Fatigue in composites: science and technology of the fatigue response of fibre-reinforced plastics

Fatigue in composites

Fatigue in composites Science and technology of the fatigue response of fibre-reinforced plastics Edited by

Bryan Harris

CRC Press Boca Raton Boston New York Washington, DC WOODHEAD PUBLISHING LIMITED Cambridge England

Published by Woodhead Publishing Limited, Abington Hall, Abington Cambridge CB1 6AH, England http://www.woodhead-publishing.com/ Published in North America by CRC Press LLC 2000 Corporate Blvd, NW Boca Raton FL 33431, USA First published 2003, Woodhead Publishing Ltd and CRC Press LLC This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go tobr/ http://www.ebookstore.tandf.co.uk/.” © 2003, Woodhead Publishing Ltd The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publishers cannot assume responsibility for the validity of all materials. Neither the authors nor the publishers, nor anyone else associated with the publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from the publishers. The consent of Woodhead Publishing and CRC Press does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing or CRC Press for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress. ISBN 0-203-48371-5 Master e-book ISBN

ISBN 0-203-58826-6 (Adobe e-Reader Format) Woodhead Publishing ISBN 1 85573 608 X (Print Edition) CRC Press ISBN 0-8493-1767-3 (Print Edition) CRC Press order number: WP1767

Contents Preface

vii

Acknowledgements

x

Contributor contact details

xi

Part I Introduction to fatigue in composites 1 A historical review of the fatigue behaviour of fibre-reinforced plastics B.Harris , Materials Research Centre, University of Bath, UK 2 Fatigue test methods, problems and standards G.D.Sims , National Physical Laboratory, London, UK 3 Fatigue under multiaxial stress systems M.M.Shokrieh , Iran University of Science and Technology, Tehran, Iran, and L.B.Lessard , McGill University, Montreal, Canada Part II Micromechanical aspects of fatigue in composites 4 The effects of aggressive environments on long-term behaviour F.R.Jones , University of Sheffield, UK 5 The effect of the interface on the fatigue performance of fibre composites C.Galiotis and C.Koimtzoglou , Institute of Chemical Engineering and High Temperature Processes, Foundation for Research and Technology, Greece and Materials Department, University of Patras, Greece 6 Delamination fatigue R.Martin , Materials Engineering Research Laboratory, UK 7 The fatigue of hybrid composites G.F.Fernando , Cranfield University, UK and F.A.A.Al-Khodairi , Saudi Basic Industries Corporation, Saudi Arabia 8 Non-destructive evaluation of damage accumulation A.P.Mouritz , RMIT University, Australia Part III Fatigue in different types of composites

1

2 42 73

132

133 170

199 217

280 309

9 Short-fibre thermoset composites G.Caprino , University of Naples “Federico II”, Italy 10 Woven-fibre thermoset composites N.K.Naik , Indian Institute of Technology, Bombay, India 11 Fatigue of thermoplastic composites E.K.Gamstedt and L.A.Berglund , KTH, Sweden 12 Fatigue of wood and wood panel products M.P.Ansell , University of Bath, UK Part IV Life-prediction methods for constant stress and variable stress 13 Physical modelling of damage development in structural composite materials under stress P.W.R.Beaumont , Cambridge University, UK 14 Micromechanical models K.Reifsnider and S.Case , Virginia Tech, USA 15 A computational meso-damage model for life prediction for laminates P.Ladevèze and G.Lubineau , LMT Cachan, France 16 A statistical study of the fatigue performance of fibre-reinforced composite laminates X.Diao , PreciCad Inc., Canada, L.Ye and Y-W.Mai , University of Sydney, Australia 17 Analysis of matrix crack-induced delamination in composite laminates under static and fatigue loading M.Kashtalyan , University of Aberdeen and C.Soutis , University of Sheffield, UK 18 Fatigue strength of composites under variable plane stress T.P.Philippidis and A.P.Vassilopoulos , University of Patras, Greece 19 Life prediction under service loading spectra L.J.Lee and K.E.Fu , National Cheng Kung University, Taiwan 20 A parametric constant-life model for prediction of the fatigue lives of fibre-reinforced plastics B.Harris , University of Bath, UK 21 A neural-network approach to fatigue-life prediction J.A.Lee and D.P.Almond , University of Bath, UK Part V Fatigue in practical situations 22 The fatigue performance of composite structural components M.D.Gilchrist , University College Dublin, Ireland 23 Fatigue of joints in composite structures J.Schön and R.Starikov , Swedish Defence Research Agency, Sweden

310 340 359 388 415

416

473 494 505

537

575 599 622

649 673

674 705

24 Fatigue in filament-wound structures D.Perreux and F.Thiébaud , Laboratoire de Mécanique Appliquée RC, France 25 Fatigue of FRP composites in civil engineering applications J.M.C.Cadei , FaberMaunsell Ltd, UK 26 Fatigue in aerospace applications A.J.Davies , QinetiQ, UK and P.T.Curtis , Dstl, UK 27 Fatigue and durability of marine composites P.Davies and D.Choqueuse , IFREMER, Centre de Brest, France and A.Roy, CRITT Matériaux, Rochefort, France Index

731

746 776 801

825

Preface I first became aware of the phenomenon of fatigue in 1955 when, as a metallurgy student at the University of Birmingham, I attended a final-year course on the subject given by Dr Trevor Broome. In my mind, there are still two strongly associated memories from that time. The first is that almost the top item in Broome’s reading list was, unexpectedly, Neville Shute’s novel No Highway. This novel, written in 1948, paints an uncannily prescient picture of the in-flight fatigue failure of the tail-plane of a transatlantic airliner. The second memory from that time is that the Head of Department at Birmingham, Professor A J Murphy, was heading a government inquiry into the catastrophic mid-air failures of the De Havilland Comets as a result of low-cycle fatigue crack growth. Shute’s explanation of fatigue as being due to some ‘nuclear’ process that led to ‘crystallization’ and therefore brittleness may have been wide of the mark, but his description of the large-scale fatigue testing of a tail-plane at the Royal Aircraft Establishment at Farnborough (now, sadly, known as Dstl or QinetiQ (!), depending on which part of the establishment you are dealing with) was to become a reality at the RAE following the Comet disasters, and many years later, when I became a regular visitor to Farnborough, the sight of a similar, if larger-scale test on a Concorde tail-plane never failed to remind me of No Highway, Trevor Broome, and the Comets. Curiously, there remains a very active interest in the Comets, with a dedicated website, and a recent British television programme raised a few hackles among survivors of the design team. After leaving the university, I had nothing more to do with fatigue until after I began working on carbon-fibre composites at the University of Sussex. Under the tutelage of Dr Leslie Phillips from the RAE, one of the co-inventors of the process of making highperformance carbon fibres from polyacrylonitrile, I began work in 1966 with Peter Beaumont on a study of the fatigue behaviour of the newly available carbon-fibrereinforced plastics (CFRPs) and since that time, neither Beaumont nor I have ever stopped working on the fatigue of composites. During the 1960s and 1970s it was frequently difficult to persuade aircraft engineers that the new-fangled CFRPs suffered from fatigue. They weren’t metals, after all, and everyone knew that only metals suffered from fatigue. And this, despite the fact that there had been published reports on the fatigue behaviour of glass-fibre-reinforced plastics (GRPs*) since the early 1950s. How things have changed! *In this book, we shall use the abbreviations CFRP and GRP. This is the most common usage, and reflects the fact that GRPs were known and named long before carbon fibres were invented. It also avoids the potential confusion often caused by American insistence on calling carbon fibre ‘graphite’, even though it was well established right from the early days that the structure of carbon fibres was turbostratic and not truly graphitic. In US terminology, then, GFRP often means graphite-fibre-reinforced plastic.

By a strange quirk of coincidence, as preparations for this book were getting under way, another airliner accident was reported from the USA. In November 2001 the tail fin of an American Airlines Airbus A300 fell off seconds before that plane crashed after take-off in New York. In all, 265 people were killed, and questions were immediately raised about the composite make-up of that tail fin. In an area where the tail connects to the fuselage, ultrasonic tests revealed a flaw which was described as a possible tiny ply separation within the layered carbon fibre. A report published in November 2002 indicates that the investigation into the cause of the failure is still proceeding, and that the cause will probably not be decided until next year. The investigation has now shown that the jet twice ran into the wake of a Boeing 747 five miles ahead of it, at which time the rudder began to swing back and forth violently. Seven seconds later, the composite tail fin started to break off. This was apparently the first time that anyone had been aware of the in-flight failure of a major aircraft structural component made of composite materials. Investigators have learned since the accident that sharp rudder actions can put sufficient stress on the tail fin to cause it to snap off. So far, no mention appears to have been made of the possibility of fatigue, and indeed it may be that fatigue is not implicated. But the official reaction to the incident is interesting. The planes were not taken out of service, an Airbus spokesman claiming that ‘If damage is not visible, then we know it does not affect the strength of the material, and it will not grow during the service life of the airplane. A visual inspection will be adequate to find any anomaly that would be of concern.’ Is such confidence well-founded? It is now well established that fibre composites, like metals, exhibit a form of degradation in service that can be described as ‘fatigue’. A simplistic description of the phenomenon is that under cyclic loading conditions, the load-bearing capacity of the material falls with time and this results in failures at stress levels which are often well below the ordinary (monotonic) engineering strength. The mechanisms by which this deterioration occurs in composites are quite different from, and much more complicated than, those which are responsible for fatigue phenomena in metals, but the problems facing the designer are similar. From the engineer’s point of view, the challenge is to choose materials and use them in such a way as to avoid failures within the design life of a component or structure. In order to achieve this, it is necessary to understand the mechanisms of degradation in service and to be able to predict the life of a given composite under particular design conditions. In principle, achievement of the first of these should lead with confidence to the second, but at the present time our progress towards a state of understanding where one follows from the other is less than perfect. Research into the fatigue response of fibre composites has been carried out since the materials themselves first began to be a subject of serious study. Some of the first papers on the fatigue behaviour of glass-reinforced plastics, for example, were published in the USA by Boller in the 1950s and 60s, and shortly after this Owen and his collaborators at Nottingham University in the UK were reporting the results of work on early carbonfibre-reinforced plastics (CFRPs). Simultaneously, Baker and co-workers at Rolls Royce, also in the UK, were laying the foundations for an understanding of the fatigue behaviour of metal-matrix composites (MMCs). While much of this early work on fatigue involved phenomenological studies, it quickly became apparent that an understanding of the microstructural damage mechanisms responsible for failure under cyclic loading was a prerequisite for the development of new fatigue-resistant materials and, in the longer

term, for the prediction of fatigue life, and the names of Reifsnider in the USA and Talreja in Denmark (now also in the USA) began to be associated with key developments in the emerging field of damage mechanics. And since the build-up of fatigue damage is essentially a stochastic process, vital statistical interpretations of fatigue behaviour, again with life prediction as the objective, were made, among others, by Hahn, Talreja, Whitney, and Yang. Initially, research into the fatigue behaviour of fibre-reinforced plastics (FRPs) was driven largely by the aerospace industry, and much of the work was funded by that industry and by government. In the half-century or so since FRPs were first developed, the picture, as far as applications are concerned, has changed substantially and aerospace is now only one of several fields where designers are seeking (and using) the latest of these materials which offer them the desirable benefits of high strength and stiffness combined with low density. It is perhaps for this reason more than any other that it seems an appropriate time to produce a new survey of our current level of knowledge of the Achilles heel—the fatigue behaviour of composites—and extend it to deal with the wider range of problems met with by designers in automotive, marine, and structural engineering. It is intended that this work will provide a practical encyclopaedic text book for designers as well as being an authoritative reference source for materials scientists.

Acknowledgements I am indebted to Woodhead Publishing Limited for offering me the opportunity to edit a major reference work that deals with a subject on which I have spent most of my research career. The task has been enormously eased and simplified by the care and professionalism of the company’s editorial staff, and I should particularly like to thank Emma Starr for taking on the major organizational burden and for executing it so smoothly in the background that I have been almost unaware of it. A book of this kind is naturally only as good as the papers that it contains, and in this I count myself most fortunate to have contributions from a group of authors who are established and acknowledged leaders in their individual fields. Many of these authors I also count as my friends, since the composites fatigue community has been sufficiently small in the past for it to be possible to know almost all of the leading authorities. I offer my sincere thanks to all of the contributors for finding the time to write their chapters in the course of what I know from experience are very busy lives. I hope that in time the book will repay them for their efforts. Bryan Harris Materials Research Centre University of Bath, Somerset, England

Contributor contact details Chapters 1 & 20 Professor Bryan Harris Materials Research Centre Department of Engineering and Applied Science University of Bath Bath Somerset UK Tel: +44 (0) 1225 826447 E-mail: [email protected] Chapter 2 Dr Graham D.Sims National Physical Laboratory Materials Centre Teddington Middlesex TW11 0LW UK Tel: +44 (0) 20 8943 6564 Fax: +44 (0) 20 8614 0433 E-mail: [email protected] Chapter 3 Professor Mahmood M.Shokrieh Mechanical Engineering Department Iran University of Science and Technology Narmak Tehran 16844 Iran Tel.: +98 911288 7925 Fax: +98 21 749 1206 E-mail: [email protected] Professor L.B.Lessard Department of Mechanical Engineering McGill University 817 Sherbrooke St West Montreal Quebec

Canada H3A 2K6 Tel: +1 514 398–6305 Fax: +1 514 398–6305 E-mail: [email protected] Chapter 4 Professor F.R.Jones Department of Engineering Materials University of Sheffield Sir Robert Hadfield Building Sheffield S1 3JD UK Tel: +44 (0) 114 222 5477 E-mail: [email protected] Chapter 5 Professor C.Galiotis1,2 & Dr C.Koimtzoglou1 1 Institute of Chemical Engineering and High Temperature Processes Foundation for Research & Technology—Hellas Stadiou Street Platani PO Box 1414 GR-265 04 Patras Greece 2 Materials Science Department School of Natural Science University of Patras GR-265 04 Patras Greece Tel: +30 610–965 255 Fax: +30 610–965 223 E-mail: [email protected] [email protected] Chapter 6 Dr Rod Martin Materials Engineering Research Laboratory Ltd Tamworth Road Hertford SG13 7DG UK

Tel: +44 (0) 1992 510803 Fax: +44 (0) 1992 586439 E-mail: [email protected] Chapter 7 Dr G.F.Fernando Engineering Systems Department Cranfield University RMCS, Shrivenham Swindon SN6 8LA UK Tel: +44 (0) 1793 785146 E-mail: [email protected] Dr F.A.A.Al-Khodairi Polymer Research Technology Saudi Basic Industries Corporation PO Box 42503 Riyadh 11551 Saudi Arabia Chapter 8 Professor A.P.Mouritz School of Aerospace, Mechanical and Manufacturing Engineering RMIT University GPO Box 2476V Melbourne Victoria 3001 Australia Tel: +61 3 9925 8069 Fax: +61 3 9925 8099 E-mail: [email protected] Chapter 9 Professor G.Caprino Department of Materials and Production Engineering University of Naples “Federico II” Piazzale Tecchio 80 80125 Napoli Italy E-mail: [email protected] Chapter 10 Professor N.K.Naik Aerospace Engineering Department

Indian Institute of Technology—Bombay Powai Mumbai—400 076 India Tel: +91 22 2576 7114 Fax: +91 22 2572 2602 E-mail: [email protected] Chapter 11 Dr E.K.Gamstedt Department of Solid Mechanics Royal Institute of Technology (KTH) SE-10044 Stockholm Sweden Tel: +46 8 790 7553 Fax: +46 8 4112418 E-mail: [email protected] Professor L.A.Berglund Department of Aeronautical and Vehicle Engineering Royal Institute of Technology (KTH) SE-10044 Stockholm Sweden Tel: +46 8 790 8118 Fax: +46 8 796 6080 E-mail: [email protected] Chapter 12 Dr Martin P.Ansell Department of Engineering and Applied Science University of Bath Bath BA2 7AY UK Tel: +44 (0) 1225 386432 Fax: +44 (0) 1225 386098 E-mail: [email protected] Chapter 13 Dr P.W.R.Beaumont Cambridge University Engineering Department Trumpington Street Cambridge UK Tel: +44 (0) 1223 332600 Fax: +44 (0) 1223 332662 E-mail: [email protected]

Chapter 14 Professor K.Reifsnider, Alexander Giacco Professor of Engineering Science and Mechanics and Professor S.Case 120 Patton Hall Virginia Tech Blacksburg VA 24061–0219 USA E-mail: [email protected] Chapter 15 Professor P.Ladevèze and Dr G.Lubineau ENS Cachan CNRS Université Paris 6 61 avenue du President Wilson 94235 Cachan Cedex France Tel: +33 (0) 1 47 40 22 41 Fax: +33 (0) 1 47 40 27 85 E-mail: [email protected] Chapter 16 Professor Lin Ye and Professor Yiu-Wing Mai Centre for Advanced Materials Technology (CAMT) University of Sydney Sydney NSW 2006 Australia Tel: +61 2 9351 2290/2341 Fax: +61 2 9351 3760 E-mail: [email protected] Dr Xiaoxue Diao PreciCad Inc. 350 Boulevard Charest Est, 1st floor Quebec G1K 3H4 Canada Tel: 514 485 4292 Fax: 514 485 4234 E-mail: [email protected] Chapter 17 Professor C.Soutis Head of Aerospace Engineering University of Sheffield Faculty of Engineering

Mappin Street Sheffield S1 3JD UK Tel: +44 (0) 114 2227811 Fax: +44 (0) 114 2227890 E-mail: [email protected] Dr M.Kashtalyan School of Engineering and Physical Sciences University of Aberdeen Fraser Noble Building King’s College Aberdeen AB24 3UE UK Tel: +44 (0) 1224 272519 Fax: +44 (0) 1224 272519 E-mail: [email protected] Chapter 18 Professor T.P.Philippidis & Dr A.P. Vassilopoulos Section of Applied Mechanics Department of Mechanical Engineering and Aeronautics University of Patras PO Box 1401 University Campus 265 04, Rion Greece Tel/Fax: +30 261 0997235 E-mail: [email protected] [email protected] Chapter 19 Dr K.E.Fu and Professor L.J.Lee Institute of Aeronautics and Astronautics National Cheng Kung University Tainan Taiwan 70101 ROC E-mail: [email protected] Chapter 21 Dr J.A.Lee and Professor D.P.Almond Department of Engineering and Applied Science University of Bath Bath

BA2 7AY UK E-mail: [email protected] Chapter 22 Professor M.D.Gilchrist Department of Mechanical Engineering University College Dublin Belfield Dublin 4 Ireland Tel: +353 1 7161884 Fax: +353 1 2830534 E-mail: [email protected] Chapter 23 Dr J.Schön Swedish Defence Research Agency FOI SE-172 90 Stockholm Sweden Tel: +46 8 55503595 Fax: +46 8 55503869 E-mail: [email protected] Dr R.Starikov Swedish Defence Research Agency FOI FFA SE-172 90 Stockholm Sweden E-mail: [email protected] Chapter 24 Professor D.Perreux and Dr Frédéric Thiébaud Laboratoire de Mécanique Appliquée RC 24 rue de l’Epitaphe 25000 Besançon France Tel: +33 (0) 3 81 666012 Fax: +33 (0) 3 81 66 67 00 E-mail: [email protected] Chapter 25 Dr John M.C.Cadei FaberMaunsell Ltd 160 Croydon Road Beckenham Kent

BR3 4DE UK Tel: +44 (0) 870 905 0906 Fax: +44 (0) 20 8663 6723 E-mail: [email protected] Chapter 26 Dr A.J.Davies QinetiQ Farnborough Hampshire UK E-mail: [email protected] Professor P.T.Curtis Dstl Farnborough Materials and Structures Group Hampshire UK E-mail: [email protected] Chapter 27 Dr Peter Davies Materials & Structures Group (TMSI/RED/MS) IFREMER Centre de Brest BP70 29280 Plouzané France Tel: +33 2 98 22 4777 Fax: +33 2 98 22 4535 E-mail: [email protected] Mr Dominique Choqueuse Materials & Structures Group (TMSI/RED/ MS) IFREMER Centre de Brest BP70 29280 Plouzané France Tel: +33 2 98 22 4163 Fax: +33 2 98 22 4535 E-mail: [email protected] Dr Annette Roy CRITT Matériaux BP 115–40 bis avenue Marcel Dassault 17303 Rochefort Cedex France Tel: 05 46 83 92 03 Fax: 05 46 99 65 88 E-mail: [email protected]

Part I Introduction to fatigue in composites

1 A historical review of the fatigue behaviour of fibre-reinforced plastics B.Harris, Materials Research Centre, University of Bath, UK 1.1 Introduction The engineer’s perception of the phenomenon of fatigue is so closely linked with the behaviour of homogeneous, isotropic, metallic materials that there has often been a tendency to treat modern fibre composites as though they were metals. At the outset, the test methods used to study fatigue in composites were the same as those used for metals, and the interpretation of the results of such tests has often been clouded by ideas about what constitutes metallic fatigue failure. It is normal that a designer wanting to substitute a composite for a metal component should want to test the new material by applying a cyclic loading régime of the same kind as that which the component would be required to sustain in service in order to prove that the composite will perform as well as the metal. But it is wrong to assume a priori that there is some universal mechanism by which fluctuating loads will inevitably result in failure at stresses below the normal monotonic failure stress of the material. Metallic fatigue, which accounts for a large percentage of engineering failures, has been intensively studied for more than a century. Design data have been accumulated for every conceivable engineering metal and alloy, and the engineer has access to a comprehensive set of rules, some empirical and some based on scientific understanding, with which to deal with any given design requirement. The fact that designers often choose to ignore these rules accounts for the many fatigue failures that should never have happened. Fatigue in metals often progresses by the initiation of a single crack and its intermittent propagation until catastrophic failure which occurs with little warning. In ordinary high-cycle (low-stress) fatigue, the properties of the metal remote from the crack may be only slightly changed during fatigue. The usual effect of fatigue at low stresses is simply to harden the metal slightly. Generally speaking, a stronger material will have a higher fatigue resistance, the fatigue ratio (fatigue limit divided by tensile strength) being roughly constant. It was common at one time for users of composite materials to express the belief that composite materials—more specifically, carbon-fibre-reinforced plastics—did not suffer from fatigue. This is all the more astonishing in view of the fact that from the earliest days of composites development, their fatigue behaviour was a subject of serious study. What was usually implied was that, because most CFRPs were extremely stiff in the fibre direction, the working strains in practical components at conventional design stress levels were usually far too low to initiate any of the local damage mechanisms that might

A historical review of the fatigure behaviour

3

otherwise have caused deterioration under cyclic loads. The use of composites like CFRPs only at very low working strains raises two important issues. The first is the obvious one that, by using expensive, high-performance materials at small fractions of their available strength, we are over-designing and using them uneconomically. The second is that since anisotropy is a characteristic of composites that we accept and must design for, a stress system that develops only a small working strain in the main fibre direction may nevertheless cause strains normal to the fibres or at the fibre/resin interface which are high enough to cause the kind of deterioration that we call fatigue damage. In designing with composites, therefore, we cannot ignore fatigue. It follows that, in addition to needing to understand the mechanisms by which fatigue damage occurs in composites, we need access to procedures by which the development and accumulation of this damage, and therefore the likely life of the material (or component) in question, can be reliably predicted. 1.2 Fatigue phenomena in fibre composites 1.2.1 Damage in composites Unlike metals, composite materials are inhomogeneous (on a gross scale) and anisotropic. They accumulate damage in a general rather than a localized fashion, and failure does not always occur by the propagation of a single macroscopic crack. The micro-structural mechanisms of damage accumulation, including fibre breakage and matrix cracking, debonding, transverse-ply cracking, and delamination, occur sometimes independently and sometimes interactively, and the predominance of one or the other may be strongly affected by both materials variables and testing conditions. At low levels of stress in monotonic loading, or early in life during cyclic loading, most types of composite sustain damage. This damage is distributed throughout the stressed region, and although it does not always immediately reduce the strength of the composite, it often reduces the stiffness. Such strength reductions as might occur (in the process described as ‘wear-out’) are sometimes off-set in the early stages of life by slight increases in strength, or ‘wear-in’. These increases may be a result of the slightly improved fibre alignment which follows small, stress-induced, viscoelastic or creep deformations in the matrix. Later in life the amount of damage accumulated in some region of the composite may be so great that the residual load-bearing capacity of the composite in that region falls to the level of the maximum stress in the fatigue cycle and failure ensues, as shown schematically in Fig. 1.1. This process may occur gradually, when it is simply referred to as degradation, or catastrophically, when it is termed ‘sudden-death’. Changes of this kind do not necessarily relate to the propagation of a single crack, and this must be recognized when attempting to interpret composites fatigue data obtained by methods developed for metallic materials. When a pre-existing crack is present in a composite it may or may not propagate under the action of a cyclic load, depending upon the nature of the composite. In highly anisotropic composites of high Vf, for example, the crack will often refuse to propagate normal to the fibres (mode 1) but will be diverted into a splitting mode, sometimes resulting in end-to-end splitting which simply eliminates the crack. By contrast, in GRP

Fatigue in composites

4

laminates containing woven-roving or chopped-strand mat reinforcement crack tip damage may remain localized by the complex geometry of the fibre array and the crack may proceed through this damaged zone in a fashion analogous to the propagation of a crack in a plastically deformable metal.1

Fig. 1.1 Degradation of composite strength by wear-out until the residual strength σR falls from the normal composite strength σc to the level of the fatigue stress, at which point failure occurs. Howe and Owen2 (1972) studied the accumulation of damage during cyclic loading with the object of obtaining useful working relationships of the Miner-rule type3 that might be used in design. With the aid of optical microscopy they studied the development of debonding sites and resin cracks in chopped-strand-mat/polyester composites and they suggested that, although debonding did not itself cause reductions in strength, it served to initiate resin cracks which did weaken the material. For resin cracking they proposed a non-linear damage law, independent of stress level, which gives the damage ∆ as [1.1] where n is the number of cycles sustained by the composite at a stress which would normally cause failure after N cycles, and A and B are constants. B is negative and ∆ is equal to unity at failure. They used a modification of this law to predict residual strength after cycling of CSM/polyester laminates, this strength being dependent upon the growth of resin cracks. Different damage mechanisms accumulated damage at different rates through the life cycle, as shown in Fig. 1.2. The damage development laws are likely to be different for each specific damage mechanism and will also be structure dependent, as illustrated by the results of crack-density measurements shown in Fig. 1.3.4 These measurements were made on a T800/5245 CFRP laminate of [(±45,02)2]S lay-up, and it can be seen that the development of cracks in the outer (unconstrained) and inner

A historical review of the fatigure behaviour

5

(constrained) 45° plies proceeds at quite different rates: the saturation levels for the two types of crack are also quite different. The observed changes in the mechanical properties of fatigued composites are unlikely to be caused by a single damage mechanism. Detailed studies of the damage processes occurring during cycling of CFRP materials5 show that sequences of damage occur throughout life, and these sequences can be mapped, as shown in Fig. 1.4, on a conventional σ/log Nf diagram. It seems likely that each damage-mechanism curve, including the final failure curve (i.e. the σ/log Nf curve), represents part of an S-shaped decay curve of the kind postulated by Talreja,6 although in the experimental window we see only a part of each curve. It is also supposed that at sufficiently low stresses, corresponding to some notional endurance limit, all curves will flatten out and converge at large numbers of cycles. The concept of accumulation of damage leading to ultimate failure is embodied in the early cumulative-damage theory of Hashin and Rotem.7

Fig. 1.2 Normalized plots of two types of damage, which occur during the fatigue cycling of a CSM/polyester laminate (redrawn from Howe and Owen2).

Fatigue in composites

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Fig. 1.3 Density of cracks in 45° plies in a [(±45,02)2]S T800/5245 CFRP laminate during cycling at a peak stress of 1 GPa and an R ratio of 0.1.4 1.2.2 Experimental scatter and the definition of failure Smith and Owen8 demonstrated the extent to which variability affects the results of fatigue tests and emphasized the importance of replicate testing. This variability stems not only from the statistical nature of the progressive damage which leads to failure, but is more particularly due to the variable quality of many commercial composite materials. They also pointed out that in many kinds of composite the number of cycles to complete separation of the broken halves of a sample is a definition of failure that becomes quite meaningless if the sample has lost its integrity and its ability to sustain an applied stress as a result of extensive resin cracking, arguing the need for careful (and relevant) definition of the failure criterion, although they accept that the use of debonding or the onset of resin cracking, say, as failure criteria would drastically impair the economic use of a material like GRP. It is not surprising, given the nature of composites, that the variability of their fatigue response is even greater than that associated with metallic materials. Stress/life data may be obtained by testing single samples at many different stress levels, or by carrying out replicate tests at rather fewer stresses: the latter is usually considered to be the more satisfactory method because it provides statistical information at each stress, and provides probability/ stress/life curves in addition to median-life or mean-life curves. One of the problems is to know how many replicate tests should be done at each stress level since, given the cost of fatigue-testing programmes, the smaller the number of tests that can be used to establish a ‘safe’ σ/log Nf curve, the better. From a statistical point of view it is often expected that at least 20 replicate tests at each stress may be necessary before the user can have any confidence in a statistical analysis of results (see, for example, Lee et al.).9

A historical review of the fatigure behaviour

7

Fig. 1.4 Schematic damage mechanism maps for a T800/5245 [(±45,02)2]S CFRP laminate tested in repeated tension fatigue (R=0.1).5 A variety of distributions have been used to characterize fatigue lives, but the threeparameter Weibull function is often considered to be the most appropriate model for this purpose. The form of the cumulative distribution function used for fatigue is: [1.2] where P is the probability of a life Nf, and a, the location parameter, defines a number of cycles for which there is zero probability of failure. For metallic materials, the value of the shape parameter m is often in the range 2<m106 cycles). While some individual application requirements are being met by fatigue tests at the low stresses involved using frequencies of 60 Hz, the full S–N curve cannot be obtained at this frequency. For a major fatigue test programme, it would be worthwhile determining the optimum test frequency for each stress level. Although not within the current ISO 13003 standard, the use of a constant loading rate approach (cf. constant frequency) has been used by others and is recommended in the textbook based on the Imperial

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College/National Physical Laboratory/Queen Mary and Westfield testing course.36 Further validation is required before this approach can be considered for standardization. Ultimately, there may be a requirement to decide between the alternative philosophies of, firstly, only testing final or prototype components under service or simulated service conditions with limited fundamental understanding or carry-over to a different set of circumstances, and secondly, testing representative units (e.g. fully aligned material) and extrapolating through failure models and empirical frameworks to materials of different lay-ups and loading situations. The latter approach seems more likely to manage the range of composite materials (e.g. fibre type including hybrids, fibre format and matrix material), different manufacturers and loading conditions. 2.11 Acknowledgements The author is pleased to recognise the support of many co-workers over the last 35 years, especially the late Den Gladman. 2.12 References 1. ISO 13003, Fibre reinforced plastics: determination of fatigue properties under cyclic loading. 2. SIMS G D and BASCOMBE D (1998), ‘Continuous monitoring of degradation during fatigue testing’, 6th ICCM/2nd ECCM, 3, pp. 161–171, London. 3. ISO 1172, Textile glass reinforced plastics—determination of loss on ignition. 4. ISO/DIS 14127, Composites—determination of resin, fibre and void content of composites reinforced with carbon fibre. 5. ISO 6721–11, Plastics—dynamic mechanical properties, determination of glass transition temperature. 6. ISO 11357, Plastics—differential scanning calorimetry. 7. EN ISO 1268, Fibre reinforced plastics—test plate fabrication methods. 8. FOREMAN A, DAVIES A, SIMS G D and SHAW R (2001), ‘Composites machining and specimen preparation’, NPL Measurement Good Practice Guide No. 38. 9. SIMS G D and GLADMAN D G (1978), ‘Effect of TestConditions on the Fatigue Strength of Glass Fabric Laminate—Part A, Frequency’, Plastics and Rubber: Materials and Applications, 1, pp. 41–48. 10. HEYWOOD R B (1958), ‘Present and potential fatigue and creep strengths of reinforced plastics’, RAE Technical Note Chem. 1337. 11. ASTM D 3410, ‘Standard test method for compressive properties of polymer matrix composites with unsupported gage section by shear loading’. 12. EN ISO 14126, Fibre-reinforced plastic composites—determination of the in-plane compression strength. 13. EN ISO 527–4, ‘Plastics—determination of tensile properties—Part 4: Test conditions for isotropic and orthotropic fibre reinforced plastic composites’. 14. EN ISO 527–5, ‘Plastics—determination of tensile properties—Part 5: Test conditions for unidirectional fibre reinforced plastic composites’. 15. BROUGHTON W R, GOWER M R L, LODEIRO M J and SHAW R M, ‘Through-thickness fatigue testing of polymer matrix composites’. 16. ASTM D5379, Standard test method for shear properties of composite materials by the Vnotched beam method.

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17. NPL drafts for through-thickness tension and compression specimen drafts, 1999. 18. EN ISO 14125, ‘Fibre reinforced plastic composites—determination of flexural properties’. 19. Japanese flexural PP spacer. 20. SIMS G D and GLADMAN D G (1982), ‘A framework for specifying the fatigue performance of glass-fire reinforced plastics’, NPL Report DMA(A) 59. 21. SIMS G D and GLADMAN D G (1980), ‘Effect of test conditions on the fatigue strength of glass fabric laminate: PartB, Specimen condition’, Plastics and Rubber: Materials and Applications, 3, pp. 122–128. 22. NPL draft methods for open hole tension and open hole compression, 1999. 23. ASTMD 3479, ‘Standard Test Method for Tension–Tension Fatigue of Polymer Matrix Composite Materials’. 24. ASTM D 6115, ‘Standard Test Method for Mode I Fatigue Delamination Growth Onset of Unidirectional Fiber-Reinforced Polymer Matrix Composites’. 25. ASTM D 5528 ‘Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites’. 26. EN ISO 15024, Determination of Mode I delamination resistance of unidirectional fibrereinforced polymer laminates using the double cantilever beam. 27. DAVIES P (1999), ‘Comparison of test configurations for the determination of Mode 2 GII—an international round-robin’, P Davies et al. Plastics, Composites and Rubber, November. 28. MARTIN R H, ELMS T and BOWRON S (1998), ‘Characterisation of Mode II delamination using the 4ENF’, Composites: Testing and Standardisation Conference 5, Lisbon. 29. ASTM work item draft on ‘bearing fatigue testing’, 2001. 30. ASTM D5961, ‘Standard practice for testing of bolted bearings. 31. ISO 14269, Petroleum and natural gas industries—Glass Reinforced Plastic Piping (4 Parts). 32. EN 12245, Fibre wrapped gas cylinders. 33. ISO Guide to uncertainties of measurement. 34. ISO 5725, ‘Accuracy (trueness and precision) of measurement methods and results’. 35. ASTM E 691, ‘Standard practice for conducting an interlaboratory study to determine the precision for specimen preparation’. 36. Mechanical Testing of Advanced Fibre Composites, ed. J M Hodgkinson, Woodhead Publishing Ltd., 2000.

3 Fatigue under multiaxial stress systems M.M.Shokrieh, Iran University of Science and Technology, Tehran, Iran, and L.B.Lessard, McGill University, Montreal, Canada 3.1 Introduction Although there is an extensive amount of research on biaxial/multiaxial fatigue of metals,1 research in the same field on composite materials is less complete. Literature reviews and results of research of multiaxial and biaxial fatigue loading of composite materials have been presented by Shokrieh,2,3 Degrieck,4 Quaresimin,5 Philippidis,6 Found,7 and Chen and Matthews,8 and these papers state that further research is needed. The idea of using polynomial failure criteria for predicting fatigue failure of composite laminates has been used by many authors;9–20 however, the application of this idea, due to experimental difficulties, is limited to special cases. A deep understanding of the behaviour of a composite lamina under multiaxial fatigue loading, with arbitrary stress ratios, is a key point for studying the behaviour of a complicated problem. 3.2 Fatigue failure criteria Under fatigue loading conditions, the material is loaded by a stress state which is less than the maximum strength of the material, therefore there is no static mode of failure. However, by increasing the number of cycles, the material properties degrade and eventually lower to the level of the stress state and, at this point, catastrophic failure occurs. The idea of using polynomial failure criteria to predict the life of a composite ply under multiaxial fatigue loading has been utilized by many investigators.9–20 They used the fatigue strength, as a function of number of cycles, in the denominators of failure criteria instead of the static strength of the material. This strategy is potentially beneficial; however, in practice, the application of their models are restricted to very specific conditions. To show the restriction of application of fatigue failure criteria in traditional forms, consider the following fatigue failure criterion introduced by Hashin11 for fibre tension fatigue failure mode of a unidirectional ply under a two-dimensional state of stress (biaxial fatigue), [3.1] where Xt(n, σ, κ) is the residual longitudinal tensile strength of a unidirectional ply under uniaxial fatigue loading, and Sxy(n, σ, κ) is the residual in-plane shear strength of a

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unidirectional ply under uniaxial shear fatigue loading conditions. Both Xt and Sxy are functions of n, σ, κ which are number of cycles, stress state and stress ratio, respectively. The fatigue behaviour of a composite lamina varies under different states of stress. For instance, under high level state of stress, the residual strength as a function of number of cycles is nearly constant and it decreases drastically at the number of cycles to failure (Fig. 3.1). The sudden death model94,95 is a suitable technique to describe this behaviour. However, at low level state of stress, the residual strength of the lamina, as a function of number of cycles, degrades gradually (Fig. 3.1). The wear out model96 is a suitable technique to present this behaviour. It should be mentioned that for each state of stress, the S–N curve passes through the point (catastrophic failure point) of the residual strength curve, as shown in Fig. 3.1. In practice, designers must deal with a wide range of states of stress, varying from low to high. Therefore, in order to apply equation [3.1], the residual longitudinal tensile fatigue strength and residual in-plane shear fatigue strength of a unidirectional ply (Xt(n, σ, κ) and Sxy(n, σ, κ)) must be fully characterized under different stress levels and stress ratios. This requires a large quantity of experiments just to predict the fibre in tension fatigue failure mode of a unidirectional ply under simple biaxial fatigue loading conditions. By considering the other modes of failure and the multiaxial states of stress which are encountered in the real fatigue design of composite structures, the proposed method is faced with severe difficulties. To overcome the difficulties arising from the large quantity of experiments required at different stress states and stress ratios to characterize the material, many investigators9–20 restricted their models to specific stress ratios. A summary of different stress ratios utilized by authors is presented in Table 3.1. This assumption is too restrictive for general cases. For example, in the analysis of a pin/bolt fatigue loaded composite laminate, using a constant stress ratio leads to incorrect results. Clearly, for this problem there are different states of stress at different points in the material. Also, after applying fatigue load on a notched composite laminate, failure initiates near the stress concentrations and

Fig. 3.1 Strength degradation under different states of stress.

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Table 3.1 A summary of different load ratios utilized by authors References

Utilized stress ratios (κ) 9

Sims and Brogdon Hahn

10

0.818, 0.5 and 0.313 0 and 0.1

11,12

Hashin

−1 to establish failure criteria 0.1 for experiments 13

Rotem & Hashin

0.1 16

Ellyin and El-Kadi Wu19

Ryder and Crossman21 Tennyson et al.18

0.05 in tension (20 in compression)

the material property degrades, therefore the stress ratio and the state of stress are not constant at different points. This means that, in practice, stresses redistribute during the fatigue loading. By considering the different behaviour of a unidirectional ply for each combination of the stress state and stress ratio, an infinite number of experiments would be required in order to fully characterize the residual properties of a unidirectional ply under arbitrary state of stress and stress ratio. To eliminate the aforementioned obstacle of using the quadratic polynomial failure criteria for a wide range of stress state and stress ratio, a technique is established in this study which will be explained in detail in the next section. In the following, a set of quadratic polynomial fatigue failure criteria capable of distinction of different modes of failure of a unidirectional ply under multiaxial fatigue loading conditions are established. The fatigue failure criteria for different modes of failure are similar to static failure criteria, except that the material properties are not constants but functions of number of cycles, stress state and stress ratios. It should be added that the effects of material nonlinearity on the fatigue failure criteria are also considered similar to the static loading conditions. 3.2.1 Fibre tension fatigue failure mode For fibre tension fatigue failure mode (σxx>0) of a unidirectional ply under a multiaxial state of fatigue stress, the following criterion is used: [3.2]

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where Xt(n, σ, κ) is the longitudinal tensile residual fatigue strength of a unidirectional ply under uniaxial fatigue loading, Sxy(n, σ, κ) is the in-plane shear residual fatigue strength of a unidirectional ply under uniaxial shear fatigue loading, Exy(n, σ, κ) is the inplane shear residual fatigue stiffness of a unidirectional ply under uniaxial shear fatigue loading, Sxz(n, σ, κ) is the out-of-plane shear (in x–z plane) residual fatigue strength of a unidirectional ply under uniaxial shear fatigue loading and Exz(n, σ, κ) is the out-of-plane shear residual fatigue stiffness of a unidirectional ply under uniaxial shear fatigue loading conditions. Also n, σ, κ and α are number of cycles, stress state, stress ratio and parameter of material nonlinearity, respectively. It should be mentioned that the parameter of material nonlinearity (α) is assumed to be a constant, not a function of number of cycles, stress state and stress ratio. In order to express the relationship between the parameter of material nonlinearity and number of cycles for various stress states and stress ratios, further research is needed. 3.2.2 Fibre compression fatigue failure mode For fibre compression fatigue failure mode (σxx