uni-directional elongation is the drawing of a fluid in one direction, say in direction x, as one would extend a solid at the strain rate k in a tensile test. Figure 8.8 presents a fluid bar extended in the x direction. Since the substance is a fluid the total possible strain is much greater than for solids in tension. For most solids the possible strains are so small that assumed constant L - L0 applies. Thus a constant k test may be conducted at a constant velocity v such that [19] 1 dL

v

---- ~ = - L dt L0

(8.11)

For fluid systems with large strains we have L - L(t). With constant velocity applied to the fluid we immediately know the form of L(t): (8.12)

L(t) - Lo + vt

Rearranging eqs. (8.11) and (8.12) yields k-

+t

and k is not constant. After integrating and rearranging eq. (8.11) one obtains k t L(t) - Lo eet

(8.13)

l n ( L / L o ) or

(8.14)

Thus, for constant k, both L and v are exponentially increasing functions of time. For constant applied v, k is a decreasing function of time for large strains. For most forming processes the strain rate will vary during the procedure. By analogy with the shear stress/shear strain rate relation in eq. (8.3) the elongational stress is

......y" ...........i"""

Fig. 8.8. Uniaxial elongation of a rectangular fluid element.

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S.G. Advani et al.

r~x = r/Ek

(8.15)

where OE is the elongational viscosity. A Newtonian fluid has a single shear viscosity defined as/z. It can be shown that there is a single value for the elongational viscosity of Newtonian fluid given by the Trouton relation 0E - 3/z

(8.16)

This equation also holds for unfilled polymer melts when ~ is small enough (creeping flow) to keep the response within the Newtonian range. In this case r/+ - 3 r / ~ . However, such strain rates are too small to be of use in a commercial process. From the discussion of transient behavior above one could easily presume that in elongation a shear thinning fluid would behave like a Newtonian liquid in creeping flows and then show greater deviation as k increases. This is correct except that the direction of the deviation is reversed. Where the shear thinning fluid has a reduced Os with increasing y, the same fluid will have an r/+ that rises above the Newtonian curve as ~ increases. Figure 8.9 shows this for a polystyrene melt [20] at 170 ~ For - 0 . 0 0 6 3 s -1 r/+ follows the Newtonian curve up to 100 s elapsed time. Then the non-Newtonian rise in ~+ occurs. As k increases the non-Newtonian performance occurs at earlier times. This phenomenon is shear hardening. In elongation the slowest ~ test forms an envelope curve, but for ~+ it is a lower bound envelope.

8.2.2. Filled viscous fluids The material functions and unfilled melt behavior discussed above are the starting point for understanding the rheology of filled polymers. To obtain the properties required of thermoformed systems the polymers must be filled with a reinforcement of particles or fibers. Volume fractions of fillers can reach 60% and the possible effect on the rheology under some flow conditions can be substantial. Filler interactions by direct contact, change in orientation or relative motion modifies the flow field. Local flows may change the material response from that expected applied flow condition. 1010

......

10 9

.

+111

0 0.0063 Q 0.02 ~ 0.063 ,o.,

108 10 7

~ " 10 6

lllll

10 5

lO-I

lOo

I I I IIIIII

lO+

lO2

I II IIIII lO,+

Seconds Fig. 8.9. Transient elongational velocity of polystyrene at 170~ [20].

Rheology of longfiber-reinforcedcomposites

339

8.2.2.1. Viscosity and relaxation in shear flows The effect of fillers on the shear viscosity can be surprising. A shear thinning fluid can be converted into a shear thickening mixture. Non-linear transients may be introduced at shear rates where linear visco-elasticity applied in the unfilled melt. These and other effects will be summarized here. Shear thickening. One qualitative change that fillers can introduce is that the suspension may become shear thickening from shear thinning. The first change in the behavior of shear thickening fluids is shown in fig. 8.2. At low shear rates the fluid behaves like a Newtonian liquid, but, as ~ reaches a critical speed yr the viscosity increases with rising shear rate. Finally, at sufficiently high rates the fluid may become shear thinning [21]. The strain rate at the peak viscosity is Ym, the maximum thickening rate. In the region between ~r and y~, the power-law relation, eq. (85), may be applied with values of n greater than 1. The factor contributing to thickening is the lack of interaction of the filler particles to one another. Particles that form an adhering network within the fluid will not shear thicken [22]. Adhering particles increase 00 but demonstrate decreasing viscosity under flow as the network breaks. Thus, shear thickening requires particles that are either neutral or repulsive. Barnes summarized the characteristics that control shear thickening [23]; they are: particle volume fraction, particle size, particle size distribution, particle shape. Increasing the filler volume fraction decreases ~. For low volume fractions the material may still shear thicken but ~ may be outside the range of interest or the limits of the viscometer. Increasing the particle size also decreases y~. Spreading the filler over a range of sizes reduces shear thickening. A clay with a broad particle size distribution had much lower viscosity at 0.7 volume fraction than one with a narrow size distribution at 0.6% loading [24]. Finally, anisotropic particles enhance shear thickening. Most polymers of industrial use are shear thinning. Effect of filler aspect ratio on shear phenomena. One measure used to describe a filler is the aspect ratio, ar. This is the ratio of the particle's greatest length to its shortest. Nearly spherical particles have ar of nearly 1. Reinforcing fibers can have an ar from 5 to well over 1,000. For small particles and short fiber fillers, at < 50 and it is possible to measure the response to shear strain using conventional equipment as described later if the diameter of the fibers is a few microns. The effect of aspect ratio on shear stress in a filled polyamide was measured by Laun [25]. Figure 8.10 shows the results for a fixed ~ (0.1 s-l), filler volume fraction (30%) and three at of the glass filler: 1 (beads), 7.3 and 25.1 (short fibers 13.5 ~tm diameter). The neat melt shows a rapid rise to steady ryx (28.4 Pa) at small strain. The glass beads extend the total strain required to reach steady ryx to 24 and they increase the apparent viscosity. The randomly oriented fibers increase 0s and add a stress overshoot effect. Table 8.1 summarizes the viscosity changes from that experiment. The stress overshoot is the result of the initial random orientation of the short fibers [25]. When flow begins those fibers that are perpendicular to the flow (or nearly so) inhibit the deformation and the stress rises. As the flow continues these fibers align with the flow direction and the stress falls to the steady stress. Therefore, this

340

S.G. Advani

150

Aspect Ratio O 27 E] 7.3 9 1 9 Neat

100

§

e t al.

,50

OF 0

50

100

150

Fig. 8.10. The effect of aspect ratio on the shear response of a polyamide with 30 vol. % filler [25] ) = 0.1 s.

TABLE 8.1 Effects of a r on shear viscosity of a polyamide melt at ~ = 0.1 s -1 and f = 0.30 (Pa s)

ar

rls

Neat 1 7.3 27

284 420 419 794

Peak r/~ (Pa s)

849 1421

stress overshoot should not be confused with the neat non-linear visco-elastic fluid stress overshoot discussed above. To compare the two overshoots, fig. 8.11 presents Laun's [25] for an ar of 27 glass-filled polyamide and a schematic of a neat non-linear visco-elastic fluid. After the stress has relaxed the neat fluid will repeat the initial stress growth response with overshoot. However, the filled polyamide resumes the flow without an overshoot because the initial random fiber orientation does not return. 4

00 (a)

5

10

15

(b)

Fig. 8.11. Stress overshoot of (a) non-linear visco-elastic fluid and (b) a short fiber-filled fluid [25].

20


341

Although both ar of 1 and 7.3 show the same increase in apparent viscosity the a r o f 7.3 filler produces an overshoot. The a r of 25.1 filler demonstrates that there is a viscosity increase for larger ratios. This may only be due to the increased entanglement of the longer fibers (at the same volume fraction) as they attempt to rotate into the flow planes of the Couette apparatus. For a given f/yx there is only a certain amount of stress energy available to remove the tangles and align the fibers. Once the fibers are in equilibrium with the resulting ryx no further improvement occurs in the array. Mutel and Kamal [26] showed this with the experiment in fig. 8.12. When a sample of glass fiber-filled polypropylene shears at 0.04 s-~ it shows a slight stress overshoot before approaching ryx. When f/yx suddenly increases to 0.06 there is another overshoot before the approach to ryx at the new rate. Next a new sample sheared at 0.06 s-1 approaches the same ryx as the first sample deformed at the same rate. Both samples had the same stress energy available to align the fiber array since both deformed at 0.06 s-]. Finally, a sample initially sheared at 0.20 s-1 has its shear rate reduced to 0.06. The resulting ryx is lower than for the first two samples. The higher stress level provided the extra energy needed to improve the orientation of the fibers. This shows that the effect of increasing a r on the change in apparent viscosity may be different for different initial and final fiber orientations. Note that we cannot directly calculate r/s for the filled experiments and must be satisfied with apparent viscosity values. As discussed below, there are theories that suggest the relative motion of the fillers increases the local y and thus the effective f/yx is uncertain. However, by analogy to engineering stress and strain one can calculate an apparent viscosity for the systems using the applied global shear rate. Thus the addition of fillers increases the apparent viscosity of the system and greater a r have a larger effect. Details on short fiber rheology and flow can be found in Milliken and Powell [27] and Tucker and Advani [28]. Theories f o r filled s y s t e m s in shear. Many theories have been presented for predicting the viscosity of a filled fluid based upon the character of the filler and the Os of the fluid. Einstein presented a relation for the viscosity of a suspension [29]. r/-- r/o(1 + 2.5~b) 2000

eL

+~

(8.17) ,

1500

,

1/sec

1000 500

[ 0

0

250

I

0.04 l/sec

-

500

!

750

I

1000

Seconds Fig. 8.12. Effect of short fiber entanglement on apparent viscosity [26].

342

S.G. Advani et al.

where 4~ is the volume fraction of the filler. This linear relationship is suitable only under several restrictions. The filler must be spherical or nearly so. The filler particles must not interact or form a structure within the fluid, which usually is the case only for dilute suspensions. As filler concentration grows the interaction of the particles lead to deviations from the linear growth depicted and another model must be employed. For concentrated packing of spheres Frankel and Acrivos [30] developed a relation for the filled fluid viscosity r/' recast by Christensen [31] as rl'

r/s@)

--+

27Cm

1011

-

-

(C/r

as c ~ Cm

(8.18)

where r/s is the viscosity of the neat fluid at the applied y and Cm is the maximum packing fraction for uniform spheres. Pipes [32] and Christensen [31] have developed relations for the transverse (rlyz) and longitudinal (Oyx) shear viscosity of highly aligned concentrated fiber arrays. Figure 8.13 displays the geometry of these shear flows for highly aligned arrays. Pipes applies a micromechanics approach to obtain: rlyz = rlyx = XOs(i/)

(8.19)

with 7 the applied longitudinal shear rate as shown in fig. 8.13. Here the transverse and longitudinal shear viscosities are the same. Note that eq. (8.19) contains no a r effect. The effective shear viscosities are related to the matrix viscosity through the fiber volume fraction parameter, x: ,c =

(8.20)

1 -v/7/F

Fig. 8.13. Geometry of shear modes.


343

where f is the fiber volume fraction and F is the maximum possible packing fraction for a given geometric fiber array. The parameter x depends solely upon the fiber packing geometry and concentration. Since eq. (8.19) contains no effect of ar the fibers could be short or continuous in this micromechanics approach. However, the experiment shown in fig. 8.10 demonstrates that for fixed applied y and f , the 27 ar filler reached a steady viscosity 1.9 times greater than that of the 7.3 at melt. Christensen [31] used the fluid mechanics approach developed by Frankel and Acrivos [30] to obtain expressions for the longitudinal and transverse shearing viscosities. For a hexagonal packing array of fibers in a Newtonian fluid he developed the following semi-empirical expressions for the longitudinal shearing viscosity:

1 + aft~F)

)

x/,(1 _ tiff~F))(1 - (f/F)) rl;

r/12 --

(

)3

(8.21)

a = 0.8730, t3 = 0.8815

and for the transverse shearing viscosity:

023 -

v/(1

-

1 + a(f/F) fl(f /F))(1 (f /F))

O;

-

a = -0.1930,/3 = 0.5952

(8.22)

8.2.2.2. Viscosity in elongational flows The elongational viscosity of filled systems shows a dramatic change from the neat fluid response. The phenomenon discussed next demonstrates that the change in local flow within the filled melt shifts the dominant mechanism. Elongation phenomena for low aspect particles. As shown in fig. 8.9, typical neat fluid r/e demonstrates rising viscosity with increasing k. Particle-filled fluids can manifest the shift from this reaction to a more shear-similar response. That is, creeping flows produce the maximum r/E envelope and further increases in decreases r/~:. This is demonstrated by the carbon-black particle-filled polystyrene [20] in fig. 8.14. The particles were sub-micron size. At 20 vol. % there is no strain hardening and increasing k reduces the r/+ curve. The ~ = 0.0063 envelope curve moves to higher r/+ than for the neat melt. At 25 vol. % the rise in the envelope 1010

1010

10 g

10 9

~o 7 "~

o o.,~ [] o.,~

w lO e F

10-I

.

-

100

a o.oes

10 S~ond8

102

,o 7

~

o o.**a 0.,2

/*~ /

103

lO 0 I -

10-1

_ _

100

I a o.os.~

10 ,~ond8

Fig. 8.14. Carbon-black-filled polystyrene in elongation. Compare with fig. 8.10 [20].

102

10'I

344

S.G. Advani et al.

curve is even more pronounced. The change in the magnitude of r/+ with the particles added is best demonstrated by comparing the lowest k envelope curves in fig. 8.15. Table 8.2 summarizes the numerical results of the changes in filler content and k. First the effect of the filler at k - 0.0063 shows that r/+ (10) increases by 22 times with 20 vol. % carbon black added. The 25% filler melt has an r/~ (10) 51 times as great as the neat polystyrene. The change from elongation to shear-dominated behaviour appears in the change in 0+ as k increases for each material. Neat polystyrene shows little change in 0+ (10) until k reaches 0.2 s-1. Then the strain hardening becomes apparent with the elongational viscosity increasing 263%. The filled melts have a drop in r/+ (10) with each k increase. The percentage change from one rate to the next is similar for both filled fluids. The higher packing of low aspect ratio fillers has little effect on additional local shear flow. Elongation phenomena with fiber-filled melts. Data for short fiber-filled melts in elongation is scarce. Several studies have been performed with fiber spinning of

10 10 10 9

aI +m ~"

10 8 10 7 10 6 10 5

!L ~

~

-----

10-1

Filler 25% [] 20% /X Neat g - 0.0063 0

100

101

102

103

Seconds Fig. 8.15. Envelope r/+ curves for polystyrene melts in elongation [20]. TABLE 8.2 Change in 17+ at 10 s elapsed time for polystyrene melts (s -1) 0.0063 0.02 0.063 0.2 (S-1) 0.0063 0.02 0.063 0.2

Neat melt r/+ (IO)(MPa s)

Change from prior k (%)

13.3 " " 35.1

0 0 + 263

20% particles 0+ (1 O) (MPa s)


25% particles r/+ (1 O) (MPa s)


289 132 76 4

--54 -42 -45

679 270 173 98

-60 -36 -43


345

Newtonian oils with low concentrations of short fibers [33-35]. Weinberger and Goddard [35] showed that the short fibers increased shear viscosity by 8% but increased elongational viscosity by one order of magnitude. Mewis and Metzner showed elongational viscosity increased by 260 times for longer aspect ratios [33]. Thus the effect of short fibers in elongation is much greater than in shear. A recent study of long discontinuous fiber (LDF) filled polyether-ketone-ketone (PEKK) shows shear dominated reaction to simple elongation [36]. The "global" elongation causes "local" shearing between the fibers. The material is extreme in both fiber content (60 vol. %) and aspect ratio, which is around 8,000. Figure 8.16 shows both the stress and equivalent r/e +. When compared to fig. 8.5, the performance in elongation is similar to a non-linear visco-elastic fluid flow in simple shear. Theories for filled systems in elongation. Several models have been proposed for the elongational response of filled melts. Batchelor proposed a solution for suspensions of large ar fibers in a fluid [37]. The length of the fibers is L, the diameter of the fiber is D and the center to center fiber spacing is S, as shown in fig. 8.17. If L ~>S~> D, the fiber spacing is close but without them contacting one another. The elongation velocity gradient applied in the x-direction (the fiber direction) moves each fiber with the velocity of its centroid: u~ = x ~

(8.23)

where u~ is the velocity of fiber c~, x~ is the distance of c~'s centroid from the origin. Under a no-slip condition the velocity of the fluid at the fiber surface is also u~. The fibers at the edge of the cell shown by the dashed lines have zero velocity relative to the top fiber. Now the fiber array is replaced by the cell model with zero velocity at the cell edge and velocity u -- u~ at the fiber surface. Batchelor [37] solved Laplace's equation for u = (L/2)k at r = D/2 and u = 0 at r = S. The solution is

u-

kL ln(r/S) 2 ln(D/2S)

(8.24)

250 200

~

-

~ ~ 10"1

150

~-:" 100 ~ lo-4

50

l 0 F.

I 0.02

* 10-5 ...... ] 0.06 0.08

I 0.04

~:| a) ~

growth function.

Fig. 8.16. Elongation of LDF/PEKK [36].

§ ~

~"

0.10

t -" lo-4

E

_.~ 10 0

I 100

I 200

J_O_ 10-3 I 300 400

Seconds b) ElongMIonld vi~oslty function.

346

S.G. Advani et al.

Fig. 8.17. Fibre spacing for shear and elongation models.

where D / 2 N] (~'yx)

~x

;,y+x(~yx.t) ~ f..yx(~yx) N+(ryx, t) ~ Nl(ryx)

(1), Yyx

ryx(O), ~/yx)

Measure

CalculateTransients '

r

i

t

y

-1

I

~yx t

t

o m"

) [1].

5ol

I

I

I

I

I

-i 400 1

350

4O

(/)

m= :3 "O O

--

Young's modulus

n

30

E o~ 20 C

/

%

-

-

250

-

-

200

-

15o

E ~ j::: % r

tensile strength

O >-

300

U3

_=_

~:

11)0

~i 0

50

I

I

I

I

I

15

30

45

60

75

o 90

angle to wale direction [o]

Fig. 10.9. Angle-dependency of a knitted-carbon-fiber-reinforced polyamide 12 which has been slightly drawn in the wale direction prior to consolidation. The angle-dependency was fitted with a powered cosine function [3].

PEMA-T300: The macroscopic failure behavior of knitted-fiber-reinforced PEMA is illustrated in fig. 10.10. For both test directions the stress strain curves indicate deviation from the linear elastic behavior before the maximum stress is reached. Specimens tested in the course direction show this effect at lower strains. The

416

J. Mayer and E. Wintermantel

Fig. 10.11. SEM of undrawn PEMA-T300: after tensile tests in the wale direction (left), primary failure occurs by fiber failure of the aligned fibers in the loop (--+ 1). Fiber pull-out and debonding in interlocking area can be recognized ( ~ 2). After tensile test in course direction (right), primary failure occurs by transverse cracking in the fiber-matrix interphase at the surface of the roving (--+ 1) and by subsequent debonding along the loop. The applied force direction is indicated [1,3,50]. TABLE 10.2 Comparison of tensile strength measured according to D I N 29971 and calculated from the plain fiber orientation distribution. The calculation of strength is based on the amount of fibers which are oriented between an angle of 4-7.5 ~ to the force direction. Fiber tensile failure is considered to be the first failure criterion

PEMA-T300 undrawn PEEK-AS4 13% drawn in the wale direction

Test direction

Strength [MPa] calculated

Strength [MPa] measured

wale direction course direction

190 150

149.1 -I- 17.8 79.3 4- 11.5

wale direction course direction

325 75

316 4- 33 105 + 7.0

moduli with those calculated from the two- and three-dimensional fiber orientation distributions based on X-ray data and cross-section analysis of drawn PEMA-T300. A single-fiber approach is used for both calculations [36,40,48]. The computation based on the three-dimensional distribution allows a conservative estimation of the moduli, whereas the X-ray analysis gives an overestimation. This is mainly due to projection effects which neglect those fiber portions that are out-of-plane.

Thermoforming processes for knitted-fabric-reinforced thermoplastics

417

Fig. 10.12. SEM-micrograph of PEEK-AS4 13% drawn in the wale direction. After tensile test in the wale direction (left), primary failure by brittle tensile failure of fibers that are aligned to the applied force direction ( ~ 1). Debonding and transverse cracking cannot be observed. Very short pull-out fiber lengths indicate good adhesion between fiber and matrix. After tensile test in the course direction (right) failure characteristics are comparable to those in the wale direction. Brittle tensile failure of aligned fibers is considered as primary failure (---~ 1). Debonding was not observed. Transverse cracking along the loops occurs as secondary failure.The applied force direction is indicated [50].

Fig. 10.13. Calculation of the plane Young's modulus distribution using a single fiber approach: calculation based on the three-dimensional fiber orientation distribution (right, see fig. 10.5) and based on the two-dimensional fiber orientation distribution (left, see fig. 10.4) [48].

418


The failure behavior of knitted-carbon-fiber-reinforced composites can be understood from the models proposed in fig. 10.1 and fig. 10.14. The stacking sequence of individual knit layers (fig. 10.1) is characterized by the fact that interlocks of one layer are bridged over with aligned parts of the loop in a next layer. The local strain field is then determined by the greater stiffness of the aligned part. Previous investigations indicated that the plain distribution of Young's modulus is linearly correlated to the FOD [49-51,58]. In a first failure criterion, the FOD was used to calculate the stresses for first fiber tensile failure. The results are summarized in table 10.2 showing the first failure criterion to be fiber tensile failure. They indicate that this first failure criterion works only for the PEEK-AS4 system in which the matrix failure strain clearly exceeds the local strain concentrations in transversally loaded areas. SEM investigations (figs. 10.11 and 10.12) demonstrate the influence of fibermatrix adhesion and matrix toughness on the failure behavior. As a result, a failure model has to be proposed (see fig. 10.14) that considers a strain concentration criterion: the fiber strength can only be used if strain concentration in transversally loaded areas does not exceed matrix failure strain. Otherwise, first failure occurs by transverse cracking in this area and continues by subsequently debonding into the

Fig. 10.14. Failure model for knitted, multilayer composites. The first failure criterion is based on a strain concentration criterion: the local strain level exceeds the failure strain of the matrix (left) and the properties of the fiber cannot be entirely used (example: PEMA-T300 system). The matrix failure strain is considerably higher than local strains (right) and the properties of the fiber are entirely used, then the failure behavior is brittle and fiber-dominated (example: PEEK-AS4 system) [50].

Thermoform&g processes for knitted-fabric-reinforced thermoplastics

419

interlock area. This causes ongoing disintegration of the composite. However, the proposed model is not able to distinguish whether matrix or interphase has to be considered as the weak link. With regard to the influence of fiber-matrix adhesion, recent degradation experiments on knitted-carbon-fiber-reinforced polyamide 12 [49] indicated that selective aging of the interphase causes changes in the failure behavior comparable to that of the effect of matrix toughness.

10.3. Net-shape forming of knitted fabrics for load-transmitting implants shown for an ulnar osteosynthesis plate 10.3.1. Introduction

The most common osteosynthesis techniques focus on rigid fixation of the fracture sites using stiff plates made from stainless steel [65] or titanium alloys. To achieve primary bone healing without callus formation, considerable high axial pressures are needed [66]. Homoelastic osteosynthesis is an alternative approach which integrates fast mechanisms of bone healing such as callus formation [67]. Several concepts have been discussed, such as the use of resorbable materials [68,69] or reduction of plate stiffness by the change of material or of design [70]. It has been found that the amount of external callus depends on plate stiffness [71]. The formation of callus results in higher fracture strength of the healed bone, compared to primary bone healing [72,73]. In addition, several authors have observed less bone resorption underneath homoelastic plates [67,71,72], thus correlating loss of bone density with the degree of stress protection. The premise that local bone necrosis due to high contact pressure of the plate also leads to bone resorption, is controversial [74-76]. It has been reported [77-81], that the residual strength of healed bone shows a maximum before resorption by stress shielding or necrosis takes place. Therefore, an early removal of the plates would be advantageous, the precondition being the observation of bone structure by X-ray. The achievement of a stable homoelastic fixation requires an axial stiffness comparable to that of bone [70,82]. In contrast, bending and torsional stiffness should be high to guarantee proper fixation of the fracture. In order to fulfill these conditions, numerous carbon-fiber-reinforced, non-resorbable composites have been evaluated & vitro a n d / n vivo since 1975 [4,7,9,11,14]. Multistep manufacturing methods, i.e. hot pressing and machining techniques, were used for continuous fiber-reinforced laminates. Because of the fair competitiveness of these techniques for medium scale series, injection molding of short fiber-reinforced composites has been investigated [83]. The low fiber content, problems with the control of fiber distribution and the fatigue behavior restricted the application of injection molded plates. The possibility of hot shaping the plate because of the discontinuity of the fibers was considered to be an advantage for clinical application. Thermal shaping of laminated plates [55] is restricted to intra- and inter-laminar shearing and intra-laminar transverse flow because of the rigidity of the reinforcing carbon fibers.

420


Based on the previous discussion, the requirements for a homoelastic osteosynthesis system made from anisotropic biomaterials would be as follows: 1. Three-dimensional fiber orientation because of the accumulated complex loads in an osteosynthesis. 2. Axial stiffness low enough to stimulate external callus formation because of axial micromovements in the fracture gap. 3. X-ray transparency to allow determination of the earliest possible time of removal. 4. Shaping of the plate during operation, but with minimal impact to the recipient tissue. 5. Costs comparable to metal plate manufacturing. 6. Use of screws made from composites to prevent corrosion. In the following section the results of the development of such an osteosynthesis plate is discussed. The development of cortical bone screws from continuous carbonfiber-reinforced PEEK has been described elsewhere [1]. Cortical bone screws were manufactured from carbon-fiber-reinforced PEEK in a net shape melt extrusion process. In this process, uni-directionally reinforced planks were heated above the melting point of the matrix material prior to forming and then transferred to the screw-forming cavity. The bone screw had a core-diameter of 3 mm, a fiber content of 62 vol. % and a matrix-coated surface. The fiber orientation in the screw was defined by the flow conditions during injection. In the screw head and in the upper part of the threaded bolt, fibers were generally aligned along the screw axis. Towards the tip of the screw, fibers in the core zone became more circularity oriented. In a skin zone with an approximate thickness of 0.7 mm fibers still followed the longitudinal profile of the thread. An average tensile strength of 460 N/mm 2 was determined. Young's modulus in the axial direction of a melt-extruded bone screw decreased from approximately 40 GPa at the screw head to approximately 5 GPa at the tip.

10.3.2. Experimental details The net-shape manufacturing technique for a six-hole ulnar osteosynthesis plate (fig. 10.15) uses two characteristic properties of knitted fiber structures: drapability and coherence, which allows the molding-in holes by widening single stitches. The plate is made from weft-knitted carbon-fiber-reinforced PEEK in a single step netshape pressing technique [48,54]. Net-shape pressing is defined as the thermo-induced forming of a raw material in one production step without the need for further processing. The commingled knitted fabric was rolled and pushed over the spikes of the die (fig. 10.16). After all four side walls were inserted, a stamp was lowered onto the knitting. This procedure obviated the need for cutting the fibers, as the loops were distorted into a circular fiber alignment around the spikes. This had a self-reinforcing effect with complete coating of the polymer surfaces.


421

Fig. 10.15. Six-hole ulnar osteosynthesis plate, made from knitted-carbon-fiber-reinforced PEEK in a single step net-shape pressing technique [1].

Fig. 10.16. Net-shape pressing die for the osteosynthesis plate. The knit was rolled up and pushed over the countersunk hole forming pins by widening the single loops [1].

The pressing cycle for the weft-knitted intermingled PEEK/AS4 yarn (BASF/ Hercules) was as follows: heat-up to 390~ at a rate of 18~ dwell period at 390~ for 30 min, pressure 17.5 MPa, cooling rate 10~ Bending strength and modulus were determined by a 4-point bending test (DIN 29971, 2 mm/min) at 25~ The support span was 97 mm and the pressure span was 41.2 mm. A model for the calculation of the bending modulus and the strength was derived according to the geometry of the plates, in which the plates were considered to be beams with two different cross-sections, a massive section and a reduced section, representing the holes [1,48]. The fiber volume content was measured by gravimetric and volumetric

422


methods [54]. The failure mechanisms were observed by scanning electron microscopy (SEM). To compare net-shape pressing with common lamination technologies, a laminated osteosynthesis plate of identical geometry was made from carbon-fiberreinforced PEEK laminates (APC2-AS4 from ICI). The plates had stiff outer shells (0/0/45/-45/-45/45/0/0) and weak cores ((45/-45/-45/45/0/45/-45/0/-45/45)s) to achieve a high bending (Eb = 107 GPa) to axial (Ea = 60 GPa) modulus ratio. The properties of these plates have been discussed in previous publications [1,55]. A stainless steel plate (six-hole ulnar, Aesculap, Germany ) was used as reference.

10.3.3. Structure and properties of the net-shape manufactured osteosynthesis plate In the critical cross-section of the countersunk hole, a forced fiber orientation along the plate axis as well as a slightly improved fiber content due to the formed holes can be observed (fig. 10.17). This effect results in an improvement of the mechanical properties compared to drilled plates machined from pressed knittedfiber-reinforced plates [48]. Figure 10.17 illustrates the findings for bending modulus of osteosynthesis plates made from stainless steel which had been UD-laminated, machined, and net-shape knitted. The Young modulus of cortical bone is added to fig. 10.17 in order to demonstrate a possible mechanical approach to homoelasticity with knit reinforced thermoplastics. The spatial fiber orientation around the hole, as indicated in fig. 10.18, induces a failure behavior characteristic of the net-shape plate. Compared to the laminated plate, an improvement of damage tolerance is observed in the stress-strain curves in which pseudoplastic failure is considerably increased (fig. 10.19). The correlated stainless steel

plate

(UD 01+4.5 ~

. . . . . .

I

L

I~l

i

cortical bone ~ - - ~ 1

t

t

I

I

0

50

100

150

200

~1 250

Bending modulus [G Pa] Fig. 10.17. Bending moduli of osteosynthesis plates, made from stainless steel and AS4/PEEK composites (UD-laminated and machined, knitted net-shaped and knitted machined). The Young modulus of cortical bone is added as a reference [1].

Thermoforming processesfor knitted-fabric-reinforced thermoplastics

423

Fig. 10.18. Cross-section of a plate as indicated. The hole-forming process induces a fiber alignment along the plate axis (left) and a trough thickness orientation (right). stainless steel plate

~, 1200

+,,_A-..

,,- 800

laminated plate

,=I

~, 750

,0=.

==t /5'17~176 "

~, 600

,,- 500

..... I ] plastic 4uI ~ "

0

2.5 5.0 7.5 10.0 elongation [%]

y/~

~ 400 brittle failure

250 0

net-shape plate

0

i

200 t=

2.5 5.0 7.5 10.0 elongation [%]

0

0

2.5 5.0 7.5 10.0 elongation [%]

Fig. 10.19. Comparison of the stress-strain curves for the stainless steel plate (left), the laminated plate (middle) and the net-shape pressed plate (right) [1].

stress-strain curves illustrate the different failure behavior of these materials. While steel plates became plastically deformed, laminated plates showed a well localized brittle failure. Knitted-fabric-reinforced plates have enhanced failure strain due to pseudoplastic damage accumulation as demonstrated in the following SEMs. These findings correlate with an increase of the area of damage as illustrated in the SEM images in fig. 10.20, and with the dislocation of the failure area beside the smallest cross-section, as illustrated in fig. 10.21. Primary failure occurs at the compression site: in the laminated plate, local fiber buckling of the outer 0 ~ plies (1) with subsequent delamination (2) and compression failure of the inner 0 ~ plies (3) is observed, whereas in the net-shape plate (PEEK-AS4), failure occurs beside the smallest crosssection (compare fig. 10.21) The crack path is guided by the fiber orientation in the loop. Primary failure is a compression failure of fibers which have been well aligned to the plate axis and are underneath the plate surface.

424


Fig. 10.20. Comparison of the primary failure behavior of the osteosynthesis plates at their compression site. Laminated plate (left) with well localized compression ( ~ 1) and delamination failure ( ~ 2) and netshape plate (right) where the crack path is guided by the fiber orientation along the bundles ( ~ ) [48].

Fig. 10.21. Tensile failure side of the net-shape pressed osteosynthesis plate beyond the smallest crosssection in the countersunk hole ( ~ ) [1].

An additional effect of the net-shape processing is the complete coating of the plate surface with the matrix polymer by wetting the mold surface so that release of carbon fiber particles is prevented. This is illustrated in fig. 10.22, where the surface qualities of a drilled and a molded-in hole are compared on the bases of SEMs.


425

Fig. 10.22. Surface quality of the net-shape pressed plate (left) being completely matrix coated and of the machined plate (right) showing carbon-fiber debris (--+) [1,48].

10.3.4. Compar&on of the homoelasticity & FEM calculations and stra& gauge measurements Finite element modeling (FEM) and finite element analysis (FEA) was used to evaluate the properties of osteosynthesis plates made of anisotropic carbon-fiberreinforced thermoplastics. The calculations were performed in CAEDS(I-DEAS (version 4.1) and its Integrated Finite Element Solver (IFES). The material properties were isotropic (steel plate E = 210 GPa, laminated plate E = 107 GPa, knitted plate 33 GPa, cortical steel screw 210 GPa (Aesculap, Germany), cortical composite screw 40 GPa [1], bone 18 GPa). The basic set-up of the F E M / F E A procedure is shown in fig. 10.23 [1,48]. A 3-D model of bone, plate and screws generated from linear solid brick and wedge elements (fig. 10.23) formed the basis for plate/bone system deformation analysis and for evaluation of the stress shielding effect. The bone is modeled as a thick-walled tube. Load transfer from bone to plate is modeled with gap elements between plate and screws. The constraints of the gap elements allowed the transmission of compression forces only on the countersunk holes. Friction forces were not considered as the calculations were restricted to relaxed osteosynthesis of reconsolidated bone. Between bone and screws, shared knots are used to fuse the neighboring elements. The calculations focused on global effects such as stress shielding and strain distribution. The calculated strain distributions in the plate/screw/bone model were verified in a 4-point bending test of a relaxed and reconsolidated ostesynthesis. In fig. 10.24 the set-up of the test and the location of the strain gauges is indicated. The

426


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bone

gap elements

Fig. 10.23. 3-D plate/screws/bone FE model (quarter model) of the osteosynthesis system. Brick elements are used for plate (upper), bone and screws (lower). Screws are connected by gap elements to the plate (lower fight) and shrunken elements to the bone [48].

Fig. 10.24. Four-point bending test of osteosynthesis. The location of the strain gauges is indicated (P1-P5, K1-K6). Load applied was between 100 N and 1,000 N [1].


427

strain gauges on the plate were used to measure the strain distribution along the plate in order to show the reinforcing effect of the molded in holes. The strain gauges on the bone gave the dislocation of the neutral bending axis. A woven-glass-fiber reinforced tube (E = 18 GPa) was used as a model bone and plates were fixed on the tube with cortical steel screws. FE calculation as well as strain gauge measurements indicate the most intensive stress protection for the steel plate (fig. 10.25). The reinforcing effect of the net-shape process is seen only in the strain gauge measurements. The strains around the holes are even smaller for the net-shape plate although the Young modulus of the laminate is more than 30% higher than those of the knitted plates. It was not possible to take the influence of local stiffening of the net-shape pressed plate into account for the isotropic FEM-calculations. The stress protection effect of an osteosynthesis plate is indicated by the dislocation of the neutral bending axis of the plated bone. In a homoelastic osteosynthesis, the bending axis of the bone should undergo a minimal shift from its neutral position. Table 10.3 shows the shift of the bending axis for the three osteosynthesis systems. These were calculated from the FEM model and measured by strain gauges. The osteosynthesis plate, which was made by net-shape forming of the knitted fabric, reveals the smallest shift and thus is expected to have the best homoelasticity. However, the difference between laminated and knitted plate is smaller in the strain gauge measurements than in the calculated ones. This is due to the local reinforcement of hole areas. Furthermore, the variation of the Young modulus along the plate axis of the knitted plate seems to compensate for the variations in the bearing cross-section. Therefore, the strain distribution in the bone during osteosynthesis becomes more homogeneous when using a net-shape plate as compared to a

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428


TABLE 10.3 Shift of the neutral bending axis in a plated osteosynthesis. Comparison of calculations using FEM to strain gauges measurements Shift of the neutral bending axis

Finite element calculation

Strain gauge measurements

Steel plate Laminated plate Net-shape plate

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laminated or even a steel plate. The advantageous ratio of bending and torsional stiffness to axial stiffness of the laminated plate cannot, however, be achieved in the net-shape forming process because of the homogeneous through thickness properties of the knitted-fiber-reinforced material.

10.4. Deep drawing of knitted-fiber-reinforced organo-sheets 10.4.1. Introduction Consolidated sheets of knitted-fabric-reinforced thermoplastics as semi-finished products for thermoforming techniques, i.e. deep drawing, are discussed below. The authors would like to stress on that knitted fabrics feature a unique deformation behavior in comparison to woven or braided fabrics. In contrast to those fabrics that are built up from nearly straight yarns, knitted fabrics allow tensile as well as shear deformations. In the case of uniaxial loading, the tensile deformability can be far more than 100% until the knit attains a maximal density and the interlocks are densely packed. Biaxial tensile drawing is possible until the curved fibers in the loop become straightened and the density of the knit reaches a minimum. At this point, further deformation can only be applied by shear in a manner analogous to woven textiles. The authors suggest that the deformation behavior of a knitted-fiber-reinforced sheet during thermoforming is dominated by the textile deformation characteristics of a knitted fabric. In order to substantiate this hypothesis, the deep drawing behavior of a knitted-fiber-reinforced sheet was investigated using a lab-scale diaphragm technique. Although diaphragm forming is not suited for mass production, it is expected to be adequate for knitted-fabric-reinforced thermoplastics. This technique was selected in order to compare the forming characteristics of knitted-fiberreinforced sheets to those of uni-directional and angle-plied fiber-reinforced sheets [84,85]. As the principles of diaphragm forming and related phenomena have been discussed in detail by many authors [86-90], the discussion concentrates on the specific features of knitted fabrics.

10.4.2. Experimental details The organo-sheets were hot pressed from a knitted carbon fiber (T300, 3K) reinforced polyethylmethacrylate. An unreinforced polyethylmethacrylate sheet which


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had identical dimensions was used as reference material. The knitted fabrics had a loop height of 4.4 mm and a width of 6.1 mm. 12 knit layers were stacked to construct the sheet. The global deformation field was measured from a grid which was defined by silver dots (diameter: 1 mm) applied beforehand (fig. 10.26). To determine the local fiber orientation distribution, the deformation of the loops was monitored by a co-knitted copper filament (100 ~tm diameter) as a tracing element for X-rays. The fiber orientation distribution was determined by the image analyzing technique mentioned above [1,48]. The plain Young's modulus distribution was then calculated using the single fiber approach proposed by Krenchel and Rudd [36,58] The set-up of the diaphragm die and a deep-drawn cone are shown in fig. 10.27. The forming process was carried out in an autoclave at 150~ by applying a deep draw pressure of 1 MPa for 20 min against vacuum. The sheet was held between the two diaphragm foils by an internal vacuum. The rim of the sheet was permanently clamped during deformation. 10.4.3. Flow behavior

The cone geometry of the die was shaped entirely by the sheet without the occurrence of any wrinkles or other instabilities. The outer surface of the sheet, which was in direct contact with the metal die, was smooth. The inner surface showed a noticeable roughness that correlated with the loop geometry of the knit. A smooth inner surface cannot be obtained because the softness of the diaphragm foil is unable to withstand the internal stresses of the knit in the softened matrix. Consequently, changes in the thickness of the sheet over the cone could not be measured. The deformation behavior of the knitted-fabric-reinforced sheet is qualitatively visualized in fig. 10.27. The deformation of the color dots locate maximum strains at the tip of the cone whereas the clamped outer ring remained undeformed. The material contacts the die at its outer circumference first, where deformation is hindered by friction between diaphragm foils and die. The regularity of the dots in the circumference indicates the almost isotropic flow during deep drawing.

430


Fig. 10.27. Set-up of the diaphragm die (upper) with clamping ring (A), vacuum foils (B), deep-drawn sheet (C), vacuum ring (D) and the cone-forming die (E). The cone (lower) is shown with applied color dots to illustrate the isotropy of the deformation behavior [48].

The tangential and radial strains were calculated from the deformation of the grid on the basis of the relative dislocation of the silver dots. The values for an unreinforced matrix sheet and for the knitted-fabric-reinforced sheet are shown in fig. 10.28. The radial strains along the evolution line of the cone reveal material maximum strains at the tip (torus 1) and minimal strains at the outer border for both. The unreinforced polymer sheets showed an isotropic deformation behavior as illustrated in the circular deformation distribution in the fourth torus. According to the contact conditions to the die, the strain is concentrated at the tip of the cone. The knitted fabric also allowed an isotropic deformation with respect to the circumference, although at higher strain levels in the outer torus, as indicated in

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fig. 10.28 (left). The deformation behavior along the evolution line of the cone is strongly influenced by the textile deformation characteristics of the weft-knitted fabric. The sheet can flow isotropically as long as the deformation limit of the knit is not reached. Weft knitted fabrics allow uniaxial strains of more than 150%, but these limits are heavily reduced when a biaxial strain component is added. Under equibiaxial deformation the maximum strains are limited to about 40%. As soon as this condition is fulfilled at the tip of the cone, biaxial deformation of the sheet is blocked in these areas. Due to the coherence of the knitted fabric, any further deformation that would be required to form the cone is transferred to the outer areas. This explains the observation (fig. 10.28, left), that the maximum strains of the knitted-fabric-reinforced cone is considerably lower than those of the unreinforced cone. However, due to coherence of the knit, strain is more evenly distributed over the entire surface and is therefore at a higher level.

10.4.4. Correlation between plastic flow and fiber orientation distribution The analysis of the fiber orientation distribution by means of co-knitted copper wire is illustrated in fig. 10.29, where the modulus distribution was calculated for different characteristic areas of the cone. It demonstrates the equibiaxial distribution at the tip of the cone. At the outer border, the knit is uniaxially drawn with a certain biaxial component. The area which was drawn mainly in the wale direction shows a shift of the minimal modulus from 90 ~ (course direction) to 70 ~ to wale. This illustrates the biaxial strain component which had been induced by the coherence of the knitted fabric and which guaranteed constant tangential tensile stresses in the sheet


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during deformation. Those coherence-induced stresses are seen to prevent the formation of radial instabilities.

10.5. Discussion

10.5.1. Structure-properties relationship In accordance to Planck [44] it was shown that the mechanical properties of knitted-fabric-reinforced composites depend directly on the geometry of the loop and therefore can be controlled by the drawing of the textile. It was possible to correlate quantitatively the rate of drawing of the knitted textile with the observed strain strengthening and stiffening effects. In contrast to dense knitted fabrics used by other authors [36,39,40], the low area density of our fabrics allowed the formation of a three-dimensional fiber orientation at fiber volume contents of more than 50% by the interpenetration of a multitude of stacked knit layers. Thus, the mechanical behavior of dense- and loose-knit reinforced composites obeys different rules. In a composite built up from few, dense knit layers, the mechanical properties correlate with the properties of the knitted fabric and thus increase with the area density of the knit [39]. When the composite is constructed from a multitude of interacting lowdensity knits with large loops, the mechanical properties are directly determined by the three-dimensional fiber orientation distribution in the consolidated material. They are no longer influenced by the textile properties of the knitted fabric. However, the authors would like to point out, that while on one hand, a good adhesion between fiber and matrix is the precondition to achieve a failure strength


433

that correlates to the fiber orientation distribution, on the other hand, the use of thermoplastic matrices may be of advantage. Several authors [39-41,44] propose net-shape knitting techniques using flat-bed machines to produce complex shaped parts such as helmets. However, it should be taken into account that net-shape knitting has a much lower productivity than circular knitting and that it could not be applied successfully to carbon yarns. In the second part of this chapter it was demonstrated that circular weft knits could be used in net-shape manufacturing processes by net-shape formation of the desired part, instead of net-shape knitting its preform. In order to improve the low mechanical properties of composites reinforced by dense knits, Rudd [40] and Drechsler [39] proposed the use of more stable knit types or reinforcement by weft and warp inserted yarns. However, the insertion of straight yarns would considerably reduce the drapability and would restrict the tensile deformation capability in weft and warp direction. The application of low density, large loop weft knits allows the achievement of mechanical properties which correspond to the fiber orientation distribution and which can be considerably enhanced by uniaxial drawing. Furthermore, the orthotrope symmetry of a weft knit makes it susceptible to the modeling strategies already established for composite materials. However, several aspects of the structure-properties relationship are still unknown. Fatigue and creep properties, damping, crash and impact properties have to be investigated. The development of suitable engineering and structure modeling algorithms which integrate the influence of loop deformation by draping or thermoforming into the prediction of the mechanical properties, is thought to be a prerequisite for the successful application of these materials.

10.5.2. Thermoforming Coherence of the weft-knitted fabric is considered to be one key factor in processing. The coherence defines the fiber orientation distribution as well as the homogeneity of fiber distribution during thermoforming processes even when large strains are applied. During thermoforming, the strain field is homogenized in the material flow because the coherence of a locally fully deformed knit will tend to distribute strain to neighboring areas. The drawing-induced orientation of the loops may allow the achievement of selective strengthening and stiffening (compare fig. 10.29). Net-shape forming was introduced as a single-step thermoforming technique that enabled the production of complex shaped parts including molded-in holes or, more generally, load induction areas. Net-shape forming can be applied for thin parts such as sheets or pipes as well as for voluminous parts that cannot normally be realized from composite materials. The number of manufacturing steps might also be reduced considerably by employing this technique, so that it is expected to have a positive impact on production costs. However, the internal stresses in the loops hinder the dry consolidation of the fabric. During consolidation a volume reduction from the textile to the composite of more than 200% may occur and should be considered in the set-up of the processing technique. The directional formation of holes, load induction or notched areas in knitted-fiber-reinforced composite induces

434


an orientation of fibers and will therefore selectively reinforce those critical areas. The reinforcing effect of molded-in holes on fatigue properties and notch factors for woven-fabric-reinforced composites has been shown by several authors [91-95]. In organo-sheet forming, the deep drawing behavior of knitted-fabric-reinforced sheets is characterized by their coherence, their drawability and their drapability. While these characteristics denote the main advantages, they also present inherent problems for the control of the manufacturing process. The drapability enables unhampered shaping of free forms, but the control of the fiber orientation becomes difficult when no well-defined forces or constraints, i.e. by clamping, act on the textile. Based on the experiences with co-knitting of copper wires for X-ray tracing, co-knitting of a stiff metal wire could be applied to stabilize the textile deformation of the knit during draping due to the plastic deformation of the wire. However, galvanic corrosion should be considered combining carbon fibers with metal wires. The coherence of the fiber architecture prevents wash-out of fibers even during extensive viscous flow. The transverse contraction behavior of the knitted fabric induces internal biaxial strains which hinder formation of faults, but it can limit the extent of applicable deformation. As mentioned above, it can help to distribute the deformation field in order to prevent local thinning due to strain concentrations. The internal stresses in the fibers which are introduced by the curvature in the loop influence the consolidation behavior. For these to be overcome, a pressure of about 1 MPa has to be applied. The achievement of smooth surfaces requires the use of rigid male and female dies. Consolidated preforms lose their consistence and their stiffness as soon as the matrix melts. Therefore, handling of preheated preforms needs special tools as well as the adaptation of the processing conditions which guaranties the presence of a defined force.

10.5.3. Biocompatibility aspects and applications It has been shown that the reinforcement of implants with knitted-fiber architectures enhances the structural compatibility in terms of homoelasticity and smoothness of the anisotropy compared to laminated materials or metals. Molding-in and selective reinforcement of the countersunk holes as well as the process-induced threedimensional fiber orientation improves failure security and reduces the sensitivity of the implant to variability in load cases between individuals. Process-integrated sealing of the implant surfaces with the polymer matrix prevents the possible release of fibrous particles and contributes to the reduction of manufacturing costs. Preliminary investigations proved the inter-operative, thermal adaptability of the bone plates [55]; however, an amorphous matrix has to be used to enable plastic deformation at the lowest possible temperature. The viscosity of the matrix has to be as high as possible to prevent deconsolidaton due to the eigenstresses in the compressed-fiber architecture. The concept of net-shape forming of implants can be transposed to other loadbearing implants or to surgical instruments whenever homoelasticity, X-ray transparency, and MRI-compatibility have to be combined with high multiaxial loads and complex implant geometries. The net-shape pressing technique could be preferentially


435

applied to complex-shaped bone plates for spine surgery or to stem material for artificial joints. However, for contact with bone, the material has to be coated by bioactive hydroxyapatite coatings, to be applied by plasma spraying [95,96] or biomimetic coating [97]. Using light or thermally curing matrix resins, knittedfiber-reinforced materials can be used for individually adapted dental implants, i.e. dental bridges or for the reconstruction of bone substitutes in reconstructive surgery.

10.6. Summary and conclusions It was the aim of the authors to propose knitted fabrics as reinforcement structures for high-performance thermoplastic composite materials. These materials are considered to be suited for applications of composite materials whenever net-shape forming or thermoplastic sheet forming is of special importance for the overall performance of the product. It has been shown that knitted-fabric-reinforced organo-sheets may allow drawing ratios greater than 100% isotropically. The drapability of the knitted fabric should pose no major drawbacks to the realization of complex-shaped parts. The mechanical properties will approach those of woven-fabric-reinforced materials whenever the knit is uniaxially drawn during thermoforming. The net-shape forming technique will display its main advantages in the manufacturing of bulk parts which have been hardly feasible so far by conventional composite processing techniques. This technique is characterized by the simplicity with which parts possessing threedimensional fiber orientations and selectively reinforced areas, i.e. holes or notches, can be built up. The drapability of knitted fabrics permits the realization of almost any shape including formed-in holes or integration of inserts. Critical areas may be strengthened selectively by local drawing. The low density of these fabrics enables the shaping of the outer contours of a part as an alternative to cutting and may contribute to a reduction of manufacturing-related waste. Such preforms can be thermally fixed by the co-knitting of a low melting yarn or by a curing binder. The preforms can then be impregnated by GMT, RTM or SRIM technologies. The productivity of the "contrary knitting technique" may allow its integration in an on-line production processes such as to produce consolidated semi-finished parts using a double-belt press. The manufacturing costs for knitted textiles made by circular weft knitting are comparable to or even lower than those for woven cloth. A combination of these factors make knitted-fabric-reinforced sheet materials appear to be suited to mass production technologies.

Acknowledgements The authors would like to acknowledge the contributions of all students and colleagues at the Chair of Biocompatible Materials Science and Engineering which were involved in the research on knitted-carbon-fiber-reinforced composites during the past 6 years. The work was supported by A. Buck, Technische Strickerei Produkte, Germany, and Aesculap AG, Germany.

436


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[65] Miiller, M.E., Allgoewer, M., Schneider, R. & Willenegger, H., Manual der Osteosynthese, Springer, Berlin, Germany, 1977. [66] Perren, S.M., Physical and biological aspects of fracture healing with special reference to internal fixation. Clin. Orthop. Rel. Res., 138 (1979) 175-91. [67] McKibbin, B., The biology of fracture healing in long bones. J. Bone. Joint. Surg., 60 (1978) 150-62. [68] Parsons, J.R., Alexander, H., Corcoran, S.J. & Weiss, A.B., In vivo evaluation of fiber reinforced absorbable polymer bone plates. Proc. 2nd. Int. Symp. on Internal Fixation of Fractures, Lyon, France, Sept. 1982, pp. 117-20. [69] Hench, L.L. & Ethridge, E.C., Biomaterials: An Interfacial Approach, Academic Press, New York, US, 1982, pp. 225-52. [70] Woo, S.L.-Y., Lothringer, K.S., Akeson, W.H., Coutts, R.D., Woo, Y.K., Simon, B.R. & Gomez, M.A., Less rigid internal fixation plates, historical perspectives and new concepts. J. Orthop. Res., 1 (1984) 431-49. [71] Terjesen, T. & Apalset, K., The influence of different degrees of stiffness of fixation plates on experimental bone healing. J. Orthop. Res., 6 (1988) 293-9. [72] Sarmiento, A., Mullis, D.L., Latta, L.L., Tarr, R.R. & Alvarez, R.A., Quantitative comparative analysis of fracture healing under the influence of compression plating vs. closed weight bearing treatment. Clin. Orthop., 149 (1980) 232-9. [73] Skirving, A.P., Day, R., Eng, B., McDonald, W. & McLaren, R., Carbon fiber reinforced plastic (CFRP) plates vs. stainless steel dynamic compression plates in the treatment of fractures of the tibia in dogs. Clin. Orthop. Rel. Res., 224 (1987) 117-24. [74] Stiirmer, K.M. & Scholten, H.J., Periostsch~idigung oder Stress-protection als Ursache der Porose im Plattenlager? Ein tierexperimenteller Rechts-Links-Versuch. Hefte Unfallheilkunde, 207 (1989) 255-6. [75] Perren, S.M., Cordey J., Rahn, B.A., Gautier, E. & Schneider, E., Early temporary porosis of bone induced by internal fixation implants. A reaction to necrosis, not to stress protection. Clin. Orthop., 232 (1988) 139-51. [76] Perren, S.M., Buchanan, J.S. & Schwab, P., Das Konzept der biologischen Osteosynthese unter Anwendung der Dynamischen Kompressionsplatte mit limitiertem Kontakt (LC-DCP). Wissenschaftliche Grundlagen, Design und Anwendung, Injury (Suppl.), 22, (1991) 1-44. [77] Hayes, W.C., Schein, S.S., Nunamaker, D.M., Heppenstall, R.B., Muller, G.W., Sampson, S. & Sapega, A., Mechanical properties of healing fractures treated with compression plate fixation. Proc. 2nd. Int. Symp. on Internal Fixation of Fractures, Lyon, France, Sept. 1982, pp. 81-4. [78] Liskova-Klar, M. & Uhthoff, H.K., Radiologic and histologic determination of optimal time for the removal of titanium alloy plates in beagle dogs: results of early removal. Current Concepts of Internal Fixation of Fractures, ed. Uhthoff, H.K., Springer Verlag, Berlin, Germany, 1980, pp. 404-10. [79] Slatis, P., Paavolainen, P., Karaharju, E. & Holmstrom, T., Structural and biomechanical changes in bone after rigid plate fixation. Can. J. Surg., 23 (1980) pp. 247-50. [80] Braden, T.D., Brinker, W.O., Little, R.W., Jenkins, R.B. & Butler, D., Comparative biomechanical evaluation of bone healing in the dog. J. Am. Vet. Med. Assoc., 163 (1973) 65-9. [81] Noser, G.A., Brinker, W.O., Little, R.W. & Lammerding, J.J., Effect on time and strength of healing bone with bone plate fixation. Am. Anim. Hosp. Assoc. J. 13 (1977) 559-61. [82] Woo, S.L.-Y., Akeson, W.H., Simon, B.R., Gomez, M.A. & Seguchi, Y., A new approach to the design of internal fixation plates. J. Biomed. Mater. Res., 17 (1983) 427-39. [83] Williams, D.F., McNamara, A. & Turner, R.M. Potential of polyetheretherketone (PEEK) and carbon-fiber-reinforced PEEK in medical applications. J. Mater. Sci. Let., 6 (1987) 188-90. [84] Mayer, J., Wintermantel, E., De Angelis, F., Niedermeier, M., Buck, A. & Flemming, M., Carbon fiber knitting reinforcement (K-CF) of thermoplastics: a novel composite. Advanced Structural Materials, ed. Clyne, T.W., The Institute of Materials, Cambridge, UK, 1991, pp. 18-26. [85] Niedermeier, M., Analyse des Diaphragmaformens kontinuierlich faserverst~irkter Hochleistungsthermoplaste. VDI-Verlag, DiJsseldorf, Germany, 1995 [86] Delaloye, S. & Ziegmann, G., The automation of the diaphragm forming process of CFR thermoplastic composites, 39th Int. SAMPE Symp. '94, Anaheim, USA, 1994, pp. 3068-77. [87] Smiley, A.J. & Pipes, R.B., Analysis of the diaphragm forming of continous fiber reinfroced thermoplastics. J. Thermopl. Comp. Mater., 1 (1988) 298-321.

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Chapter 11

The Forming of Thermoset Composites H a o r o n g LI and T i m o t h y GUTOWSKI Laboratory for Manufacturing and Productivity, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Contents Abstract 441 11.1. Introduction to thermoset forming 442 11.2. Kinematics 446 11.2.1. Introduction and differential geometry results 446 11.2.2. Ideal shears to form a hemisphere 449 11.2.2.1. In-plane shear 449 11.2.2.2. Inter-ply shear 450 11.2.3. Ideal shears to form a curved C-channel 451 11.2.3.1. In-plane shear 451 11.2.3.2. Inter-ply shear 454 11.3. Thermoset forming experiments and forming limit analysis 455 11.3.1. Laminate wrinkling and its modeling 455 11.3.2. Material rheology and scaling laws for compressive forces 458 11.3.3. Laminate buckling resistance 460 11.3.4. Diaphragm stiffness 461 11.3.5. Order of magnitude analysis 463 11.3.6. Thermoset forming experiments and forming limit diagrams 464 11.4. Concluding remarks 468 11.4.1. Reinforced diaphragm forming 469 11.4.2. Inflated tool diaphragm forming 470 References 471

Abstract F o r m i n g has the potential to replace the time-consuming and labor-intensive h a n d lay-up processes as a cost-effective alternate for the m a n u f a c t u r i n g of a variety of thermoset composite products. In this chapter, d i a p h r a g m forming of thermoset composites is reviewed, with the emphasis on kinematics and forming limit analysis. The unique properties of the composites lead to kinematic constraints so that the conformance of laminates to complex geometries would ideally be achieved by viscous shearing mechanisms, a m o n g which the two most i m p o r t a n t such modes are in-plane shear, where adjacent fibers slide past one another, and inter-ply 441

442

H. Li and T. Gutowski

shear where plies slide relative to each other. General methods to calculate the ideal shear strains required to form a given part are obtained by applying the theory of differential geometry. A three-point bending test is employed to understand the constitutive laws governing the deformation. The nonlinear elastic behavior of the diaphragm materials is modeled by using the established biaxial stress theory of rubbers. The balance between the mechanisms that cause and prevent wrinkling leads to the preliminary forming limit diagrams, which would allow us to predict the occurrence of undesirable modes such as laminate wrinkling. The chapter concludes with some innovative development of the diaphragm forming process at MIT.

11.1. Introduction to thermoset forming

Although many of the initial developments of advanced composites sheet forming used thermoplastic materials, it is possible to form thermoset systems by essentially the same techniques [1-4]. In fact, the largest production forming applications of advanced composites may be for the Boeing 777 empennage which are thermoset composites (see fig. 11.1). This chapter will focus on diaphragm forming of thermoset materials. This process is similar to that used for thermoplastics; however, lower temperatures and pressures are used for thermosets. This leads to simpler equipment and tooling, and reusable diaphragms. After forming, thermosets must be cured,

Fig. 11.1. Forming press for 777 advanced composite trailing-edge beams (courtesy of the Boeing Commercial Airplane Group).

The forming of thermoset composites

443

either on the forming tool or on a separate curing tool. Thermoplastics, on the other hand, solidify by cooling. Figure 11.2 shows a schematic of the diaphragm forming process. Layers of prepreg are laid-up in various directions on a platform according to design requirements and trimmed into a preform shape. This stage can be performed by hand or by various automated means. Then, the preform is placed between two high elongation rubber diaphragms, which are the supporting materials. Effective contact of the diaphragms with the preform is realized by drawing vacuum between them. Finally, by applying vacuum from beneath the bottom diaphragm and/or positive pressure on the top, the preform is deformed over the tool. In most cases, vacuum alone is sufficient to form the thermoset composite part. Figure 11.3 shows some parts of complex shape formed by double diaphragm vacuum forming of epoxy resin/graphite fiber composites. Several variations of this process exist which are particularly suited to thermoset composites, including (1) using only the top diaphragm (called "drape" forming) [5], and (2) inflating the bottom diaphragm from beneath the tool ( called "inflated tool" forming) [6]. The major differences between forming of thermoset and thermoplastic composites root from the different chemical and mechanical properties of the matrix materials. The high temperatures for forming the thermoplastic composites (e.g. 370~ for ICI APC-2 PEEK) require high temperature diaphragms [7]. The commonly used materials of superplastic aluminum or high temperature polymers (e.g. polyimides) provide excellent support during the forming process, and then are usually discarded after the part cools. Because of their high stiffness, relatively high pressures are employed (of the order of 1 MPa). The combined effect of high diaphragm stiffness and high pressure has a positive effect of suppressing laminate wrinkling, but it can also lead to part thickness variation. Thermoset composites, on the other hand can

Fig. 11.2. Schematic representation of the diaphragm forming process of thermosets.

444


Fig. 11.3. Thermoset matrix parts made by the diaphragm forming process: (a) chassis for a radiocontrolled model car, (b) scale model automotive body, and (c) roller blade.


445

be softened for forming at relatively modest temperatures (around 40~ This allows the use (and reuse) of high elongation rubbers such as silicones and, in some cases, latexes. These softer diaphragms can be formed using only vacuum (0.1 MPa). The lower pressures and softer diaphragms used with thermosets are less effective at suppressing laminate wrinkling, but have the positive effect of causing only minor thickness variation. For example, it has been observed that diaphragm formed thermoplastic composites can suffer thickness changes of the order of 17% to 200% [7], while the variation in thermoset parts is usually less than 7% [4]. Such variation is typical of parts produced on one-sided tooling. To improve the stiffness of the softer rubber diaphragms, selective reinforces such as steel rods, woven rods, and screens, etc., have been added [8]. This method effectively turns the diaphragm itself into a composite, and can greatly expand the formability range for the process (see fig. 11.4). Despite the differences discussed above, the forming mechanisms for thermoset and thermoplastic composites have much in common. For example, the deformation mechanisms are similar and the kinematics, especially the ideal kinematics are identical. Furthermore, the lower heating and pressurization requirements for thermosets make it easier to perform multiple forming experiments. Hence, while all of the discussion in this chapter is developed for thermoset composites, much of it is of a fundamental nature and may apply (under the right circumstances) to thermoplastics as well. A major barrier to the broad application of advanced composite forming processes in industry is the occurrence of a variety of failure modes such as in-plane fiber buckling, fiber misalignment, and laminate wrinkling [2,3]. Formability prediction tools are needed for a robust design and efficient manufacturing process planning. Unfortunately, the current collective knowledge of the deformation mechanisms in forming of advanced composites is quite incomplete. The technical complexities in the modeling of forming processes are related to the complex nature of the materials to be formed, as well as the large-scale, partially unsupported nature of the deformation. This chapter will review the research in this area.

Fig. 11.4. Reinforced diaphragm forming process: (a) 122 cm long part formed using reinforced diaphragms; (b) close-up of reinforcement.

446


Section 11.2 introduces the deformation modes of laminates in the forming process and identifies the desirable modes. Quantification of the deformation modes leads to the recognition of important shearing mechanisms. With the theory of differential geometry, general calculation methods for ideal mappings of various parts are obtained, and ideal shares are calculated for hemisphere and curved Cchannels. Section 11.3 combines the data from thermoset forming experiments with the constitutive behavior of the composites and the rubber diaphragm. This leads to preliminary forming limit diagrams. Finally section 11.4 presents concluding remarks and introduces some innovations to the original diaphragm forming process of thermoset composites. 11.2. Kinematics

11.2.1. Introduction and differential geometry results The unique kinematic characteristics of aligned continuous fiber composites are directly related to their structure. Under forming conditions, the fibers can be regarded as inextensible in their longitudinal direction and the composite incompressible. If, in addition to these two assumptions, one assumes that even fiber spacing is maintained (this is the "ideal composite assumption", see, for example, [9,10]) the required strains to obtain a given deformation can, in principle, be directly calculated [3,9-12]. When these results are then used with appropriate constitutive equations, statements can be made concerning the build-up of stress in the formed part. This same approach could be used with intermediate shapes during the entire forming sequence. Failure occurs when there is an alternative, lower energy deformation mode available which still satisfies the constraints of the forming process. In this section we will outline the basic "ideal" deformation modes for the composite. We start by defining two local co-ordinate systems as shown in fig. 11.5. In the material co-ordinate system, axis 1 lies along the fiber direction; axis 2 is

Fig. 11.5. Illustration of the material co-ordinate system, 1, 2, 3, and part co-ordinate system,/z, v, (.


447

perpendicular to the fibers and within the plane of a lamina; and axis 3 is vertical to the ply. (Hereinafter the terms "ply" and "lamina" are used interchangeably.) In the part co-ordinate system, axis ( is normal to the laminate; axes /z and v are two orthogonal directions within the laminate. Under the kinematic constraints noted above, the deformation modes of the composite laminate during forming are quite limited; essentially three shear modes within a lamina (illustrated in fig. 11.6) and one between plies (illustrated in fig. 11.7). For a part to be formed with only single curvature such as in simple bending, the necessary modes are: longitudinal through-the-thickness shear 1-'13 (fig. l l.6a), transverse through-the-thickness shear F23 (fig. l l.6b), and inter-ply shear (fig. 11.7) in the same order of magnitude as F13 and/or F23. The inter-ply shear, where plies slide relative to each other, can be denoted by 1-'v3 if v is defined as the direction of interply relative displacement. Parts with doubly curved geometries, on the other hand, are much more difficult to form and hence will be of major interest in the following discussion. The conformance of aligned fiber composites to these complex geometries requires an additional important shear mode: longitudinal in-plane shear F12 (fig. 11.6c), where adjacent fibers slide past one another within the lamina plane. The corresponding 3

3

2

2

(a)

)

(c) Fig. 11.6. Illustration of shear modes (a) 1-'13, (b) 1-'23 , and (c) I"12.

.... .

oo oo

'

'

.

.

. II

~

| i

....

b~6Vdc L

i

.....

i

|

1

v

Fig. 11.7. Illustration of inter-ply shear mode F3v.

448


&ter-ply shear 1-'u3 (fig. 11.7) is of considerably larger magnitude than in singly curved parts because of the different F12 between adjacent plies with different fiber orientations. If these shearing mechanisms are prohibited, then failure modes such as undesirable thickness variation, in-plane fiber buckling and laminate wrinkling may occur. The goal of forming can be simply put as enabling the desirable deformation modes while suppressing the undesirable modes. Since ideal inter-ply shear is directly determined by the ideal in-plane shear mapping of the corresponding plies, any calculation of inter-ply shear must be preceded by a detailed study of ideal in-plane fiber mapping. Here, we will outline the calculation of F12 and 1-'u3, for two important part shapes: hemispheres and curved Cchannels. In general, the required strains for ideal composites can be calculated directly only for relatively simple shapes [12]. More complex shapes would require a properly constructed CAD drawing [10-11]. To determine the in-plane shear 1-'12, consider the shear along a fiber element (fig. 11.8). If a fiber slips a total distance, 8, relative to its neighbor with inter-fiber spacing, h, then the total shear for the fiber can be written as F12 = ~

(11.1)

This can be related to the geodesic curvature, Xg, of the fiber by [10,11] L AI"12 -- / Kg(S)

ds

(11.2)

0

where L is the length of the fiber, and s is measured along the fiber. Furthermore, the above integral can be related to the Gaussian (or double) curvature K for the part surface over some region R, enclosed by M smooth curves Ci with exterior angles Oi (one of them representing the fiber of interest) by the Gauss-Bonnett theorem (fig. 11.9) [10,13]

d,+j'j/< dA-2 c

R

M

- oi i=1

• B

nr

Illlll L

F

Fiber element before deformation

Fiber element after deformation

Fig. 11.8. Quantitative definition of in-plane shear.

(II.3)


449

01

Fig. 11.9. Illustration of Gauss-Bonnet theorem.

Hence by using this result, the required shear can be determined from the part shape (K) and the fiber orientation (Oi). This procedure can be used to calculate the required ideal shears for a variety of complex shapes [10].

11.2.2. Ideal shears to form a hemisphere 11.2.2.1. In-plane shear [10] We wish to determine the in-plane shear for the fiber identified by the ideal path C 3 in fig. 11.10. Here the arcs of the closed path C are as follows: C1 is a semicircle on a great circle; C3 is a semicircle representing the fiber path of interest; and C2 and Ca are the connecting arcs that lie on a great circle. The geodesic curvature of arcs C~, C2 and Ca are all zero. The line integral in the Gauss-Bonnet theorem thus reduces to that of the fiber path C3. The exterior angles sum to 2zr, and since the Gaussian or total curvature of the hemisphere is 1

K -- R2

(11.4)

C4

C2

- - q b I---Fig. 11.10. Illustration of fiber paths

on a hemisphere.

450


the Gauss-Bonnet theorem thus reduces to -

l Xg ds -

1

K A - - ~ (~rRb) - Jr sin 4~

(11.5)

c3

or IF121 - zrsin 4~

(11.6)

11.2.2.2. Inter-ply shear [3]

Knowledge of the in-plane shear pattern for a given part geometry allows the preform shape to be calculated. Figure 11.1 l a shows the preform for a hemisphere with an orthogonal grid. Referring to the co-ordinate system with origin at the center of the preform, and considering a [0o/90 ~ laminate one can identify a series of points on both the 0 ~ and 90 ~ plies that have the same (x, y) co-ordinates. These points will move relative to one another after forming. Figure 11.11 b shows the location of the points A and B, after forming. The positions of these points after forming are determined assuming that the individual plies achieve ideal in-plane shear patterns. The relative movement of the points is given by, (11.7)

M - fiR

where R is the radius of the hemisphere, and/3 is the azimuthal angle between the points (X1, YI, Z1) and (X2, Y2, Z2) after forming. From the dot product of the vectors,

[1

fl -- COS-1 ~-~(XlX2 -[- Y1 Y2 + 2122)

]

(11.8)

or ) + sin 02 cos 01sin ( 02 ) + C 02 COS01

sinOlcosO2sin(Oo2

fl -- COS-1

cos01 cos02COS cos01

(Oo:)

cos c

(11.9)

02

Z

//

VI

1

So,

i/JI

.

Y

A&B x (a)

(b)

Fig. 11.11. (a) Preform shape for a [0090~ hemisphere, and (b) quadrant of formed part showing the relative motion of points A and B.


451

Figure 11.12 shows the relative inter-ply movement for a quadrant of a hemisphere. The maximum occurs when x = y ~ 0.934R. At this location/~ ~ 0.297. Therefore the maximum relative inter-ply movement M m a x is given by M m a x ~ 0.297R

(11.10)

This represents a rather large displacement. For example for a 7.5 cm radius hemisphere, the maximum inter-ply movement necessary to form an ideal [0~ ~] part is of the order of 2.25 cm. In practice this movement should occur in the resinrich layer that is found on the surface of most prepreg plies. The inter-ply shear required is calculated by dividing this relative movement by the thickness of the inter-ply layer, which for most materials is of the order of a few fiber diameters. This calculation yields a value for shear that is on the order of 1,000 or roughly two or three orders of magnitude larger than the in-plane shear.

11.2.3. Ideal shears to form a curved C-channel [3] 11.2.3.1. In-plane shear Figure 11.13 shows the kind of C-channel we are concerned with in this work; the two contours are arcs of concentric circles with radii R1 and R 2. Figure 11.14 shows the inner flange of radius R1. Note that the geodesic curvature of the fiber paths is not changed by unrolling the flange onto the flat. We consider the 0 ~ plies where the fibers run along the length of the C-channel, i.e. in the x-direction. The appropriate ideal fiber mapping is the one where shear is not required on the top face of the Cchannel; all shearing occurs on the flanges. The tangent angle c~ on the top is duplicated on the flange [11]. Therefore the shear at point P is simply the angle enclosed by the arc, which is c~. We can obtain a more general expression for the shear at any point on the flange by considering the geometry shown in fig. 11.15. The distance between fibers fo and fp is, A -- R I ( 1 - c o s or)

Fig. 11.12. Plot of inter-ply displacement on one quadrant of a hemisphere.

(11.11)

452


R1

Fig. 11.13. Dimension of curved C-channel.

~

0

P

P (x=otR1) X

Inner Flange-Top View

Unrolled Flange

Fig. 11.14. Illustration of a fiber path that passes along both the top and the inner flange of a curved Cchannel.

/oN

(a

_O t~

/~

Ptx=o~R1)__ -x

S

Fig. 11.15. Parameters used to determine the shear along a fiber segment, A - A o , on the inner flange of a curved C-channel.


453

The distance lateral to the fibers is given by Sn--OAo

(11.12)

PA = Sn - A = Sn - RI(1 - c o s a )

(11.13)

Then,

and the co-ordinates of the point A are given by Xa = Xp + PA sinc~ = Rlc~ + [Sn - RI(1 - cosot)] sinc~

(11.14)

YA = PA cos c~ = [Sn - R1 (1 - cos a)] cos ot

(11.15)

The length of the fiber segment A o - A is given by

If

k, dot ] + \ dot J

dot

(11. 16)

O

Therefore the shear at any location along the fiber on the inner flange can be related to the fiber length by the expression, If = 2R1 sin F12 + ( S n -

R1)F12

(11.17)

A similar analysis yields the following expression for the outer flange: If = 2R2 sin F12 - (Sn + R2)Fle

(11.18)

When R1 (or R2) and Sn are known, for any given fiber length we can calculate the shear using Newton's iterative method. A useful result, however, is that the maximum shear required to form a C-channel is simply the angle of the enclosing arc a. Figure 11.16 shows an ideal fiber mapping for a 90 ~ ply where in-plane shear is allowed on the top face. This is consistent with some experimental observations for large parts. F r o m kinematics again the maximum in-plane shear required is simply or. To determine the inter-ply shear, however we need to know the positions of all fibers

l

02

O,

Fig. 11.16. Top view of a C-channel 90~ mapping.

454


after forming. Referring to the co-ordinate system given, the parametric equations describing the curve P - B are, x = R1 cos01 - Rl(Ctl - 01) sin01 y = R1 sin01 + Rl(Ctl - 01)cos01

(11.19)

w h e r e 0 ~20, the material thickness (t) may be assumed to remain constant and the strip arc length is calculated at the mid-thickness plane. However, if the bend radius is less than 2t, thinning should not be ignored and tables, based on observed results and common experience, are consulted to calculate the bend allowances [1,7]. 12.3.3. Roll schedule and flower pattern design

It must be appreciated that a final section can be produced by following various deformation routes and the determination of this route or the roll-pass schedule is

Roll forming of sheet materials

485

Fig. 12.10. Roll flower pattern for an equal leg channel section.

(a)

(b)

Fig. 12.11. Roll flower patterns for top hat section: (a) formed from channel section, (b) formed from flat strip. the most important aspect of designing a roll forming mill. An erratic design involves the loss of material and time, and may end up producing unsaleable products. Even a simple C-section or a channel section may be formed through various roll schedules and, due to the appearance of the flange position at different stages, the cumulative pictorial representation of the sections is commonly referred to as flower diagram (fig. 12.10). The example of a slightly more complex "top-hat" section is shown in fig. 12.11, which illustrates the forming of the section from a channel or a flat strip following different roll schedules. The membrane and shear strain distributions in the sheet for producing the same section vary with the selected roll schedule and their implications will be discussed later. Flower pattern design may conveniently be considered by splitting it into four main areas: (i) section orientation, (ii) sequencing of bends, (iii) bending at each stage, and (iv) means of forming bends.

12.3.3.1. Section orientation Any section's orientation is determined by a number of (often conflicting) considerations careless orientation may result in tooling, production and quality problems. As with many other aspects of roll forming, section orientation is often a compromise, some of the factors influencing the designer's final decision are discussed in the following paragraphs. Whenever a bend is not formed by both male and female rolls, it is termed a blind bend or fresh-air bend (fig. 12.12). Such bends often result in sectional inaccuracy and are thus to be avoided if at all possible. Careful orientation may reduce fresh-air bending. Spring-back (the metal's tendency to return to its original shape) is a common problem in roll forming and there are several methods for overcoming this. Where spring-back is likely to be a problem, careful section orientation will allow the use of side rolls to "overbend" a leg. The section's orientation will be influenced by the preferred vertical centre line. The vertical centre line is a theoretical line whose position relative to the centre of the

486

S.J. Mander et al.

/

: ,

~/" BENDING

Fig. 12.12. Example of fresh air bend.

machine does not change. Where mention is made of the left-hand side or right-hand side of a section, this refers to the position relative to the section's centre line. The vertical centre line is itself often a compromise, the main criteria for choosing it being balancing horizontal forces each side of the guide line, allowing metal movement by forming rather than drawing, and selecting a vertical centre line that passes through the deepest part of the section. The surface finish of pre-finished material can be damaged by careless orientation. The pre-finished material should be orientated so as to minimise "rubbing velocity" (the relative roll velocity between opposite surfaces) and also if possible, to aid operator inspection. Staining or differential cooling may occur on sections if coolant trapping is possible this may be minimised by careful orientation of a section. Auxiliary operations such as notching, piercing, embossing and welding can obviously dictate a section's orientation. Cut-off tooling should also be considered, since with proper orientation it may be possible to eliminate additional deburring operations by altering the position of the burr. The factors mentioned above cannot be considered exhaustive, merely representative, since any section may produce unique problems and may require a unique solution demanded by equipment, tooling personnel and setting constraints.

12.3.3.2. Sequencing of bends The order in which the designer chooses to form the bends is termed the sequencing of the bends. In very simple sections such as channels and angles, there is no choice in the sequencing (since there is only one bend), but in complex sections there can be a very large number of possible permutations. Ideally, designers work from the centre line outwards in sequencing, which would mean that a bend once formed would never be subject to further deformation. However, when sequencing bends, a designer must consider a large number of


487

often conflicting factors. Hence it is often not possible to work from the centre line outwards since there are often good reasons to form by other sequences, for instance to (a) avoid fresh air bending, (b) reduce metal movement, (c) avoid excessively large bending moments, or (d) improve the smoothness of the flow of the material.

12.3.3.3. Bending at each stage After having decided how a section will be orientated and the sequence by which bends will be formed, it is necessary to decide how much bending should take place at each stage. While there are a number of techniques to aid the designer in deciding how much forming to perform, there is no one, generally accepted, method. The determination of roll schedule is complicated but, as mentioned earlier, is extremely important for the overall success of the design. As a consequence much of the research, both experimental and theoretical, has been dedicated to study the influence of the roll schedules on product quality [8-18]. However, the research has essentially been restricted to the study of "basic" profiles such as channel, top-hat and circular sections. Though more complex profiles can be degenerated into these simpler sections to understand the fundamental deformation mechanics, the experience of the tool designer plays a vital role in the final determination of the roll schedule and only a few guide rules are available to the designers [7,19]. Some salient features of roll design will be highlighted in the following sections so that the roll forming of fibre-reinforced sheets can be discussed in a proper context. Number of forming stages and roll angles. For reasons of economy, it is important to select a roll schedule with the minimum possible number of form rolls giving an acceptable range of product quality. As the terminology and the basic principle change little, the discussion will be based on a simple channel section. The most common practice is for the designers to use the forming angle method which assumes a smooth process of deformation from the beginning to the end of the roll forming mill (fig. 12.13), and the strip edge follows a straight line. The so-called forming angle

Rolt sta•

splndte c

e

H__

~

1 N

~_~ L = H~cotr N = L/d

L where H r d L N

= = = = =

Final section height. the Forming angte. • rol[ s t a t i o n pl• [ength. the r e q u l r e d ?ormlng length. • number o? rolt s t a t i o n s required.

Fig. 12.13. Diagram of forming angle method.

488

S.J. Mander et al.

is a statement of the material's formability, and for steel it is generally assumed to be 1~ Now presetting the pass length of the mill, the number of roll stations can be calculated by dividing the forming length (determined from the known flange height, H, of the final section) by the pass length. One additional roll station is included for the shape conformance of the final profile. However, this method has been criticised by researchers [11,16] for ignoring the intermittent nature of the deformation. Furthermore, to minimise the distortion of the product it is necessary to keep the deformation at the last forming stage to a minimum and the first roll station which is often used essentially to ensure proper feeding of the strip material into the roll forming machine, is usually not to have a large fold angle. These constraints clearly suggest that the hypotenuse of the forming angle diagram should not be a straight line; however, the actual shape of this flow pattern varies with the style of a designer. Ona et al. [13] suggested a cubic polynomial (fig. 12.14), to describe the deformation height y = A x 3 -Jr-B x 2 Jr- C x -Jr-D

(12.1)

which satisfies the following boundary conditions at x = 0 and x = N, d y / d x = 0 (12.2)

at x = O, y = O, and at x = N, y = H(1 - c o s 0o) The angle at any particular station is given as cos Ot = 1 + (1 - cos 00) [i2(2i - 3 N ) / N 3]

(12.3)

N is determined by an empirical method from a large database, grouped under different section types. Apparently this method works well for reported sections

Y Y = AX~ + BX2 + CX + D .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

H~(l-cos~r)/

/ /

i

//

.....L o

~r

i i

i

.,.

x

N

Fig. 12.14. Assumed flange angle during forming.


489

I

]-~

RI,RP__P ,. nI AlzA2,...,An !

RI - R2 = R3 -- ... - R . = constant Al - A2 = A3 = . . . - A~ = constant Fig. 12.15. Constant

inside radius

method

of forming

bends.

F

R1 A ~ R2 I

AIR1 = A2R~ = AsR3 = ... = A . R . = c o n s t a n t Fig. 12.16. Constant

element

length method

of forming

bends.

with some minor modifications from the designer but suffers from the major drawback of depending on the limited design style and data of a particular company.

12.3.3.4. Means of forming bends After making a decision on the sequencing and magnitude of the bends, it is necessary to decide on the means of forming bends. In general, the only parameter within the designer's control is the inside radius of the bend (although it is possible to control the shape of the bends too). The most common methods of forming bends are the constant inside radius method (fig. 12.15), and the constant element length corner method (fig. 12.16). Each method has its advantages: the constant inside radius method reduces springback and distributes deformation more evenly between passes, whereas the constant element length method reduces wear on the rolls and the likelihood of "trapping" of material. The designer should obviously decide which method is more suitable for each job; in practice, however, individual designers seem to have preferences and become skilled in minimising the disadvantages of a particular method.

12.4. Computer-aided design in roll forming There can be little doubt that the development of CAD/CAM techniques has revolutionised many aspects of roll forming. Almost all of the advantages of the computer are relevant to form roll design. In particular, the computer can carry out large numbers of complex calculations effortlessly, store large amounts of information and retrieve it quickly, produce high-quality graphical and text documentation and allow simple editing to an existing design. Amongst the benefits that have resulted from CAD/CAM systems for roll forming, have been reduced lead times, fewer calculation errors, improved design, the development of form roll databases and more efficient manufacture.

490

S.J. Mander et al.

Originally, many roll forming organisations chose to develop their own in-house systems. This perhaps reflects the idiosyncratic nature of roll forming, in which opinions vary from company to company as to what facilities a CAD/CAM system should offer. To a large extent, then, such systems effectively computerised existing procedures and standards within particular roll forming organisations. CAD/CAM systems have not only automated many of the relatively routine, nondesign tasks, but have also resulted in improved designs. Firstly, the removal of these peripheral tasks has allowed the designer to concentrate on pure design. Secondly, since the data input to these systems has been reduced, it is very simple to alter the design, thus making it possible to examine several designs and choose the most suitable one. In terms of design analysis, there is no doubt that the CAD systems have resulted in greatly enhanced visualisation through 3-D wire frame constructions. It may fairly be said, though, that deformation analysis is still very much in its infancy, and that form roll design is still largely based on the individual designer's experience of material properties, mill properties and the roll forming process. The basic components of roll forming CAD/CAM systems tend to be fairly similar, and can be summarised by fig. 12.17. The finished section, flower pattern, roll design and roll machining software form a definite route for data to flow. More advanced components, such as enhanced visualisation, deformation analysis, and data management, provide supporting functionality which may be present depending on the nature of the system. The purpose of the finished section software is to fully define the finished section and to perform the strip length calculations. The vast majority of roll-formed sections consist of linear sections separated by circular arcs, and finished section definition consists of these plus the metal thickness. Flower pattern design is central to roll design, and consists of nominating the elements to be bent at each stage, the amount of bending to take place at each stage, and manner in which the element is to be deformed. Typically flower patterns are visualised as in fig. 12.18, although various plan, side and three-dimensional views are also often employed.

Finished Section

~

~/

-oo s

Flower Pattern Software Additional Features

Roll Machining | ~ Software ..... !

.....

Roll Design

Deformation Analysis Enhanced Visualisation Data management etc.

Basic Software

Fig. 12.17. Typical components of a roll forming C A D / C A M system.


491

Fig. 12.18. Typical flower pattern generated by the COPRA | CAD system. (Courtesy of DataM GmbH.)

The purpose of roll design software is to define and draft the form rolls and to quantify the roll profile into a data file. In addition to the section and flower pattern data, the pass height and roll centre-to-centre distance, the drive and clearance surfaces and the side roll contour (if required) must be defined. The machining of the rolls is generally performed using a numerically controlled lathe. Future development may be anticipated in the area of computer-aided deformation modelling. The current restrictions on this are the intense computer resources demanded to achieve realistic results. There is also some uncertainty about the interpretation of strain results to assess forming defects and about the effects of residual stresses on forming limits.

12.5. Deformation analysis of roll forming Deformation analysis in roll forming has traditionally considered two areas: modelling the deformed surface during roll forming and modelling the strain distribution in the sheet during roll forming. Often, but not always, the former has been seen as a stepping stone to the latter. This has perhaps been a little misdirected: roll formers have for decades been skilled in judging the severity of deformation from the deformed shape of the sheet, and could learn much from visualising the deformed surface at the design stage. The more recent application of finite element methods, has the advantage of determining the deformed surface and the strain distribution simultaneously, and undoubtedly far more work can be anticipated in this direction.

12.5.1. The deformed surface in roll forming In this section it is shown that the dominant effect on the shape of the deformed surface is the shape of the rolls. Since this effect is purely geometric, the deformed surface can be approximated relatively accurately with very simple material models. It will be seen later that this is not the case when determining the strains in the sheet. For this reason, an accurate surface model is no guarantee of accurate strain prediction. As a simple model, and neglecting spring-back, the roll forming process can be considered to consist of three regions. For instance, if we consider a single pass in the roll forming of a channel section, and remove all rolls but the lower forming roll of the pass (fig. 12.19), we can identify three regions: region I where the channel does

492

S.J. Mander et al.

-\~ \\\\i I

Fig. 12.19.Typicalregionsin the roll formingprocess. not deform, region II where the channel does deform but the sheet is not in contact with the rolls, and region III where the channel deforms and is in contact with the rolls. The combined length of regions II and III is conventionally known as the deformation length of the pass. It should be noted that the deformation length is not related to the pass length (the combined length of regions I, II and III). The influence of the roll size on the deformation length is indicated by a sometimes quoted "rule of thumb" that the deformation length is equal to the centre-to-centre distance between the lower and upper rolls. By considering the work done in forming a channel to consist of transverse bending and longitudinal stretching, and minimising to find the deformation length, Bhattacharyya et al. [16] were able to derive a very useful expression for the deformation length of a channel section:

L-

V 3t

(12.4)

where L is the deformation length, a is the flange length of the channel section, t is the sheet thickness and A0 is the bend angle increment during the pass. It will be noted that since a rigid-perfectly plastic material was assumed, all of the properties in the expression are geometric. Despite this, the expression proves to be surprisingly accurate for a variety of different materials, as demonstrated by fig. 12.20. It may be noted that eq. (12.4) is a special case for a channel section, and that using the work


70

60

THEORETICAL STEEL ALb')zINItrg

X

9

493

X

z.r 9~

50

N

40

~4

,(~ X

10

20

30

40

50

DEFORMATION LENGTH (mm)

Fig. 12.20. Deformation length, theoretical and experimental results.

expressions derived by Panton et al. [20], the general case for any section with a single active bend is given by

L -- V/8J?O

(12.5)

where J is the polar second moment of the section about the fold line. Although eq. (12.4) proves to be an accurate estimate of the forming length for channel sections it does not accurately model the actual shape of the deformed surface. This is unsurprising since it neglects the geometric effects of the rolls in region III. To model the deformed surface we introduce a concept known as the "bend angle curve" [21]. Returning to fig. 12.19, if we make the assumption that the channel flange remains straight as it moves through the pass, the deformed surface is entirely described by the variation of the bend angle 0, along the pass length, the bend angle curve. The effect of the roll geometry can be mapped onto the bend angle curve at any section by the construction shown in fig. 12.21, and this defines the shape of the bend angle curve in region III. To determine the entire bend angle curve, it is necessary to determine the shape of the bend angle curve in region II, and the transition points between regions I/II and II/III. The shape of the bend angle curve in region II may be determined using the minimum energy method described in reference [16]. The transition points may be determined by assuming continuity of slope along the bend angle curve. The resulting bend angle curve is derived entirely geometrically; despite this it gives accurate results, as shown in fig. 12.22. Note that the geometric effect of the rolls is clearly evident in fig. 12.22. It should also be noted that the maximum slope of the bend angle curve occurs at the point of tangency between regions II and III, i.e. at the section where the sheet first contacts the rolls. We will see later that this indicates that the longitudinal strain will be a maximum at this point. Alternative methods of modelling the deformed surface use empirical or semiempirical methods. Kiuchi [22], for example, uses a semi-empirical approach. The

494

S.J. Mander et al.

:r

BASE OF CHANNEL

A'

YI

O'

I 1 !

02

~

1:3 Z U.I 113

....

ZA

0

(FORMING DIRECTION)

F i g . 12.21. Mapping the effects of the roll onto the bend angle curve.

90

-

, .

,

,

,,

::

:

-

80

A

60

"

"

A,

A ....

&

a

': 0''0 --i " ~

0

0

25

50

75

100

1~5

150

Distance from previous roll centre (mm) F i g . 12.22. Experimental results and theoretical predictions for the bend angle curve.

forming path of any point on the cross-section (fig. 12.23), is defined by a sinusoidal shape function - - presumably defined from empirical data. A family of surfaces may be generated by varying the value n, and the actual deformed surface is determined by a minimum energy method. It may be noted that although the geometric effects of the rolls are not directly included, the choice of the sinusoidal shape function models them indirectly.

Roll forming of sheet mater&&

495

[ ((I+1)th Stand) x

( x(z) = Xl + (X2-X,) s(z) P~ (X ~,~'~

y(z) = Y1 + (Y2-YI) s(z)

~

nd)

s(z) = sin ((rd2) (z/L)")

Fig. 12.23. Kiuchi model of the deformed surface in roll forming.

The well-known COPRA | CAD system appears to use an entirely empirical method for modelling the deformed surface. The forming path of a point is defined by a polynomial, the coefficients of which are determined from empirical data.

12.5.2. Modelling the strain distribution during roll forming With the exception of the finite element methods described in the following section, all methods of determining roll forming strains share the characteristic of further processing a model of the deformed surface. An accurate model of the deformed surface does not guarantee an accurate strain distribution. It may be shown [23], for instance, that for any roll formed surface, there is a family of potential strain distributions, and this makes it possible for the deformed surface to be modelled quite accurately but for the strain prediction to be highly inaccurate (this is demonstrated, for instance, by Zhu [24]). The simplest method for determining the strain distribution from a deformed surface is to assume that transverse sections of the strip remain plane orthogonal and a constant distance apart during roll forming. This situation has been analysed in detail by Panton et al. [20], for a general case, but in this chapter, the discussion is restricted to the basic concepts by considering the forming of a channel section (fig. 12.24a). Consider the forming path of a point on the tip of the channel, it lies in a cylindrical surface whose development can then easily be obtained (fig. 12.24b). It is clear that the length of the forming path on the tip edge is longer than that of a point in the base of the section, and that longitudinal stretching must take place. If it is assumed that the bend angle changes by an angle dO over a distance dz, then the longitudinal strain can easily be determined by the triangle in the plane development: 1 r2(d0)2

et = ~

dzz

(12.6)

496

S.J. Mander et al.

D

///

//,,

/

/

/ /

/

/

/

t

1.'~

/"/

498

S.J. Mander et al.

no shear strain (in which case there will be longitudinal strain). With metals, experimental results indicate that the real situation normally lies somewhere between these two cases. It remains to be seen whether the extreme directional properties of fibre composite materials push the strain distribution to one of the extreme cases, in which case quite accurate strain predictions may be possible geometrically using approaches like the Chebyshev net technique.

12.5.3. Finite element analysis of roll forming Although the simplified models described previously will continue to provide insight into the roll forming process, and may one day lead to a scientific basis for form roll design, the future of roll forming deformation modelling is likely to be increasingly provided by finite element analysis. The results of McClure and Li [28], and Heislitz et al. [29], show the possibilities of the method, e.g. fig. 12.27. At present, it must be said that few roll forming companies have the technical and computational resources necessary for such studies.

12.6. Roll forming of thermoplastic material Due to the relatively recent availability of continuous fibre-reinforced thermoplastic (FRTP) sheets, a large amount of commercial interest has been generated in the j

,:t+ i l I,

't

~t,

I1--T

20

dig

[ ,~-a, M

i "

:"

~"i

.o,.,

!

1o

............. '

. . . . . . . .

"'"

i'

t't__ '~ 0

-

t/,.Ii' M. JZXN l/

.0,.,

1

.

~h

i~-

Strain gauge position (mm)

I [

Distance from leading edge (mm)

J

Fig. 12.27. Experimental (left) and finite element (right) longitudinal strain results for the single pass roll forming of trapezoidal sections with differing fold angles (from reference [28]). Dotted line indicates the roll central plane.


499

development of low cycle time manufacturing techniques. It is generally accepted that thermoplastic composites lend themselves to mass production methods, due to their ability to be "reshaped" simply by the application of heat and relatively low forces. The other benefits, such as long shelf life, ease of handling and the potential for recycling, are also well recognised. In spite of this, it is felt that the benefits of FRTP composites are unlikely to be fully realised until manufacturing techniques have become more conducive to mass production. Recent efforts in forming FRTP sheets have centred on variations of pressure forming and diaphragm forming techniques [30-32]. Other methods have transposed standard sheet metal forming operations, such as matched die stamping [33] and incremental forming [34,35], to these materials. Despite the large number of processing methods now available, there still remains a well recognised demand for the ability to produce long narrow profiles, such as top hat and channel sections, from FRTP sheets. An obvious manufacturing method offering high production rates for such sections is the semi-continuous roll forming widely used in the sheet metal industry. Whilst the practice of roll forming is well established, as mentioned earlier in this chapter, the deformation mechanism that involves three-dimensional bending and stretching, is not yet fully understood. It is felt that this process, with some modifications, lends itself to be used in the production of narrow and wide profile FRTP composite sections and goes some way towards realising their full benefits. Preliminary trials of roll forming of FRTP composites have been reported by Cattanach [36], but the degree of success and the detailed methodology of these trials remains unpublished. Recently Mander et al. [37] have reported a systematic study on the roll forming of FRTP composite sections using a modified metal roll forming equipment, and have shown that useful structural sections can be easily produced at 10 m/min with a clear possibility of achieving higher line speeds. This section of the chapter outlines the findings of continuing research carried out at Auckland University. The effects of various roll schedules and other forming parameters on process reliability and product quality are closely examined. Particular attention is given to the determination of the deformation length and the development of strain in the strip. A novel method of obtaining real time strain measurements during the deformation process is introduced, which offers researchers and designers a unique opportunity to understand the deformation process of FRTP sheets. 12.6.1. Materials

Fibre-reinforced thermoplastic composite sheet materials have become increasingly popular in recent times and are now available in a variety of different product forms, ranging from stiff board-like preimpregnated sheets, to drapable commingled woven fabrics. The materials presently available can be broadly classified into two groups: those which require impregnation as part of the manufacturing process, and those that are supplied in preimpregnated (prepreg) form. Interestingly a number of manufacturers, such as Vetrotex, supply their material in either form depending on the requirements of the particular user.

500

S.J. Mander et al.

The results of a series of unpublished tests performed by the authors have shown that the roll forming process can be successfully applied to a wide range of commercially available composite sheet products. However, the experimental investigation presented here uses Plytron | (a continuous uni-directional glass fibre (v/v 35%)/ polypropylene (PP) prepreg) laminates consolidated from four plies of prepreg sheet, giving a nominal strip thickness of 2 mm. The strips were consolidated at 180~ under a 6 kPa vacuum for 20 minutes. Roll forming test specimens were cut to 1000 • 90 mm so that the control axis was aligned with the rolling direction. 12.6.2. Roll forming equipment and procedures To facilitate the roll forming investigation of F R T P sheets, a commercially available five-stand horizontal beam raft sheet metal roll forming machine was employed. The roll former was fitted with a variable speed drive to the interconnected bottom rolls. After preliminary trials a friction drive for the top roll of each stand was installed to ensure the matching of its angular velocity with that of the bottom roll. The salient features of the roll forming equipment are provided in table 12.1. A top hat section, as shown in fig. 12.29a, was selected for this study and initial trials were conducted using an industry standard flower pattern (flower A, fig. 12.28) used for producing this section in aluminium alloy or mild steel. A second flower pattern (flower B, fig. 12.28) was subsequently investigated, both roll configurations having a constant driving diameter for top and bottom rolls. To enable the F R T P sheet to be formed, a pre-heating oven was positioned on wheels close to the first stage and in line with the centre line of the roll former. The F R T P sample was placed on a Mylar T M strip in a drawer mechanism which was constructed in a way that it also served as a feed guide for the roll former. To enable the temperature of the F R T P strip to be measured during the preheating stage and subsequent roll forming operation, a fine 0.75-mm K-type thermocouple wire was consolidated in the centre core between the second and third layers along the laminate centre line with the hot junction at a depth of 200 mm from the leading edge. An optical sensor was placed prior to the first stage of the roll former TABLE 12.1 Roll former specifications Type: Number of stands: Shaft diameter: Stand width Drive: Speed control: Roll stand pitch: Vertical adjustment: Roll material: Feed stock table:

Horizontal beam raft (light-medium gauge) 5 40 mm 350 mm Bottom- chain via 3-phase AC 410 volt T o p - friction via bottom roll Infinitely variable speed, 0.1-10.0 m/min 275 mm Manual screw thread- 75 mm 1040 Steel, DelrinT M plastic 400 mm • 2000 mm


I

~

......

Flower A

Roll Station

ao

1

25

2

47

3

67

48

4

81

76

5

90

90

,.

po 0 ,, 2I

501

Flower B

47

13~ ,..0 21

.,. 67

48

(x ~

30

90 .... 90

90 90

Fig. 12.28. Roll station flower diagrams.

which enabled the position and speed of the strip to be measured throughout the forming operation. The optical sensor was triggered by strips of aluminium foil attached to the upper surface of the test sample at measured intervals. A traditional experimental approach was adopted in which each of the various roll forming parameters was examined individually while the other variables were kept constant. An optimum inlet temperature was determined which was used for all subsequent trials. Further trials investigated the influence of laminate architecture. The effect of roll forming line speed and a second roll schedule were also examined. A simple cooling ring, which consisted of a coiled perforated copper tube through which the cooling agent was passed under pressure, was installed at the exit side of stage 5. This cooling ring was then positioned between stages 4 and 5 for use with the second roll schedule (flower B). For all tests the same preheating sequence was used, namely the sample was preheated to and held for 5 min at 175~ then cooled in a controlled manner to the desired entry temperature and fed into the roll forming machine. All the roll formed samples were then compared for conformity to the desired geometrical shape (fig. 12.29a), in accordance with the normal procedures for roll formed sections. The deviation from intended formed angle 8 is defined in figs. 12.29b and c. A negative value for 3 is universally referred to in sheet forming as spring-back and hence a positive value of 3 can be termed as negative spring-back or spring-forward. The extent of curvature was measured as the amount of offset over the span length. With the condition of the fibres being an important consideration in FRTP composite structures, a visual inspection was made of the laminate to establish the degree of out-of-plane fibre buckling and in-plane fibre wrinkling.

12.6.3. Quality assessment of formed parts As with any forming operation it is important to be able to produce parts which meet high tolerances. The quality of each successfully rolled sample was assessed L--

, (3)

50mm

.d

I

Web

b)

J

c)

Fig. 12.29. Dimensions of top hat section used in this study, with definition of deviation from intended geometry 8.

502

s.J. Mander et al.

with regard to two important criteria: (i) deviation from that of its intended geometry, and (ii) severity of fibre buckling and wrinkling. All samples that were successfully roll formed were checked for conformance to the desired geometry, the results of this are shown in table 12.2. A visual rating out of 10 was given for the extent of in-plane fibre wrinkling of each sample with a high score indicating a significant presence of wrinkling. From these results it is evident that a larger scatter of formed geometry exists for those samples formed at temperatures other than at an inlet temperature of 140~ Based on this it was decided that the preferred roll forming inlet temperature for this study was 140~ Table 12.2 shows that the degree of in-plane wrinkling is greater at the higher inlet temperatures which is believed to be symptomatic of a lower than desirable matrix viscosity. The relatively high rating for wrinkling at 130~ is given due to the presence of out-of plane buckling, particularly in the flange 1 (F1)/flange 2 (F2) bend regions indicating delamination. The presence of buckling in this region may be a result of lower sample temperature due to its proximity to the strip edge. However, from temperature readings given by thermocouples situated in the middle of each flange, there appears to be no discernible temperature gradient measured across the width of the strip. It was observed during the trials that there was a considerable amount of relaxation after each stage and an appreciable amount of spring-back between F1 and F2 after exiting the roll former. This spring-back is contrary to the normal experience of spring-forward in F R T P bends [38]. A possible cause for this may be a large thermal gradient through the thickness of the sample caused by the insulating effect of the Mylar film attached to the bottom (or outer) surface. From the temperature readings it was found that, for all inlet temperatures studied, the exit temperature of the sample was such that the matrix was still in a partially molten phase, i.e. recrystallisation had not begun or was incomplete. Because of this high exit temperature the formed sections remained in a deformable or compliant state. To alleviate this problem an external cooling facility was positioned at the exit of the roll former. Some of the results of these trials, using roll schedule B, are given in table 12.3, where the relevant details for a roll formed aluminium strip are also given. Due to this introduction of cooling, some improvement in the formed geometry has been achieved; but still a large amount of variation in formed part geometry is present, particularly in the F1/F2 region. TABLE 12.2 Conformance measurements at various inlet temperatures. Line speed 5 m/min, flower A, laminate [4-15~ Temperature (~

8OFt/web(o)

8~ F2/F1 (~

Offset (mm/m)

Fibre wrinkling

170 160 150 140 130

+3 to-3 +2 to -2 +2 to -2 +1 to -1 +3 to -3

-5 -5 -10 -10 -10

2.0 0.8 0.6 0.5 -6.0

3 2 1 1 4

to-15 to -10 to -15 to -15 to -15


503

TABLE 12.3 Conformance measurements with various cooling mediums. Line speed 5 m/min (*10 m/min), flower B, laminate [+ 15~ inlet temperature 140~ Cooling medium

8~ F1/web (~

8~ F2/F1 (o)

Offset (mm/m)

Wrinkling score

None Pressurised air Water spray Pressurised air*

+2 +2 0 0

-6 -6 -2 -2

1 1.5 0 0

1 1 1 1

to to to to

-2 +5 -2 -2

to to to to

+12 -9 +5 +5

From these trials it may be concluded that the exit temperature of the strip is a significant factor in producing a component with minimal deviation from its intended geometry. It is also evident that samples formed with the water spray cooling have improved conformance to the intended geometry with a lower range of deviation. These results are expected if the sample temperatures are considered (fig. 12.30), where it may be seen that for the water cooling trials, the exit temperature is 100~ and recrystallisation has been completed. For the sample formed at 10 m/min the results are still acceptable in spite of the higher exit temperature. This establishes that higher line speeds are possible provided the temperature is correctly managed. It must also be noted that in using flower B roll schedule, the deformation process can be completed in four stages with a greater degree of deformation at stage 1, which is higher than what is practical in roll forming metallic sheets. It is generally recognised that when thermoforming FRTP sheets, fibre orientation can have a large influence on the quality of the formed part [39]. Having determined an appropriate roll schedule and temperature regime for the roll forming of Plytron, various laminate architectures were examined with the results shown in table 12.4. Of particular interest are the ratings for in-plane fibre wrinkling where a definite trend is

Fig. 12.30. Sample temperature profile during roll forming operation with cooling facility between stages 4 and 5, flower B, line speed 5m/min, laminate [+15~ .

504

S.J. Mander et al.

TABLE 12.4 Conformance measurements for various laminates. Line speed 5 m/min, flower B, inlet temperature 140~ pressurised air cooling Laminate

8~ F1/web (~

8~ F2/F1 (~

Offset ( m m / m )

Wrinkling score

[+15~

+2 +2 +0 +3 +2

-6 -4 -6 -4 -7

1.5 2.4 1 1.8 2.2

1 4 6 0.5 8

[+30~ [+45~

[0~176 s [90~176 s

to to to to to

+5 +4 +2 +5 +5

to to to to to

-9 -9 -11 -7 -12

seen, namely an increase in the presence of wrinkling with an increase in the fibre angle of the outer ply. As shown in fig. 12.31, the wrinkling is typically located on the inner radius of a bend, where compressive strains are to be expected, and most notably on the inner surface of the web. For the [45~ and [0~176 s out-of-plane buckling is evident on the inner radius of F 1 / F 2 , suggesting possible delamination.

12.6.3.1. Prediction of spring-back/forward in FRTPs The geometric conformance of a component is an important consideration in any forming operation. One well documented phenomenon in the processing of FRTP materials already observed in the roll forming trials, is the spring-forward effect which is primarily due to the anisotropic thermal properties of this class of materials notably the often large difference between longitudinal and transverse coefficients of thermal expansion. For uni-directional laminates, the spring-forward has been simply expressed mathematically by Zahlan and O'Neill [38] in the following manner: A0 -- (C~T-- C~L)0AT

(12.8)

Fig. 12.31. The influence of fibre architecture on formed part quality. Note that as the surface fibre orientation becomes more obtuse to the rolling direction the in-plane wrinkling effect becomes more severe.


505

where aT and aL are the transverse and longitudinal coefficients of thermal expansion respectively, 0 is the forming or mould angle and AT is the difference between the forming temperature and final temperature. Published experimental results generally support the above expression. However, Martin [39] and Hou et al. [40] give conflicting evidence for the influence of laminate stacking sequence on the magnitude of spring-forward. They also show that the forming speed has some influence on the magnitude of spring-forward but attribute this to fibre migration due to a lower than desirable matrix viscosity. A useful tool for predicting the distortion of bend angle in continuous fibrereinforced composite components is the finite element (FE) method. Zahlan and co-workers have shown how the technique may be used to successfully model the spring-forward, in thin carbon fibre/PEEK top hat sections. A similar analysis to that presented by Zahlan and co-workers has been undertaken by the authors in an attempt to model the distortion observed in the roll formed top hat sections presented earlier. In the interests of brevity the full details of the analysis are not given here. In keeping with the approach of Zahlan and co-workers, the model has been constructed in a (R, 0) co-ordinate system, as shown in fig. 12.32, such that only a single bend region is described. The numerical analysis may be simplified somewhat by ignoring the effects of any thermal gradients occurring within the component, thereby assuming a uniformly changing temperature field. The validity of this assumption is questionable, considering the thickness of the sample and the cold forming rolls utilised to form the bends but would seem reasonable for mouldings of "thin" cross-section. One further point that may be made regarding the modelling constraints is that the bend region is free to undergo unrestrained deformation, thereby rendering the solution independent of any specified elastic properties. However, the same could not be said if any type of elastic constraint is imposed, either internally or externally. Such would be the case in the presence of any thermal gradients, any localised crystallisation or any geometric constraints imposed by tooling.

130~

Fig. 12.32. Thermallyinduced distortion of uni-directional Plytron laminate formed to 90~

506

S.J. Mander et al.

Using this method the numerically derived spring-forward for the 90 ~ bend region has been calculated as approximately 1.5 ~, which is significantly lower than any of the results observed earlier in the roll forming trials. The most likely reason for this discrepancy may be the uniformly changing temperature field assumed to be acting over the entire section. As a comparison, one might consider the effect of a thermal gradient resulting in non-uniform property variation through the thickness of the region. In effect the deformation of this "more realistic" type of problem would become significantly dependent on the specified elastic properties, unlike the unconstrained deformation of the model described above. Clearly the effects of recrystallisation, or solidification from the melt, have a significant effect on the degree of spring-forward experienced in a forming operation and must be considered if components which meet high tolerances are to be successfully produced.

12.6.4. Temperature control In any forming operation involving FRTP composites, the forming temperature is invariably an important factor and traditionally the forming operation has been carried out at temperatures above the Tm of the matrix material (~160~ for PP). It has been shown [37,41] that polypropylene-based Plytron is capable of being formed at temperatures well below Tm providing the sample has been heated above Tm and then formed before the polymer matrix is able to reach its maximum degree of crystallinity. This is also supported by other researchers [42] who have applied differential scanning calorimetry (DSC) techniques, the results of which are shown in fig. 12.33. The large peaks and troughs shown in the graph are indicative of phase changes in the material. Upon cooling from the melt (cooling curve in fig. 12.33) recrystallisation begins at T1 (approximately 125~ and is completed at T2 (approximately 95~ During this stage the polypropylene matrix is in a supercooled liquid phase. This recrystallisation from the melt phenomenon allows a relatively large processing window, of nearly 60~ below Tm for polypropylene. The roll forming operation is particularly well suited to exploiting this material property, 25 r Cooling

g2o

T~

lO

r

Forming window

25

,

__,

20 .~

"~ 15

o

, ,

Tm

15

long

Heating ::~

5

5

o 0

25

50

75

100

125

150

175

200

225

*~

o 250

Temperature (~ Fig. 12.33. DSC heating and cooling curves for Plytron 35% v/v glass/polypropylene after reference [39].


507

being a non-isothermal deformation process performed in multiple stages over a relatively long forming time. While interpreting the results of the roll forming trials at various inlet temperatures it became apparent that the reliability of the process should be a major consideration. For samples formed at an inlet temperature of 160~ and above, there is approximately a 60% failure to complete the pass through all stages of the roll former. This is considered to be due to the relatively low stiffness of the composite caused by a lower viscosity of the molten matrix above Tm, resulting in the composite being unstable during the process. Conversely those strips formed at an inlet temperature below 135~ also demonstrated high failure rates (approximately 50%), but this can be largely attributed to the practical difficulties in supplying test pieces at a temperature close to the recrystallisation temperature of the matrix to the roll former. However, for samples formed at inlet temperatures of 150~ and 140~ a much lower failure rate was encountered (typically < 5%). It is important to note that most FRTP forming processes involve three sequential stages in their operation: heating, deformation, and cooling. To avoid the problems associated with material property variation, the deformation stage is typically carried out under conditions which are close to isothermal. In roll forming however, the actual forming process proceeds under highly non-isothermal conditions, as the deformation and cooling stages occur simultaneously. A number of authors have investigated the problems associated with non-isothermal forming of simple shapes [43,44]. Martin [43] has performed a series of simple vee-bending experiments that have highlighted the need to couple both deformation and cooling rates. It has been shown that if cooling advances at a rate which greatly exceeds that of the deformation then localised freezing is likely to occur, resulting in a component that has not fully realised the desired shape.

12.6.4.1. Development of cooling model The reliability of the roll forming process has been demonstrated to be highly dependent on the strip temperature being within the forming window indicated in the DSC graph shown in fig. 12.33. Hence it is desirable to be able to predict the temperature variation in the strip so that inlet temperatures, line speeds, and other important operating parameters can be incorporated into the development and design of such a roll forming process. With this in mind, a simple numerical cooling model is proposed that enables such a prediction to be made. Consider a strip of material as it passes through a roll forming machine at a constant line speed, v. In this analysis a local Cartesian co-ordinate system is adopted where the y- and z-directions are chosen to coincide with the strip's width and longitudinal axis respectively. The x-direction is aligned to coincide with the thickness which is assumed to remain constant throughout the deformation. In the present analysis it is assumed that the temperature variation in any given crosssection (in the x-y plane) will depend on its thermal history in addition to its current boundary conditions. Consider the section, indicated by the shaded region in fig. 12.34, moving through time and space and possessing an arbitrary temperature

508

S.J. Mander et al.

~Z

~

W Prevlous TemperQture

RolLing Dlrectlon

~ ~ -~J

J

F

i

tlme

e

t

d

~

Increment

Current Temperature Field

~

V

f Fig. 12.34. The current temperature field is assumed to depend on the current surface boundary conditions and the previous temperature field.

distribution. After some time increment, At, the same section will have moved through a distance Az and will have assumed a new temperature field. Initially, such a cross-section will possess a uniform temperature equal to that of the applied inlet temperature. As the section moves forward, the temperature field changes as the outer surfaces of the strip are exposed to various cooling mediums. If we invoke the assumptions made above, and also assume that the through-thickness temperature variation remains constant, then the equation governing the flow of heat can be simply expressed by 02T Ox2

=

10T

(12.9)

ot Pt

where ct is the thermal diffusivity, given by a kx/,OC p. The first- and second-order partial derivatives in eq (12.9) can be simply approximated by applying standard numerical finite difference methods. The transient temperature field for a section can then be evaluated at any time and simply related back to its displacement in the zdirection through the line speed. The model has also been constructed to incorporate a temperature-dependent thermal diffusivity. For instance, the value of a used in the evaluation of the temperature of the ith node after j + 1 time increments, is simply based on the temperature of the same node at the previous time step, Ti.j =

Oli,j+ 1 = ol( Ti,j)

The relationship between the through thickness thermal diffusivity, ct, and temperature in Plytron has been investigated at ICI Ltd. [42]. Their experimental data have been roughly approximated using a series of linear interpolation functions. These have been plotted in fig. 12.35, which serves to illustrate the relationship used in the analysis.


509

0.18 0.16 ~

0.14 el 0.12

".~ 0.08 C~ 0.06

~ 0.04

~

0.02 0 0

50

100

150

200

Temperature (*C) Fig. 12.35. Thermal diffusivity plotted as a function of temperature.

Boundary conditions. As the hot composite strip passes through the process it is subjected to two forms of cooling at its surface. The first of these is natural convective air cooling which occurs between the roll stands and involves the dissipation of heat to the working environment. The second form of cooling involves direct contact between the strip surface and the cold forming rolls, resulting in heat being conducted away from the strip. In both cases some information regarding the heat transfer coefficient, h, is required in order to accurately describe the surface boundary condition. However, in the absence of any such data a number of simplifying assumptions can be made. Between the roll stands, the surface of the strip is assumed to be insulated from any thermal effects arising from the surrounding environment. This can be somewhat justified by considering the thermal properties of the material in question. Both the glass fibres and polypropylene matrix are relatively poor conductors of heat and can thus be generally classified as good insulators. Moreover, an insulated boundary condition is relatively simple to implement in a numerical finite difference model such as the one described above. The conduction of heat away from the strip due to contact with the forming rolls is rather more complicated, the actual time depending largely on the line speed and deformation length of the strip. Rather than adopting a complicated boundary condition that would vary with position and time, an effective roll contact time is assumed, whereby the entire width of the strip is subjected to a temperature equal to that of Tro.. Therefore the boundary conditions may be summarised as: (i) Air cooling (between roll stands) 0T

m 0

OX x=O,h

(ii) Roll cooling over an effective contact time

TIx=o,h =

Troll

The input parameters used in the model are detailed in table 12.5.

510

S.J. Mander et al.

T A B L E 12.5. Roll forming variables used in the cooling model Inlet temperatures: Line speed: Roll temperature: Effective roll contact time: Strip thickness: Pitch distance:

130, 140, 150, 160~ 5 m/min 20~ 0.3 s 2 mm 275 mm

The results of the model are presented in fig. 12.36. Good correlation can be seen between the experimental temperature variation at the core and that predicted by the model. It appears as if the assumptions used in the analysis are valid for temperature measurements taken at, or around, the mid-plane of the strip. However, if more accurate predictions of temperature variation around the strip surface are required then it would be necessary to alter the applied boundary conditions. As already stated, the application of a more realistic surface condition relies upon some knowledge of a heat transfer coefficient. The model does, however, provide the framework within which to interpret the influence of various important processing parameters such as line speed, the number of roll stations, and inlet temperature. 12.6.5. Deformation length and strain development 12.6.5.1. Strain measurement

In order to quantify the amount of strain during the roll forming process, realtime strain measurement experiments have been conducted. This has been achieved by using a novel technique which involves bonding electrical resistant strain gauges 180 170 160

v

f~ 150

~

Model 130oC

P

14o

130

.'~.-~ 9

~

A

A 140oC

~

13 150~ X 160~

~,

120 110 100

2

3

4

5

Roll Stand # Fig. 12.36. A comparison between the numerical cooling model and experimentally obtained results.


511

onto fibre bundles arranged in a ribbon form. These ribbons are then consolidated, with the appropriate electrical connections, into the laminate with the fibre ribbon aligned with the fibres in the outer lamina. The samples can then be roll formed at the predetermined conditions enabling the recording of real-time strain measurements. An example of a typical strain profile is shown for a [0~176 laminate in fig. 12.37. This strain profile is in reasonable agreement with Zhu's [45] measurements for sheet metals at similar deformations. In the interest of brevity the full details of this technique are not given here. This method of real-time strain measurement in molten FRTP composites is of invaluable use to the manufacturing personnel, as it enables for the first time in-situ strain measurement during the deformation of FRTP sheets.

12.6.5.2. Deformation length In published sheet metal forming trials, the deformation length is often measured in a static condition after the sample has been partially deformed, either in situ, or once it has been removed from the forming rolls. However, due to the requirement that FRTP sheet be formed in a molten state, this approach would not seem to be viable. This is due to the large amount of relaxation which occurs in the deformation zone prior to the thermoplastic matrix recrystallising or solidifying. To this end it is necessary to measure the deformation length instantaneously with the aid of photography. This has been achieved by positioning two 35-mm SLR cameras at the inlet side of stage 1. While this method of measurement is inherently less accurate than those afforded by static measurement techniques, it is considered that it provides satisfactory confidence levels of • In general the results of the deformation length trials followed the same trends as those commonly observed for sheet metals. Not surprisingly, as the deformation, or roll angle is increased from 20 ~ to 40 ~, the deformation length of all samples is observed to increase, as shown in fig. 12.38. As a comparison, the deformation length, as predicted for metallic sheet material using eq. (12.4), has also been plotted on the same graph. It is interesting to note the similarity in trends between the deformation lengths of the FRTP material and those predicted using the theory

1250

9

9

,

m

,

9

9

,

,

.

9

,

.

.

o

,

.

.

9 9

i

750

r~

-250 -750

: Roll Stand # 1

" 2

: 3

: 4

: 5

Fig. 12.37. Longitudinal membrane strain of [0~176 laminate as a function of position within the roll former measured at the interface of laminae 2/3 and 3/4. Inlet temperature 140~ line speed 5 m/min, no cooling.

512

S.J. Mander et al.

300

,.••

250 13 13

200

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Q

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O

~o 15o

Theory 35ram ....... Theory 4 0 m m

I00

,

:

I0

20

. . . . . . .

:

:

30

40

50

Deformation Angle (degrees) Fig. 12.38. Comparison of deformation lengths of various laminates and those lengths predicted using existing sheet metal theory.

derived for sheet metals, particularly when one considers that the theoretical model for metals is independent of any material properties. However, the results have to be interpreted with caution given the overwhelming differences in the constitutive behaviour of both materials [46,47]. 12.7. Concluding remarks

This chapter has briefly introduced the basic considerations of roll forming sheet materials and has clearly eastablished the possibility of applying the technique in the area of continuous fibre-reinforced thermoplastic sheets. With the recent advent of these relatively cheap sheet materials based on propylene and aramid 6, this development would be significant from the high-productivity, manufacturing point of view. Entry temperature and the cooling rate have been shown to have a significant influence on the quality of the manufactured product and its production viability. These parameters encompass many other importants issues in roll forming, such as the forming speed, feeding mechanism and shape conformance. Thus, unlike in metal sheets, the heating system becomes one of the prime design concerns in roll forming of composites and can prove to be the biggest barrier to achieving high production speeds. The ply lay-up is another complexity which is absent in sheet metals but for composite materials, it influences the design of feeding mechanism and subsequently affects the shape conformance of formed products. However, at the same time composite sheets appear to accommodate large deformations at various roll stands and also lend themselves to be roll formed with relatively small load requirement, resulting in the possibility of designing lighter and smaller rolling mills. The springback and spring-forward phenomena may also be wisely used having mutually cancelling effects to produce little distortions on the manufactured items. It is interesting to note that the development of membrane strains, while roll forming FRTP sheets,


513

follows a t r e n d similar to t h a t o b t a i n e d in metallic sheets. T h e d e f o r m a t i o n zones u n d e r v a r i o u s roll stations, h o w e v e r , a p p e a r to be generally larger in the case o f c o m p o s i t e sheets.

Acknowledgements T h e a u t h o r s wish to a c k n o w l e d g e the g r a n t s received f r o m the F o u n d a t i o n for R e s e a r c h Science a n d T e c h n o l o g y ( N e w Z e a l a n d ) a n d D u P o n t ( U S A ) . T h e y are also t h a n k f u l for the help received f r o m H o r t o n I n d u s t r i e s (NZ), Borealis ( N o r w a y ) a n d Mitsui-Toatsu (Japan).

References [1] Hobbs, R.M., Duncan, J.L., Roll Forming, Metals Engineering Institute, American Society of Metals, Ohio, USA (1979). [2] Gold, R., Roll forming is out of this world, Precision Metal, 40 (1983) pp. 11-15. [3] O'Leary, M., Space Industrialisation, CRC Press, Boca Raton, FL, USA (1982) pp. 102-105. [4] G.T. Halmos (ed.), High Production Roll Forming, Society of Manufacturing Engineers, Marketing Services Department, Dearborn, MI, USA (1983). [5] Tsclikov, A.I., Smirnov, V.V., Rolling Mills, Pergamon Press, Oxford, UK (1965). [6] Ivaska, J., Lubricants help expand roll forming capabilities, High Production Roll Forming, ed. G.T. Halmos, SME Marketing Services Department, Dearborn, MI, USA (1983) pp. 107-109. [7] Ivaska, J., Analysis of lubrication problems in roll forming, High Production Roll Forming, ed. G.T. Halmos, SME Marketing Services Department, Dearborn, MI, USA (1983) pp. 110-122. [8] Suzuki, H., Kiuchi, M., Nakajima, S., Experimental investigations on cold roll forming process, Report of the Inst. of Ind. Sci., Univ. of Tokyo, Tokyo, Japan, 22, (1972), pp. 84-172. [9] Kokado, J.I., Onada, Y., On longitudinal curvature and transition of strain of sheet metal in forming a groove with wide flanges by cold roll forming, Kyoto Univ. Faculty of Eng. Memoirs, Kyoto, Japan, 36, No. 4 (1974), pp. 443-457. [10] Suzuki, H., Kiuchi, M., Nakajima, S., Ichidayama, M., Takada, K., Experimental investigation of cold roll forming process II, Rep. of the Inst. of Ind Sci., Univ. of Tokyo, Tokyo, Japan, 26, No. 8, (1978), pp. 291-346. [11] Noble, C.F., Sarantidis, T.M., A study of cold roll forming, Proc. 1st Int. Conf. on Rotary Metal Working Processes, London, UK (1979), pp. 411-424. [12] Jimma, T., Ona, H., Optimum roll pass schedules on the cold roll forming process of symmetrical channels, Proc 21st Int. M.T.D.R. Conf., (1980), pp. 63-67. [13] Ona, H. Jimma, T., Fukaya, N., Experiments into the cold roll forming of straight symmetrical channels, J. Mech. Working Technology, 8, No. 4 (1983) pp. 273-292. [14] Bhattacharyya, D., Smith P.D., The development of longitudinal strain in cold roll forming and its influence on product straightness, Advanced Technology of Plasticity, JSTP, Tokyo, Japan, 1 (1984), pp. 422-427. [15] Kiuchi, M., Analytical study on cold roll forming process, Report of the Inst. of Ind. Sci., Univ. of Tokyo, 22, No. 2 (1972), pp. 1-43. [16] Bhattacharyya, D., Smith, P.D., Yee, C.H., Collins, I.F., The prediction of deformation length in cold roll forming, Journ. Mech. Work. Tech., 9 (1984), pp. 181-191. [17] Kiuchi, M., Koudabashi, T., Automated design system of optimal roll profiles for cold roll forming, Proc 3rd Int. Conf. on Rotary Metalworking Processes, Kyoto (1984), pp. 423-428. [18] Bhattacharyya, D., Panton, S.M., Research and computer-aided design in cold roll forming, Modernization of Steel Rolling, ed. Zhao Linchun et al., International Academic PublishersPergamon Press, Oxford, UK (1988) pp. 464-471.

514

S.J. Mander et al.

[19] Bhattacharyya, D., Smith, P.D., Cold roll f o r m i n g - engineers' dilemma and artisans' art, Trans. Inst. Prof. Engineers NZ, 12, No. 3 (1985), pp. 179-191. [20] Panton, S.M., Zhu, S.D., Duncan, J. L., Fundamental deformation types and sectional properties in roll forming, Int. J. Mech. Sci, 36 (1994), pp. 725-735. [21] Panton, S.M., Zhu, S.D., Duncan, J.L., Geometrical constraints on the roll forming of channel sections, Proc. Instn Mech. Eng., Part B: J. Engng Manufact., 206 (1992), pp. 113-118. [22] Kiuchi, M., Koudabashi, T., Development of simulation model of roll forming process: multipurpose CAD system for roll forming process, J. Japan Soc. Technol. Plasticity, 27, No. 306 (1987), pp. 874-881. [23] Panton, S.M., Duncan, J.L., Zhu, S.D., Longitudinal and shear strain development in cold roll forming, Journal of Materials Processing Technology, 60 (1996), pp. 219-224. [24] Zhu, S.D., Theoretical and experimental analysis of roll forming, Ph.D. Thesis, University of Auckland, Auckland, New Zealand (1993). [25] Zhu, S.D., Panton, S.M., Duncan, J.L., The effect of geometric variables in roll forming a channnel section, Proc. Instn Mech. Eng., Part B: J. Engng Manufact., 210 (1996), pp. 127-134. [26] Chiang, K.F., Cold roll forming, ME Thesis, University of Auckland, Auckland, New Zealand, 1984. [27] Duggal, N., Ahmetoglu, M.A., Kinzel, G.L., Altan, T., Computer aided simulation of cold roll forming - - a computer program for simple section profiles, Journal of Materials Processing Technology, 59, (1996), pp. 41-48. [28] McClure, C.K., Li, H., Roll forming simulation using finite element analysis, Manufacturing Review, 8 (1995), pp. 114-122. [29] Heislitz, F., Livatyali, H., Ahmetoglu, M.A., Kinzel, G.A., Altan, T., Simulation of roll forming process with the 3-D FEM code PAM-STAMP, Journal of Materials Processing Technology, 59 (1996), pp. 59-67. [30] Mallon, P.J., O Bradaigh, C.M., Pipes, R.B., Polymeric diaphragm forming of complex curvature thermoplastic composite parts, Composites, 20 (1989), pp. 48-56. [31] Smiley, A.J., Diaphragm forming of carbon fiber reinforced thermoplastic composite materials, Ph.D. Dissertation, University of Delaware (1988). [32] Okine, R.K., Analysis of forming parts from advanced thermoplastic composite sheet materials, J. Thermoplast. Compos. Mater., 2, (1989), pp. 50-56. [33] Friedrich, K., Hou, M., Stamp forming of continuous carbon fibre/polypropylene composites, Composites Manufacturing, 2, (1991), pp. 3-9. [34] Strong, A.B., Hauweller, P., Incremental forming of large fibre reinforced thermoplastic composites, 34th International SAMPE Symposium, (1989), pp. 43-54. [35] Miller, A.K., Gur, M., Peled, A., Payne, A., Menzel, E., Die-less forming of thermoplastic matrix continuous fibre composites, J. Compos. Mater., 24, (1980), pp. 346-381. [36] Cattanach, J.B., Cogswell, F.N., Processing with aromatic polymer composites, Developments in Reinforced Plastics, Vol. 5. ed. G. Pritchard, Elsevier Applied Science Publishers, (1986), pp. 1-38. [37] Mander, S.J., Bhattacharyya, D., Collins, I.F., Watson, P., Roll forming of fibre reinforced composite sheet, Proc. Tenth Int. Conf. on Composite Materials, Vol. III, ed. A. Poursartip and K. Street, Woodhead Publishing Ltd., Cambridge, UK (1995) pp. 413-420. [38] Zahlan, N., O'Neill, J.M., Design and fabrication of composite components: the spring-forward phenomenon. Composites 20, (1989), pp. 77-781. [39] Martin, T.A., Bhattacharyya, D., Deformation characteristics and formability of fibre reinforced thermoplastic sheets. Composites Manufacturing 3 (1992), pp. 165-172. [40] Hou, M., Friedrich, K., Stamp forming of continuous carbon fibre/polypropylene composites, Composites Manufacturing, 2, No. 1, (1991), pp. 3-9. [41] Krebs, J., Bhattacharyya, D., Friedrich, K., 3-D component manufacturing with fibre-reinforced composite sheets, to be published in Composites: Part A. [42] Cuff, G., Fibre Reinforced Industrial Thermoplastic Composites, Woodhead Publishing Ltd., Cambridge, UK (1995). [43] T.A. Martin, Forming fibre-reinforced thermoplastic sheets, Ph.D. thesis, University of Auckland (1993).


515

[44] Soil, W., Gutowski, T.G., Forming thermoplastic composite parts, SAMPE Journal, 24, No. 3, May (1988), pp. 15-19. [45] Zhu, S.D., Theoretical and experimental analysis of roll forming. Ph.D. thesis, University of Auckland (1993). [46] Martin, T.A., Bhattacharyya, D., Collins, I.F., Bending of fibre-reinforced thermoplastic sheets, Composites Manufacturing, 6, (1995), pp. 177-187. [47] Martin, T.A., Mander, S.J., Dykes, R.J., Bhattacharyya, D., Bending of continuous fibre-reinforced thermoplastic sheets, this volume, pp. 371-401.


A U T H O R INDEX

Numbers refer to pages on which the author (or his work) is mentioned. Numbers between brackets are the reference numbers. No distinction is made between first author and co-author(s).

Beaussart, A.J., 348 [44]; 348 [45] Becraft, M.L., 352 [52] Bellamy, A.M., 173 [10]; 373 [5]; 428 [89] Bellet, M., 86 [35] Berglund, L.A., 60 [30] Bergsma, O.K., 176 [13]; 254 [18] Bersee, H.E.N., 362 [71]; 363 [71] Bhattacharyya, D., 148 [52], [53]; 159 [59]; 226 [7]; 234, 236 [14]; 238, 239 [17]; 240 [14]; 241 [17]; 242 [14], [17]; 243 [14]; 372 [4]; 377 [18], [19]; 382 [21]; 383 [19], 388 [19]; 476 [18]; 487 [14], [16], [18], [19]; 488 [16]; 492 [16], 493 [16], 499 [37], 503 [39], 505 [39], 506 [37], 506, [39], [41]; 512 [46], [47] Billoet, J.L., 179 [17] Binding, D.M., 352 [50]; 352 [51]; 364 [50]; 364 [51] Bird, R., 390 [24] Bird, R.B., 329-331,335, 348 [8] Birley, A.W., 78 [3] Blanlot, R., 179 [17] Bowden, F.P., 200, 203, 205 [37] Braden, T.D., 419 [80] Bradford, I.D.R., 374 [11], [12] Bradley, J., 404 [13], [9]; 419 [9] Bradley, J.S., 404, 419 [7] Bradley, S., 231 [13] Brady, D.G., 50 [8] Brandis, H., 249 [3] Brandt, J, 405, 406 [45] Breuer, U., 147 [51]; 159 [62] Brinker, W.O., 419 [80]; 419 [81] Broutman, L.J., 140, 144 [48] Brown, S.A., 405 [33] Bruschke, M.V., 324, 358 [1]; 358 [59] Buchanan, J.S., 419 [76]

Acrivos, A., 342, 343 [30] Adkins, J.E., 83 [30]; 228 [11] Advani, S.G., 100 [22]; 234, 235 [15]; 254 [17]; 324 [1], [2]; 341 [28]; 345 [36]; 354 [54]; 358 [1], [57], [58], [59]; 364 [36] Ahmetoglu, M.A., 497 [27]; 498 [29] Akeson, W.H., 404, 419 [14], [70], [82] Alexander, H., 419 [68]; 434 [92] Allard, R., 80 [13] Allgoewer, M., 419 [65] Allred, R.E., 54 [19] Altan, T., 497 [27]; 498 [29] Alvarez, R.A., 419 [72] Amiel, D., 404, 419 [14] Andersson, P.A., 409 [61] Andro, R., 86 [35] Apalset, K., 419 [71] Armstrong, R.C., 329-331,335 [8]; 390 [24] ,~strfm, B.T., 358 [57] Bafna, S.S., 358 [60] Bahadur, S., 199 [34] Baird, D.G., 358 [60] Balasubramanyam, R., 359 [63] Barlow, C.Y., 405 [17]; 405 [23] Barnes, A.J., 95 [8]; 158 [58] Barnes, H.A., 339 [23] Barnes, J.A., 100 [23]; 115, 125 [39]; 170, 172 [6]; 359 [64] Barone, M.R., 198 [31]; 359 [62] Bartenev, G.M., 199 [33] Bartolomucci, J.P., 50 [11] Bartos, O., 80-83, 86 [18] Batchelor, G.K., 345, 347 [37] Batchelor, J., 78 [3] Bathe, K.J., 80 [10] Beaussart, A., 254 [32] 517

518

Author index

Buck, A., 407 [56]; 428 [84] Bunsell, A.R., 54 [18]; 55 [18] Butler, D., 419 [80] Caddell, R.M., 4, 6 [1]; 239 [18] Cai, Z., 358 [56]; 361 [66] Cakmak, M., 252 [15] Caldwell, D.L., 43 [4] Canavan, R.A., 258, 277, 307 [40] Cantwell, W., 405 [22] Cantwell, W.J., 405 [26] Carley, J.F., 83 [26], [27] Carlsson, L.A., 94 [6]; 109 [33] Carreau, P.J., 331,360 [13] Cattanach, J.B., 95 [8]; 158 [58]; 228 [9]; 250 [13]; 499 [36] Caulk, D.A., 198 [31]; 359 [62] Chang, I.Y., 325 [4]; 364 [73] Chang, L.W., 434 [93] Charrier, J.M., 80 [13] Chawla, J., 140, 144 [48] Chey, S., 254 [20]; 442 [2], [4]; 443 [6]; 445 [2], [4], [8]; 455 [2]; 457 [4]; 469 [8]; 470 [6] Chou, S., 405, 406, 433 [41] Chou, T.W., 123 [41]; 434 [91], [93] Christensen, R.M., 342, 343, 361,362 [31]; 397 [28] Christie, G.R., 221 [5]; 226 [7] Chu, E., 218, 219 [1] Chuang, Y., 410 [63] Claes, L., 404 [4], [10]; 419 [4] Coffin, D.W., 285, 303 [57]; 348 [42], [43]; 361 [42]; 362 [43] Cogswell, F.N., 36 [2]; 58, 59, 60, 66 [2]; 93, 95 [1]; 100 [18], [23]; 101 [1]; 115, 125 [39]; 165 [1]; 170 [5], [6]; 172 [6]; 173 [1]; 174 [5]; 181 [1]; 189 [5]; 228 [9]; 249 [2]; 250 [13]; 258, 259, 283, 307 [2], 348 [46], 351 [46], 359 [64], 362 [68], 362 [69], 372 [1], 372 [3], 382 [1]; 499 [36] Collins, I.F., 226 [7]; 377 [19]; 383 [19]; 388 [19]; 487, 488, 492, 493 [16]; 499, 506 [37]; 512 [46] Colton, J.S., 363 [72] Comtet, J.J., 404 [8] Corcoran, S.J., 419 [68] Cordey, J., 419 [75] Coutts, R.D., 404, 419 [14]; 419 [70] Creasy, T.S., 345, 364 [36]

Cuff, G., 97, 100 [12]; 228 [9]; 506, 508 [42] Cutolo, D., 94 [3] Daniel, I.M., 57 [27] Darcy, H., 357 [55] Davies, P., 405 [22]; 405 [26] Day, R., 419 [73] De Angelis, F., 428 [84] de Haan, J., 407, 410, 412 [58]; 413 [64]; 415, 418, 429 [58] Delaloye, S., 428 [86] de Lorenzi, H.G., 80 [15], [16], [17]; 81, 82 [16] De Luca, P., 250 [6] Demarmels, A., 85 [34] Desiderato, R., 404 [6] de Waele, A., 331 [12] Diefendorf, R.J., 54 [20] Dillon, G., 254 [19], [20]; 442 [4]; 443 [6]; 445 [4], [8]; 446, 448, 451 [11]; 457 [4]; 469 [11]; 469 [8]; 470 [6] Drechsler, K., 405 [39]; 405 [45]; 406 [39]; 406 [45]; 432, 433 [39] Duckett, R.A., 409 [62] Duggal, N., 497 [27] Dumas, P., 404 [8] Duncan, J.L., 19 [4]; 218, 219 [1]; 221 [3], [4]; 474, 475, 484 [1]; 493 [20], [21]; 495 [20], [23]; 496 [25]; 497 [20], [23] Dutta, A., 252 [15] Dykes, R.J., 377 [18]; 512 [47] Eckert, K.-L., 435 [97] Eckold, G., 57 [26] Einstein, A., 341 [29] El'kin, E.I., 199 [33] Eng, B., 419 [73] England, A.H., 374 [11]; 374 [12] Ericson, M.L., 60 [30] Eringen, A.C., 83 [31] Esteghamatian, M., 79 [8] Ethridge, E.C., 419 [69] Evans, J.T., 374 [13] Fife, B., 405 [17] Fines, R.E., 50 [11] Fitzer, E., 100 [20] Fitzpatrick, J.E., 50 [13] Flemming, M., 428 [84], [88]

Author index

Francis, D., 405 [32] Frankel, N.A., 342, 343 [30] Fredrickson, G.H., 347 [41] Freundlich, H., 339 [22] Friedrich, K., 97 [13], [13]; 100 [15], [16], [21], [24], [26], [27]; 101 [28]; 111 [38]; 159 [59], [63], [64]; 181 [18], [19]; 254, 307 [31]; 373 [6], [10]; 386 [10]; 405 [21]; 499 [33]; 505 [401; 506 [411 Fritz, U., 409 [60] Fukaya, N., 487, 488 [13] Gachon, H., 179 [17] Galanty, P.G., 50 [7] Gautier, E., 419 [75] Gere, J.M., 457 [16] Ghafur, M.O., 80, 82 [19]; 86 [36], [38] Ghasemi-Nejhad, M.N., 405 [24]; 434 [91] Ghosh, A., 80 [13] Giacomin, A.J., 353 [53] Giesekus, H., 334 [18] Giorgetta, S., 410 [63] Goddard, J.D., 345 [35]; 347 [39], [40] Gogos, C.G., 77 [2]; 260 [44]; 359 [61] Gold, R., 475 [2] Golden, K., 254 [28]; 446, 448 [12] Gomez, M.A., 419 [70]; 419 [82] Gonzalez-Zugasti, J., 254 [19]; 446, 448, 451,469 [11] Goshawk, J.A., 373 [7] Green, A.D., 83 [29], [30] Green, A.E., 228 [11] Griese, R.A., 405 [29] Grosch, K.A., 200 [36] Groves, D.J., 173 [10]; 181, 210 [21]; 258, 259 [37]; 351, [49]; 373 [5]; 428 [891 Gunderson, S.L., 434 [94] Gur, M., 499 [35] Gutowski, T.G., 100 [25];, 165 [2]; 181 [25]; 252 [14]; 254 [19]; 254 [20], 254, 307, 314 [21]; 361 [65]; 361 [66]; 372 [2]; 373 [8]; 373, 379 [9]; 428 [90]; 442 [4]; 443 [6]; 445 [4]; 445 [8]; 446 [101; 446 [11]; 448 [10], [11], 449 [10], 451 [11], 455 [10], 457 [4], 458 [18], 469 [8], [10], [11]; 470 [6]; 507 [44] Gysin, H.J., 249 [4]

519

Ha, S.-W., 404 [3]; 406 [51], [53]; 407 [58]; 408, 409 [3]; 410 [58]; 412 [58]; 414, 415 [3]; 415 [58]; 416 [3]; 418 [51], [58]; 429 [51], [58]; 431,432 [51]; 435 [96], [97] Haessly, W.P., 80, 82 [19] Hailer, K.D., 234 [16] Halmos, G.T., 475 [4] Hancox, N.L., 53-55 [16] Hang, E., 250 [6] Hassager, O., 329-331,335, 348 [8]; 390 [24] Hastings, G.W., 404 [7]; 404 [9]; 419 [7], [9], [11], 404 Hatebur, A., 406, 410, 419, 422, 434 [55] Hauweller, P., 499 [34] Haworth, B., 78 [3] Hayes, W.C., 419 [77] Hearle, J.W.S., 348 [44], [45] Hehne, H.J., 404 [6] Heisley, F.L., 234 [16] Heislitz, F., 498 [29] Hench, L.L., 419 [69] Heppenstall, R.B., 419 [77] Herrington, P.D., 200 [38] Hickman, G.T., 406 [46] Hill, R., 14 [2] Hobbs, R.M., 474, 475, 484 [1] H6ger, A., 104, 119 [29] Holmstrom, T., 419 [79] Horn, W.J., 405 [30] Hosford, W.F., 4, 6 [1]; 239 [18] Hou, M., 97 [13]; 100 [13],[24], [26], [27]; 101 [28]; 159 [60], [61], [63], [64]; 373, 386 [10]; 499 [33]; 505 [40] Hoult, D., 254 [19]; 446, 448, 451,469 [11] Hsiue, E.S., 141 [49] Huisman, J., 254 [18] Hull, B.D., 254, 311 [26]; 456 [14], [15] Hull, D., 405 [42], [43]; 406 [42], [43] Htittner, W., 404 [4], [5]; 419 [4] Hylton, D., 85 [32] Ichidayama, M., 487 [10] ICI Thermoplastic Composite Handbook 1992, 207 [42] Igl, S.A., 82 [24] Ishai, O., 57 [27] Ishida, H., 405 [15] Ivaska, J., 481 [6], [7]; 484, 487 [7]

520

Author index

J/iger, H., 100 [20] Jammet, J.C., 86 [35] Jang, B.Z., 42 [3] Jeffreys, H., 334 [17] Jenkins, R.B., 419 [80] Jimma, T., 482, 487 [12]; 487, 488 [13] Johnson, A.F., 176 [15] Johnson-Nurse, C., 404 [7]; 404 [9]; 419 [7],

[9] Jones, A.D., 339 [22] Jones, R.S., 181 [22]; 359 [63]; 373 [7] Kaliakin, V.N., 255 [33] Kalpakjian, S., 140, 144 [48] Kamal, M.R., 341 [26]; 351,352 [47] Kaprielian, P.V., 181 [23]; 258 [39]; 310 [54]; 362, 363 [70] Karaharju, E., 419 [79] Kardos, J.L., 165 [4] Kardos, L.J., 405 [35] Karger-Kocsis, J., 406 [52]; 410 [63] Kausch, H.H., 405 [22]; 405 [26] Kazomer, D.O., 80 [17] Keefe, M., 234, 235 [15]; 254 [17] Kempe, G., 405 [27] Ketzer, V., 159 [62] Keuscher, G., 404 [5] Kinzel, G.A., 498 [29] Kinzel, G.L., 497 [27] Kinzl, L., 404 [10] Kirch, M., 413 [64] Kiuchi, M., 487 [10]; 487 [8], [15], [17]; 493, 497 [22] Kizior, T.E., 345 [34] Klenner, J., 249 [3] Klinkmiiller, V., 100 [21] Ko, F.K., 123 [41]; 405 [37] Koch, B., 406 [51]; 406 [53]; 406, 410 [55]; 410 [63]; 418 [51]; 419, 422 [55]; 429, 431, 432 [51]; 434 [55] Koch, P., 140 [47] Koch, S.B., 95 [9] Kokado, J.I., 487 [9] Korger-Roth, G., 405 [27] Kouba, K., 80 [18], [19]; 81, 82 [18]; 82 [19]; 83 [18]; 86 [18], [36], [37], [38] Koudabashi, T., 487 [17]; 493, 497 [22] Krauss, H., 405 [27] Krebs, J., 159 [59]; 506 [41]

Kroschwitz, J.I., 109 [32] Krueger, W.H., 364 [73] Kuczynski, K., 14 [3] Kutz, J., 405 [37] Lam, R.C., 165 [4] Lammerding, J.J., 419 [81] Latta, L.L., 419 [72] Laun, H.M., 339 [25]; 340 [25]; 352 [25] Laursen, T.A., 313 [56] Leach, D.C., 100 [18]; 372 [3] Lee, D., 224 [6] Lennon, J.J., 201,209, 212 [40] Levenetz, B., 404, 419 [14] Li, H., 254 [20]; 442 [3], [4]; 443 [6]; 445 [3], [4], [8]; 446, 450 [3]; 451,455, 457 [3]; 457 [4]; 464, 465, 469 [3]; 469 [8]; 470 [6]; 498 [281 Li, H.L., 140 [47] Lind, D.J., 158 [57] Liskova-Klar, M., 419 [78] Little, R.W., 419 [80], [81] Livatyali, H., 498 [29] Lobe, V.M., 338 [20]; 343, 344 [20] Lodge, A.S., 388 [23] Lothringer, K.S., 419 [70] Ludema, K.C., 199 [34] Lfischer, P., 408, 409, 415 [59] Lustinger, A., 405 [18], [20], [25] Maher, E.J., 211 [43] Mai, Y.-W., 159 [60] Mallon, P.J., 95 [7]; 139 [45], [46]; 142 [46]; 144 [45]; 170 [7]; 179, 181 [16]; 181 [27], [28], [7]; 198 [30]; 201,209, 212 [40]; 249251 [5]; 259 [43]; 271 [48]; 277, 285 [5]; 286 [501; 287 [51, [481; 289 [51; 308, 311 [531; 314 [53]; 443, 445 [7]; 499 [30] Mander, S.J., 499 [37]; 506 [37]; 512 [47] Mgmson, J.A.E., 93 [2]; 405 [28] Marangou, M., 80 [13] Marciniak, Z., 14 [3]; 19 [4] Martin, T.A., 148 [52-54]; 150 [54]; 226 [8]; 234, 236 [14]; 238 [8], [17]; 239 [17]; 240 [14]; 241 [17]; 242 [14], [17]; 243 [14]; 372 [4]; 377 [18-20]; 382 [21]; 383 [19], [20]; 388 [19]; 503, 505, 506 [39]; 507 [43]; 512 [46], [47]

Author index

Matsuoka, S., 333 [16] Matthews, J.V., 404, 419 [14] Maxwell, J.C., 333 [14] Mayer, J., 404 [1]; 406 [48-55]; 407 [58]; 408 [1], [50], [59]; 409 [48], [59]; 410 [48], [50], [55], [58], [63]; 411 [1], [48]; 412 [1], [58]; 413 [1], [64]; 414 [1]; 415 [58], [59]; 416 [1], [50]; 417 [48], [50]; 418 [49], [50], [51], [58]; 419 [49], [55]; 420 [1], [48], [54]; 421 [1], [48]; 422 [1], [48]; 422 [54], [55]; 423 [1]; 424 [1], [48]; 425 [1], [48]; 426 [1], [48]; 427 [1]; 428 [84]; 429 [1], [48], [51], [58]; 430, 431 [48]; 431 [51]; 432 [48], [51]; 434 [55]; 435 [96], [97] Mayer, R.M., 53-55 [16] McClure, C.K., 498 [28] McCormack, B., 405 [31] McDonald, W., 419 [73] McEntee, S.P., 250, 255 [12] McGuinness, G.B., 250 [10], [11]; 255 [10], [11]; 258 [40], [41]; 267 [47]; 277 [40], [41], 307 [40], [41] McKibbin, B., 404 [9]; 419 [9], [67] McLaren, R., 419 [73] McNamara, A., 405 [34]; 419 [83] Medwin, S.J., 327, 364 [6] Melander, A., 218, 219 [2] Menzel, E., 499 [35] Merrit, K., 405 [33] Metzner, A.B., 333 [15]; 345, 347 [33]; 347 [38] Mewis, J., 345, 347 [33] Middleton, V., 405 [36], [40]; 406, 415 [36], [40]; 429, 432 [36]; 432, 433 [40] Miles, J.N., 362 [67] Miller, A.K., 254, 307 [22]; 314 [22]; 499 [35] Miller, D.M., 55 [22] Milliken, W.L., 341 [27] Mirza, F.A., 82 [22], [23] Mitsoulis, E., 78 [4] Moet, A., 405 [33] Molden, G.F., 362 [67] Monaghan, M.R., 139, 144 [45]; 170 [7]; 181 [27], [28], [7]; 198 [30]; 259 [43]; 271 [48]; 286 [50]; 287 [48]; 308, 311,314 [53]; 443, 445 [7] Monasse, B., 86 [35] Mooney, M., 81, 84 [20] Morgan, R.J., 54 [19]

521

Morigaki, T., 361 [66] Morris, S.R., 181, 184 [26] Moulin, C., 405 [22] Moy, P., 50, 53 [6] Moyen, B., 404 [8] Mulholland, A.J., 170, 181 [7] Muller, G.W., 419 [77] Mfiller, M.E., 419 [65] Mfiller, U., 409 [60] Mullis, D.L., 419 [72] Murtagh, A.M., 175, 177 [12]; 179 [16]; 181 [12], [16], [27], [28]; 188 [12]; 201 [40]; 206, 208 [12]; 209 [40]; 211 [12]; 212 [40]; 213 [12]; 283 [49]; 308 [49], [53]; 311 [49], [53]; 314 [49], [53]; 317 [49] Murty, N.K., 362 [67] Mutel, A.T., 341 [26]; 351,352 [47] Muzzi, J., 194 [29] Muzzy, J., 94 [4] Muzzy, J.D., 363 [72] Nakajima, N., 173, 174, 181, 188 [11]; 258 [38]; 405 [19] Nakajima, S., 487 [8], [10] Neitzel, M., 147 [51]; 159 [62] Neoh, E.T., 458 [17] Nestor, T.A., 258, 277, 307 [40] Neugebauer, R., 404 [10] Newatz, G.M., 405 [20] Newaz, G.M., 405 [25] Newman, S., 406 [47] Nguyen, H.X., 405 [15] Nied, H.F., 80 [15], [16]; 81, 82 [16] Niedermeier, M., 428 [84], [85], [88] Nield, E., 405 [17] Nietert, M., 404 [5] Noble, C.L., 487, 488 [11] Norpoth, L., 94 [4], [29] Noser, G.A., 419 [81] Nunamaker, D.M., 419 [77] Br~tdaigh, C.M., 95 [7]; 100 [17]; 139 [45], [46]; 142 [46]; 144 [45]; 248 [1]; 249 [5]; 250 [5], [8-12]; 251 [5]; 254 [1]; 255 [8-12]; 258 [40], [41]; 259 [42]; 260 [8]; 261, 262 [8], [9]; 263 [1], [46]; 264 [42]; 267 [47]; 268 [46]; 271 [48]; 277 [5], [40], [41]; 282 [46]; 285 [5]; 287 [5], [48]; 289 [5]; 307 [40], [41]; 443, 445 [7]; 499 [30]

522

Author index

Oakley, D., 181 [22] Oakley, J.G., 353 [53] O'Conell, P.A., 409 [62] Oden, J.T., 80 [9], 82 [9] Ogden, R.W., 81, 84 [21] Okine, R.K., 254 [16], [32]; 325 [3]; 345 [36]; 348 [42], [44], [45]; 361 [42]; 364 [36]; 499 [321 O'Leary, M., 475 [3] Ona, H., 482, 487 [12]; 487, 488 [13] Onada, Y., 487 [9] O'Neill, J.M., 119, 127 [40]; 128 [42]; 181 [23]; 254 [27]; 310 [54]; 362,363 [70]; 374 [14]; 386 [22]; 502, 504 [38] Osswald, T.A., 82 [24] Ostrom, R.B., 95 [9] Ostwald, W., 331 [11] Oswald, H.J., 140 [47] O'Toole, B.J., 327 [5] Otsubo, Y., 339 [21] Owen, M.J., 405 [36], [40]; 406, 415 [36]; 415 [40]; 429 [36]; 432 [36], [40]; 433 [40] Owens, G.A., 158 [57] Ozisik, M.N., 107 [30] Paavolainen, P., 419 [79] Padscheider, J., 410 [63] Panton, R.L., 329, 330 [9] Panton, S.M., 476, 487 [18]; 493 [20], [21]; 495 [20], [23]; 496 [25]; 497 [20], [23] Parnas, R.S., 324, 358 [1] Parsons, J.R., 419 [68]; 434 [92] Parvizi-Majidi, A., 405 [24] Payne, A., 499 [35] Peacock, J.A., 405 [17], [23] Peled, A., 499 [35] Perdikoulas, J., 78 [7] Perren, S.M., 419 [66], [75], [76] Peters, D.M., 108 [31] Petitmermet, M., 407, 410, 412, 415, 418, 429 [58] Petrie, C.J.S., 337 [19] Phelan, F.R., 358 [58] Pickett, A.K., 250 [6] Pigliacampi, J.J., 55 [21] Pinruethai, P., 434, 435 [95] Pipes, R.B., 95 [7]; 100 [17], [19], [22]; 139 [45], [46]; 142 [46]; 144 [45]; 148 [52], [53]; 234 [14], [15]; 235 [15]; 236 [14]; 238, 239

[17]; 240 [14]; 241 [17]; 242 [14], [17]; 243 [14]; 249 [5]; 250 [5], [8-101; 251 [5]; 254 [17], [32]; 255 [8-10], [33]; 259 [42]; 260, 261 [8], 262 [8], [9]; 264 [42]; 271 [48]; 277, 285 [5]; 287 [48], [5]; 289 [5]; 342 [32]; 348 [42]; 348 [43]; 348 [44], [45]; 352 [51]; 358 [57]; 361 [42]; 362 [43]; 364 [51]; 372 [4]; 382 [21]; 397 [27]; 428 [87]; 443 [7]; 445 [7]; 499 [30] Pipkin, A.C., 255 [35]; 270 [35]; 311 [55]; 375, 379 [16]; 394 [25]; 446, 468 [9] Planck, H., 405, 433 [44] Potter, K.D., 141 [50] Powell, R.L., 341 [27] Pratte, J.F., 325 [4]; 364 [73] Prevorsek, D.C., 140 [47] Price, C.R., 339 [24] Queckborner, T., 250 [6] Rahn, B.A., 419 [75] Ramakrishna, S., 405 [42], [43]; 406 [42], [43] Ranganathan, S., 358 [58] Rasmussen, M.L., 150 [56] Reber, R., 413 [64]; 435 [97] Reddy, J.N., 150 [56] Reinicke, R., 159 [62] Richardson, J.J., 50 [7] Rivlin, R.S., 228 [10]; 462 [20] Robertson, R.E., 141 [49] Robroek, L.M.J., 94 [5]; 362 [71]; 363 [71] Rodriguez, F., 331,333, 349 [10] Rogers, T.G., 128 [42]; 173 [9]; 254 [25-28]; 255 [25], [35]; 256 [25]; 258 [39]; 270 [35]; 311 [26], [55]; 374 [11], [12], [14]; 375 [16]; 377 [17]; 379 [16]; 394 [25]; 446 [12], [9]; 448 [12]; 456 [14], [15]; 468 [9] Rosen, B.W., 56 [24] Rudd, C.D., 405 [36], [40]; 406 [36]; 415 [36], [40]; 429, 432 [36], [40]; 433 [40] Ruffieux, K., 406 [51], [53-55]; 410 [55]; 418 [51]; 419 [55]; 420, 422 [54], [55]; 429, 431 [51]; 432 [51]; 434 [55] Rumelhart, C., 404 [8] Ryan, M.E., 80 [13] Sabbaghian, M., 200 [38]

Author index

Sampson, S., 419 [77] Samuelsson, A., 254 [30] Santini, R., 404 [8] Sapega, A., 419 [77] Sarantidis, T.M., 487, 488 [11] Sarmiento, A., 419 [72] Sastry, A.M., 348 [44] Saunders, D.W., 462 [20] Savadori, A., 94 [3] Scardino, F., 405 [38] Schedin, E., 218, 219 [2] Schein, S.S., 419 [77] Schepers, E.J.G., 434, 435 [95] Scherer, R., 100 [15], [27]; 111 [38]; 181 [18], [19]; 254 [31]; 307 [31]; 373 [6] Schmidt, L.R., 83 [26], [27] Schneider, E., 419 [75] Schneider, R., 419 [65] Scholten, H.J., 419 [74] Schulten, T., 406, 410, 419, 422, 434 [55] Schwab, P., 419 [76] Schwarz, P., 409 [60] Scobbo, J.J., 173, 174, 181, 188 [11]; 258 [38] Scobo, J.J.R., 405 [19] Seferis, J.C., 405 [16], [28] Seguchi, Y., 419 [82] Seyer, F.A., 345 [34] Shaikh, F.M., 405 [30] Shalaby, S.W., 50, 53 [6] Shapery, R.A., 56 [23] Shaqfeh, E.S.G., 347 [41] Shrivastava, S., 80 [13] Shuler, S.F., 348 [42]; 352 [51]; 354 [54]; 361 [42]; 364 [51] Sickafus, E.N., 141 [49] Siegling, H.F., 405, 406 [45] Silvermann, E.M., 405 [29] Silvi, N., 78 [6] Simacek, P., 255 [33], [34]; 348, 361 [42] Simo, J.C., 313 [56] Simon, B.R., 419 [70], [82] Skirving, A.P., 419 [73] Slatis, P., 419 [79] Smiley, A.J., 100 [19]; 428 [87]; 499 [31] Smirnov, V.V., 479 [5] Smith, P.D., 487 [14], [16], [19]; 488, 492, 493 [16] Soeganto, A., 405 [30]

523

Soil, W., 373 [8]; 507 [44] Soil, W.E., 181 [24]; 252 [14] Solt~sz, U., 404 [6] Song, W.N., 82 [22], [23] Sowerby, R., 218, 219 [1] Spencer, A.J.M., 128 [42]; 173, 176, 181 [8]; 228 [12]; 254 [24], [26], [28]; 255 [24]; 311 [26]; 374 [15]; 394 [26]; 397 [26]; 446, 448 [12]; 456 [14], [15] Spescha, G., 410 [63] Steffee, A.D., 405 [33] Stocks, D.M., 173 [10]; 258, 259 [37]; 351 [49]; 373 [5]; 428 [89] Strong, A.B., 499 [34] Struik, D.J., 448 [13] Stiirmer, K.M., 419 [74] Suemasu, H., 101 [28] Sun, C.T., 181, 184 [26] Suzuki, H., 487 [8], [10] Tabor, D., 199 [32]; 200, 203, 205 [37] Tadmor, Z., 77 [2]; 260 [44]; 359 [61] Takada, K., 487 [10] Talbot, M.F., 254, 307, 314 [22] Tam, A.S., 100, 181 [25]; 254, 307, 314 [21]; 373, 379 [9]; 428 [90]; 443 [5]; 446, 448, 449, 455 [10]; 458 [18]; 469 [10] Tanaka, K., 199, 205 [35] Tanner, R.I., 85 [33] Tarr, R.R., 419 [72] Taske II, L.E., 50, 51 [10] Taylor, C.A., 80 [15], [17] Taylor, D., 405 [31] Taylor, R., 56 [25] Taylor, R.L., 80 [11], [12]; 263 [45] Tayton, K., 404, 419 [9] Tayton, K.J.J., 404 [12], [13] Terjesen, T., 419 [71] Thomas, K.L., 108 [31] Thompson, E.G., 254 [30] Throne, J.L., 76, 83 [1]; 200 [39] Timoshenko, S.P., 457 [16] Tobolsky, A.V., 49 [5] Tognini, R., 406 [51], [53]; 406 [54]; 418 [51]; 420, 422 [54]; 429, 431,432 [51] Toll, S., 409 [61] Treloar, L.R.G., 83 [25] Tsclikov, A.I., 479 [5] Tucker, C.L., 254 [29]; 341 [28]

524

Author index

Tucker, C.L. III, 442, 456 [1] Turner, R.M., 405 [34]; 419 [83] Uhthoff, H.K., 419 [781 Uralil, F.S., 405 [25] Vantal, M.H., 86 [35] Van West, B.P., 100 [22]; 176 [14]; 234, 235 [15]; 254 [17] Varughese, B., 94 [4]; 194 [29] Vetter, S., 407 [57] Vlachopoulos, J., 78 [4-7]; 80 [18], [19]; 81 [18]; 82 [18], [19], [22], [23]; 83 [18]; 86 [18], [36-38] Vlcek, J., 78 [6], [7] Vogel, J.H., 224 [6] Wagner, M.H., 85 [34] Wang, E.L., 372 [2] Warby, M.K., 80 [14] Ward, I.M., 83 [28]; 461 [19] Watson, P., 499, 506 [37] Watt, D.F., 79 [8] Watterson, E.C., 50 [12] Weeton, J.W., 108 [31] Weinberger, C.B., 345 [35] Weiss, A.B., 419 [68] Weiss, R., 404, 419 [4] Wenz, L.M., 405 [33] Wheeler, A.B., 359 [63] Wheeler, A.J., 165 [3] White, J.L., 333 [15]; 338 [20]; 343, 344 [20] Whiteman, J.R., 80 [14] Whitney, N.M., 434 [94] Wild, U., 413 [64] Willenegger, H., 419 [65] Williams, D.F., 405 [34]; 419 [83] Williams, D.J., 406 [46] Williams, R., 405 [32]

Windle, A.H., 405 [23] Wintermantel, E., 404 [1-3]; 406 [49], [50], 406 [51-55]; 407 [58]; 408 [1], [3], [50], [59]; 409 [3], [59]; 410 [50], [55], [58], [63]; 411 [1]; 412 [1], [58]; 413 [1], [64]; 414 [1], [3]; 415 [3], [58], [59]; 416 [1], [3], [50]; 417 [50]; 418 [49-51], [58]; 419 [49], [55]; 420 [1], [54]; 421,422 [1], [54], [55]; 423-427 [1]; 428 [84]; 429 [1], [51], [58]; 431,432 [51]; 434 [55]; 435 [96], [97] Wirz-Safranek, D.L., 95 [9] Wittich, H., 100 [16] Woo, S.L.-Y., 404, 419 [14], [70]; 419 [82] Woo, Y.K., 419 [70] Wood, R.D., 254 [30] Wu, C.J., 405, 406, 433 [41] Wu, R., 80 [13] Wu, X., 363 [72] Xiang, Wu, 181 [20] Yamada, Y., 199, 205 [35] Yau, S.S., 434 [93] Ye, L., 100 [21]; 159 [60] Yee, C.H., 487, 488, 492, 493 [16] Yeh, G.S.Y., 141 [49] Yuan, Q., 406 [52] Zahlan, N., 100 [15]; 119, 127 [40]; 181 [19]; 254 [31]; 307 [31]; 386 [22]; 502, 504 [38] Zamani, N.G., 79 [8] Zema, W., 83 [29] Zhang, Z.T., 221 [3], [4] Zhu, S.D., 493 [20], [21]; 495 [20], [23], [24]; 496 [25]; 497 [20], [23]; 511 [45] Ziegrnann, G., 428 [86], [88] Zienkiewicz, O.C., 80 [11], [12]; 254 [30]; 263 [45] Zimmerman, M., 434 [92]

SUBJECT INDEX Cetex fabric, 179, 180, 182, 196, 197, 211-214 Clamping pressure, 141, 145 Coefficient of friction, 200, 205, 213 versus sliding velocity, 209 Coefficient of thermal conductivity (CTC), 52 Commingled fibres, 93 Commingled materials, 59 Commingled reinforcement, 47 Composites, 29, 55-60 applications, 37 mechanical properties, 56-60 thermal properties, 55-58 Compression moulding, 93 Compressive strain contour map, 242, 244 Computer-aided design in roll forming, 489-491 Computer simulation of thermoforming, 75-89 Consistency index, 390 Consolidation quality and lay-up, 172 Constitutive relationships, 11, 86, 256 Continuous fibre-reinforced composites, 164 Continuous fibre-reinforced pre-consolidated laminates, 97 Continuous fibre-reinforced thermoplastics (CFRT), 92, 100, 125, 147, 227 formability, 372 rheological behaviour of, 371-401 sheets, 91-162, 218, 233, 498-512 Continuous glass-fibre reinforced thermoplastic composite, 96 Continuum mechanics analysis, 254 Contour maps, 225 Contrary knitting technique, 435 Controlled strain rate forming, 364 Couette flow, 311,329 Coulomb friction, 198 Covalent bonds, 32, 34 Crosslinks, 34 Crystal conformation, 32 Crystal structure, 4 Crystalline melting point, 49 Crystallinity and stamping velocity, 131 Crystallinity degree, 33, 34 Cubic Hermite basis functions, 222

Adhesion theory, 199 Admissible stress fields, 379-380 Aerodynamic fairing, 230 Amorphous structures, 33, 34, 35, 78, 104 Angular displacement, 129-130 Anisotropic biomaterials, 404-405 Anisotropic flow rules, 6 Anisotropic materials, yielding, 3-4 Anisotropy, 412-4 13 APC-2, 172, 173, 181, 182, 184, 187, 192-195, 197, 200, 201,203,204, 206, 208, 210-214, 286 Arrow diagram, 225, 229, 233-237, 241,243 Aspect ratio, 339, 340 Axial intra-ply shear deformation, 361-362 Axial stress, 272, 278, 280, 282, 283, 291,296-298 Barrelling effect, 166 Bend angle and stamping time, 119 Bend forming, 489 Bending, 19, 80, 371-401,487-489 constraint conditions and kinematics, 374-376 idealised viscous model, 374-376 under tension, 22-23 without tension, 19-20 Bending angle, 123, 127-130 Bends, sequencing, 486 Bi-cubic Hermite element, 222 Biocompatibility, 434-435 Blister fairing, 230-234 Buckling, 112, 116, 146, 239, 252, 383, 460, 483 CAD/CAM systems, 489-491 CAEDS(I-DEAS), 425 Calendering, 78 Capillary rheometer, 350-352 Carbon-black-filled polystyrene, 343 Carbon fibre/PEEK composites, 57, 58, 60 Carbon fibre/PEEK laminates, 130, 132 Carbon fibre/PP laminates, 109, 110, 133, 134 Carbon fibres, 40, 43, 97, 164, 181,328 Carreau relation, 332 Cauchy-Green deformation tensor, 81, 85 Cauchy-Green strain tensor, 220 C-channels, 451-454, 466, 467, 468

Darcy's law, 358

525

526

Subject &dex

Deep drawing, 17-19, 68 knitted-fibre-reinforced organo-sheets, 428-432 Deformation, principal element, 4-5 Deformation analysis of roll forming, 491-498 Deformation behaviour and rheological properties, 329 Deformation gradient tensor, 225 Deformation length, 492, 511-512 Deformation modes in thermoset composite forming, 446-455 Deformation processes, 232, 373 Deformation theory, 199 Degree of crystallinity, 33, 34 Deviatoric stresses, 5 Diaphragm failure, 254 Diaphragm forming, 69, 94, 95, 146-159, 169, 249, 250, 252 assessment and characterisation of thermoformed parts, 148-152 experimental comparisons, 286-303 experimental details and procedures, 96-100, 147-148 friction, 197-213 inflated tool, 470-471 large strain analysis technique, 148-150 materials employed, 96-97 occurrence of defects and thickness variations, 150-152 pre-consolidated laminates, 98-99 recommendations, 157-159 reinforced, 469-470 thermoset composites, 443 variation of forming parameters and rating of part quality, 152-157 Diaphragm stiffness, 461-463 Diaphragm viscosity, 270-273, 275-279, 281 Differential scanning calorimetry (DSC), 106, 130, 132, 133, 506 Diffuse neck, 13 Digitised mesh diagram, 242 Double-belt press (DBP), 45, 63-64 Drape forming, 443 Draping theory of textile fabrics, 234-238 Effective strain, 6 Effective stress, 6 Elastic limit, 7 Elastic modulus, 83 Elastic-perfectly plastic model, 11 Elongational flows, 336-337, 343-348 Elongational rheometers, 355 Elongational velocity, 338 Elongational viscosity, 354-355

Explicit finite element method, 250 Extensional deformation, 364 Extra stress, 256 Extrusion, 78 Fabrics, 123, 328 draping theory, 234-238 inter-ply slip, 179, 189, 190 intra-ply shear, 174-175 transverse flow, 166 Failure criterion, 418 Failure model, 418 FEFORM, 263, 264, 291,310 Fibre architecture, 407-409 Fibre distribution, 114 Fibre-filled melts, 344 Fibre migration, 382 Fibre movement studies, 133-135 Fibre orientation, 186, 198, 210, 236 Fibre orientation distribution (FOD), 406, 407-409, 415, 431 Fibre-reinforced fluid constitutive model, 176 Fibre reinforcement, 42, 327, 328, 382 Fibre rotation, 255 Fibre straightening factor (FSF), 179 Fibre volume fraction, 116-118 Fibre wrinkling, 383, 384 Filled polymers, 351-352 Filled systems, 341,343 Filled viscous fluids, 338-348 Filler aspect ratio, 339 Film stacked prepregs, 93 Finger strain tensor, 85 Finite element analysis osteosynthesis plates, 425-428 roll forming, 498 Finite element equations, 83 Finite element formulations, 80-83 Finite element methods, 75, 79 explicit, 250 implicit, 247-322 osteosynthesis plates, 425-428 simulation code, 254 strain analysis, 224 Finite element software package, 86 Finite element solution technique plane deformation, 308-309 plane stress problems, 261-263 Flow behaviour, 210, 429 Flow mechanism, 100, 311 Flow rules, 5 anisotropic, 6 Flow stress, 24 Flower diagram, 485

Subject index Folding, 70 Forming characteristics of sheet metals, 6-12 Forming limit diagram, 14, 15, 464-468 Forming limits for sheet metal, 12-15 Forming pressure, 156 Forming ratio, 154-156 Forming temperature, 110-115, 153-154 Forming velocity, 156 Friction, 197-213 diaphragm forming, 197-213 effects of surface temperature, 204 influence of normal load, 205 mechanisms, 199 theories, 199 Friction power-law model parameters, 214 Friction sled, press forming, 201-202 Friction tests, 200-213 twin platen arrangement, 202 Frictional behaviour, 163-216 Frictional forces in press forming, 169-170 Gauss-Bonnet theorem, 450 Giesekus model, 335 Glass fibre fabric/PEI laminates, 97, 125, 126, 141-143 Glass fibre/PP laminates, 109, 143-144, 146-159 Glass fibres, 39, 43, 96, 97, 328 Glass-mat-reinforced thermoplastics (GMT), 48, 71-72, 95 Glass transition temperature, 49, 83, 86 Glass/PA composites, 58, 59 Glass/PP composite, 58 Green-Lagrange strain tensor, 81 Green-Lagrange strains, 84 Grid strain analysis, 217-245 application, 219 diagnostic applications, 238-241 technique, 241 Heat conduction model, 108 Heat transfer, 52 Heating temperature profile, 109 Heating time in relationship to laminate thickness, 110 Hemispherical dome, 235, 238 Hooke's laws, 11 Hot stamping, 326 Hydrocarbon polymers, 30 Hydrodynamic friction, 198-199 Hydroforming, 68 Hydrostatic stress, 5 Ideal fibre-reinforced fluid (IFRF), 255-258, 308, 309, 311,313

527

Image processing, 408 Implant materials, 404-405, 419-428 Implicit finite element modelling, 247-322 Incompressibility constraint, 257 Inextensibility condition, 257 Inflated tool forming, 443, 470-471 Injection moulding, 326 In-plane fibre movement, 106 In-plane shear, 449, 451-454 Integrated Finite Element Solver (IFES), 425 Interface temperature, 198 Inter-laminar rotation, 101 Intermittent matched-die consolidation, 65 Intermolecular structure, 32 Inter-ply forming mechanisms, 251 Inter-ply shear, 373, 386, 447, 448, 450, 454-455 deformation, 362-364 mechanism, 307 Inter-ply slip, 100, 113, 114, 167-168, 177-197, 305, 306, 314, 317 effect of lay-up variation, 187 effect of normal pressure, 186 effect of processing temperature, 190 effect of temperature, 184 fabrics, 179, 189, 190 laminates, 191 mechanism, 201 power-law model parameters, 197 test set-up, 182 velocity increments, 183 Intramer structure, 31 Intramolecular structure, 31 Intra-ply shear, 101, 166, 173-177 Isotropic materials, yielding, 2-3 Jeffreys fluid, 335, 336 Joining, 93 K-BKZ model, 86-88 Kevlar, 41,328 Knitted-carbon-fibre-reinforced composite materials, 405-419 Knitted-fabric-reinforced thermoplastics, 403-440 Knitted fabrics, net-shape forming, 419-428 Knitted-fibre-reinforced composites, mechanical properties, 412-4 19 Knitted-fibre-reinforced organo-sheets, deep drawing, 428-432 Lagrangian strain tensor, 220 Laminate dimensions, 141-142 Laminate stacking sequence, 115, 143

528

Subject index

Laminate thickness and lay-up, 157 and stamper radius, 126 and stamping pressure, 118-119 Laminate wrinkling, 455-458, 464--465 Large strain analysis, 218-224 Lay-up and consolidation quality, 172 inter-ply slip, 187 and laminate thickness, 157 Least squares fitting, 224-226 Linear variable differential transformer (LVDT), 170, 191,286, 287 Long discontinuous fibres (LDF), 46, 240 Long fibre-reinforced composites, rheological properties, 323-369 Manufacturing techniques, 60-72 Matched-die consolidation, 62-63 Matched-die forming, 250, 252, 259, 364-365 Matched-die moulding, 66-67, 71-72 Material behaviour in thermoforming, 83-86 Material functions, 329 Mathematical modelling, 79 Matrices, 29-38, 48-53, 327 mechanical properties, 52-53 migration, 114 thermal and rheological properties, 49-52 thinning, 239 Maxwell equation, 333 Melt impregnation, 45-46 Membrane formulations, 80-82 Memory effect, 119 Mesh sensitivity, 291-293 Mooney-Rivlin model, 84 Mould geometry and stamping time, 120 Mould surface finish, 200 Mould surface/release agent, 198 Moulding compounds, 48 Multi-axial stress conditions, 11 Multi-directional sheet analysis, 282-283 Multi-ply laminates, 311 Multi-valued function, 221 Navier-Stokes equation, 359 Necking, 13, 14 Net-shape forming, 433, 434 Newton-Raphson method, 82 Newtonian fluid, 330, 332, 338, 359 Newtonian viscosity, 330 Non-linear elastic models, 83 Normal loading effects, 212 Normal pressure, 198 Nylons, 36

Ogden model, 84, 86-88 Optical microscopy, 105 Order-of-magnitude analysis, 463-464 Organic fibres, 41-43, 328 Organo-sheets, 428-432, 434 Oscillatory shear experiments, 373 Osteosynthesis plates finite element analysis (FEA), 425-428 finite element modelling (FEM), 425-428 Oven bags, 99 Parallel-plate "squeeze flow" apparatus, 170 Penalizing, 313-314 Petroleum pitch, 40 Piola-Kirchhoff stress tensor, 84 Plane deformation finite element solution technique, 308-309 modelling, 307-308 numerical solution, 305-315 Plane stress problems, 258-263 analysis application, 303-305 finite element solution technique, 261-263 problem formulation and solution scheme, 260-261 Plastic flow, 2-6, 431 Plastic strain, 4 Plastic work, 6 Plastic yielding, 2-3 Platen angle, 389, 396 Ploughing of asperities, 199 Plug-assisted forming, 76 Ply contact formulation, 311-315 Plytron, 95, 96, 99, 153, 226-230, 238, 239, 241, 242, 380, 387, 389-391,395, 396, 398 Poisson's ratio, 11, 57 Polyacrylonitrile (PAN), 40 Polyamide (PA), 36, 41,328, 339, 340, 407, 414 Poly(amide imide) (PAl), 38 Poly(aryl sulfone) (PAS), 38 Poly(butylene terephthalate) (PBT), 36 Polyesters, 36 Poly(ether ether ketone) (PEEK), 33, 38, 50, 51, 59, 70, 95, 205, 212, 328, 407, 410, 415, 417, 418, 421 Poly(ether imide) (PEI), 38, 114, 123, 328 Poly(ether ketone) (PEK), 38 Poly(ether ketone ketone) (PEKK), 38, 95, 328, 343 Poly(ether sulfone) (PES), 38, 328 Polyethylene (PE), 30, 33, 36, 42 Poly(ethylene terephthalate) (PET), 36 Polyethylmethacrylate (PEMA), 407, 410, 414--416 Polyimide (PI), 38

Subject index

Polyisoprene, 31 Polymer matrix. See Matrices Polymer morphology, 30 Polymer structures, influencing properties, 31-34 Poly(phenylene sulfide) (PPS), 38, 328 Polypropylene (PP), 30-33, 36, 96, 328 Polystyrene (PS), 49, 338, 343, 344 Polysulfone (PSU), 38 Powder impregnation, 46-47, 94 Power hardening law, 11 Power-law strain rates, 332 Pre-consolidated laminates, 97-100 diaphragm forming, 98-99 Preheating time, 107-109 Preimpregnated reinforcement. See Prepregs Prepreg lay-up, 61 Prepregs, 43-44 comparison of types, 47 consolidation, 61 film stacked, 93 Press forming, 14, 203-204, 249, 250 friction sled, 201-202 frictional forces in, 169-170 Pressure loading, 275-282 Principal element, 2, 6 deformation, 4-5 Principal strain, 5 Principal stresses, 2, 3, 5 Processing temperatures, 50 Pull-out tests, 189, 373 Pultruded bands, 94 Pultruded continuous carbon fibre (CF) polypropylene (PP)-tape, 97 Pultruded continuous glass fibre (GF) polypropylene (PP)-tape, 97 Pultrusion, 93, 326 Punch deformation experiments, 266 Punch experiments with circular unidirectional sheets, 264-265 Quasi-isotropic laminates, 284, 285, 289, 290, 299, 300 Quasi-isotropic preforms, 289 Quasi-isotropic sheet, 301 r-value, 8 Radial pressure, 273-275 Radial velocity, 265-273 Rayon, 40 Reaction injection moulding (RIM), 324 Reaction stress, 256 Reinforced diaphragm forming, 469-470 Reinforcement-matrix interaction, 42-43 Reinforcements, 38-43

529

impregnation, 35 mechanical properties, 54 thermal properties, 54 Relaxation, 332, 339-343 Relaxation modulus, 49 Relaxation parameter, 334 Relaxation phenomena, 329-336 Relaxation time, 333 Release agent, 198, 201, 210-211 Residual stresses, 22 Resin interlayer, 208 Resin percolation, 100, 165, 357-358 Resin thickness measurements, 207 Resin transfer moulding (RTM), 324, 406 Rheological measurement of composite shear viscosities, 258 Rheological parameters in thermoforming, 364-366 Rheological properties application in sheet forming, 356-366 continuous fibre-reinforced thermoplastic, 371-401 and deformation behaviour, 329 long fibre-reinforced composites, 323-369 measurement techniques, 348-355 Roll angles, 487 Roll forming, 70, 473-515 computer-aided design, 489-491 defects, 482-483 deformation analysis, 491-498 equipment and procedures, 500--501 equipment and tooling, 476--483 finite element analysis, 498 form roll design, 483-489 operating conditions, 481 quality assessment, 501-506 section orientation, 485-486 strain distribution during, 495-498 temperature control, 506-510 thermoplastic material, 498-512 Roll lubrication, 481 Roll quality, 481 Roll schedule, 484-485 Roll setting, 482 Rolling mills, 479-480 auxiliary equipment, 480 Rotational rheometer, 351 Rotational viscometers, 348-350 Rubber-die moulding, 67 Scaling laws, 458-460, 464 Semicrystalline polymers, 33-36 Semicrystalline thermoplastics, 49 Shear buckling, 249, 251,253, 263-285

530

Subject index

Shear deformation, 311 Shear flows, 329-336, 339-343 Shear magnification effect, 346 Shear modes, 342, 447 Shear rate, 342, 389, 390 modified constant shear rate tests, 392-399 Shear rheometers, 353 Shear stress, 270, 275,276, 279, 281,282, 332, 339 Shear thinning, 206, 330-331,339, 347 Shear viscosity, 51,353, 389, 391 Shearing characterisation, 163-216 Shearing velocity/shear stress relationship, 186 Sheet forming, 65-72 implicit finite element modelling, 247-322 mechanisms, 250 philosophy, 325-327 processing methods, 327 Sheet metal forming characteristics of, 6-12 limits for, 12-15 mechanics of, 1-25 Sheet stamping, 325 Single-curvature forming, 305-307 Sliding velocity versus coefficient of friction, 209 Solvent impregnation, 44-45 Specialty fibres, 42 Specific heat, 108 Spherical dome, 226-230 Spring-back, 19, 119, 193, 504-506 Spring-forward, 504-506 Squeeze flow viscometers, 353-354 Stability considerations, 285 Stamp forming, 94, 95, 97, 100-146 characterisation methods, 105-107 description of stamping process, 104-105 experimental details and procedures, 96-100, 102-104, 139-140 experimental set-up, 138-139 force analysis, 141 forming temperature, 110-115 materials employed, 96-97 mechanisms, 140-141 optimised processing window, 135-137 processing parameters, 103 recommendations, 145-146 Stamper radius and laminate thickness, 126 and stamping time, 122 Stamping pressure and laminate thickness, 118-119 and stamping time, 120, 121 and stamping velocity, 115, 123-124 and weaving of tracer wires, 135 Stamping time

and bend angle, 119 and mould geometry, 120 and stamper radius, 122 and stamping pressure, 120, 121 Stamping velocity, 112 and crystallinity, 131 and stamping pressure, 115, 123-124 Stokes flow, 262 Strain analysis technique, 148-150 Strain distribution, 236 during roll forming, 495-498 Strain energy function, 84 Strain-hardening, 13 Strain measurement, 51 0-511 Strain rate, 83, 336 sensitivity index, 24 Strain space diagram, 225, 226, 229, 230, 233,237 Strain tensor, 335 Stress equilibrium, 377 Stress growth, 334 Stress-strain characteristics, 7 Stress-strain curve, 7-13 Stress-strain equations, 129 Stress-strain properties, 11 Stress-strain relationship, 19 Stress tensor, 376 Stretch forming, 15-17 Structure-properties relationship, 415-4 19, 432-433 Superplasticity, 23-24 Surface coatings, 200 Surface fibre orientation, 200, 209 Surface release agent, 201 Surface resin layer, 208 Surface roughness measurements, 201 Tangential stress, 280, 283-285, 300-302 Tape laying, 64-65, 326 Tape winding, 93 Tear drop region, 232 Tensile failure behaviour, 413-415 Tensile strain contour map, 238 Tensile test, 6, 11, 12 Tension mass matrix, 263 Tepex, 95 Textile fabrics. See Fabrics Thermal analysis, 106-107, 130-133 Thermal conductivity, 108 Thermal expansion coefficients, 128 Thermal Mechanical Analysis (TMA), 107, 128, 130 Thermoforming, 93, 326 rheological parameters in, 364-366 Thermoplastics, 34

Subject index Thermoplastics (continued) composite sheet forming, 27-73 constituents, 29-48 polymer matrices, 34-38 sheet production, 77-78 Thermosets, 34 composite forming, 441-472 background, 442-446 deformation modes, 446-455 kinematics, 446-455 forming experiments, 464-468 Thick sheet formulations, 82-83 Time to surface degradation, 51 Tolerance to degradation, 51 Total Lagrangian (TL) formulation, 80 Tow straightening effect, 189 Transition temperatures, 49, 50 Transverse flow, 165, 170-173, 306 fabrics, 166 mechanism, 125 process, 100 Transverse shear behaviour, 392 vee-bending test, 393-394 Transverse shear viscosity tests, 395-399 Transverse squeeze flow, 358-361 Transverse stress, 274, 277 Trellis angle, 174, 175 Trellis deformation, 232 Trellis effect, 141, 167, 228 Trellis structure, 228, 230 Tresca yield criterion, 3 Trouton relation, 338 Ulnar osteosynthesis plate, 419-428 Ultimate tensile strength (UTS), 8 Unfilled polymer melts, 329 Uniaxial elongation, 337

531

Updated Lagrangian (UL) formulation, 81 Vacuum bag, 61-62, 148 Vacuum forming, 76, 326 van der Waals forces, 199 Vee-bending, 374 experimental procedures, 380-382 kinematic model, 378-379 modified test, 392 tests, 373 transverse shear behaviour, 393-394 Viscoelastic behaviour, 388 Viscoelastic fluids, 333 Viscoelastic models, 85 Viscoelastic response, 334 Viscoelasto-plastic constitutive relation, 86 Viscosity, 50, 329-336, 339-348 in elongational flows, 336-337 Viscosity ratio, 275, 279, 280, 398 von Mises yield criterion, 3 Wall thickness distribution, 142-143, 144 White-Metzner equation, 333 Williams-Landel-Ferry (WLF) transform, 200, 458 Work-hardening, 8 Woven fabric, 122 Yield locus, 18 Yield point, 7, 8 Yield strength, 8 Yield stress, 194-195 Yielding, anisotropic materials, 3-4 Young's modulus, 11, 412, 417, 418 Zero shear rate viscosity, 331


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