Cambridge Solid State Science Series D. Hull and T. W. Clyne
N
ONE WEEK LOAN
AN INTRODUCTION TO COMPOSITE
M ATE R I...
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Cambridge Solid State Science Series D. Hull and T. W. Clyne
N
ONE WEEK LOAN
AN INTRODUCTION TO COMPOSITE
M ATE R I A L S , Second Edition Cambridge Solid State Science Series EDITORS
Professor D. R. Clarke Department 0/ Materials Science and Engineering, Ulli versity 0/ California , Santa Bm'bara
Professor S. Suresh I\1I 'h(/rd
I ~·.
,""iIlIIlIlJIIS Pro/essor, Department o/Materials Science and Engineering, Massachusells In stitute 0/ Technology
Professor I. M. Ward FRS I RC ill PolJ'mer Science and Technology , University 0/ Leeds
Titles in prin t in this series
AN INTRODUCTION TO COMPOSITE MATERIALS Second Edition
S. W. S. McKeever Th ermoluminescence 0/ so lids
P. L. Ro ssiter The electrical resisti vity 0/ metals and al/oys
D . HULL
D . I. Bower a nd W . F. Maddams
Emerilus Professor
Th e vibrational spectroscopy o/poly mers
Universily
S. Sures h
0/ Cambridge
AND
Fatigue oj'materials
T . W. C LYNE
J . Zarzyck i Glasses and the vitreous state
Reader in Mechan ics of Maleria/s, Deparlmenl of Maleria/s Science and Melallurgy,
R . A. Street
Universily of Cambridge
H y drogenated amorphous silicon
T .-W. C hou Micr ost ru ctural design o/jiber composites
A. M . Donald a nd A . H. Windle Liquid crystalline poly mers
B. R . La wn Fracture oj' brittle solids - second edition
T. W. C lyne and P. J . Withers An introduction 10 metal matrix composites
V. J . McBricrty a nd K. J. Packer Nuclear maglletic resonance in solid poly mer s
R. H. Boyd and P. J. Phillips T he sciellce
0/ poly mer
molecules
D. P. Woodru ff' and T. A. Dclchar M odei'll t(,(,/lI1ilfll(,s or sill/ace sciell ce
second edit ion
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CA MBRIDGE UNIVEI{SITY PI{ESS
Contents
Publi shed by the Press Syndicate of the Un iversit y of Ca mbrid ge The Pit[ Building, Trumpington Street, Ca mbrid ge C B2 I RP 40 West 20th Street, New York , NY 10011-42 11 , USA 10 Stamford Road , Oakleigh , Melbourne 3 166, Au stralia (' ) Ca mbrid ge University Press 198 1, 1996 First publi shed 198 1 Second editi o n 1996 Printed in Great Britain a t the University Press, Ca mbrid ge
A ca falogue record/or fhis book is available/i'om fh e Brifish Library Librarr or Congress calaloguing in publicafion dalO Hull , Derek. An introduction to co mposite material s / D. Hull and T. W. C1yne. - 2nd cd. p. cm. (Cambridge solid state scien ce series) Includ cs bibliographical referen ces. ISBN 0-52 1-38190-8 (ha rdco ver). - ISBN 0- 52 1-38855-4 (pbk.) I. Compos it e mat erial s. I. C1y ne, T. W. 11 . Title. Ill. Series. TA4 18.9.C6H85 1996 620.1 ' 18 d e20 96- 5701 C IP
From the preface to First Edition Prelace to Second Edition
1.1 1.2
1.3 2 2. 1
ISBN 0 52 1 38 190 8 hardback ISBN 0 52 1 38855 4 paperback
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General introduction Types of composite material Design of composite materals The concept of load transfer Refe rences and furth er reading Fibres and matrices Reinforcements 2 .1 .1 Carbon fibre s 2.1.2 Glass fibres 2.1.3 Organic fibres 2. 1.4 Silicon carbide 2. 1.5 Alumina and aluminosilicates The strength of reinforcements 2.2.1 Thermal stability Comp ressive strength 2.2 .2 Fibre fracture and flexibility 2.2.3 A sta tistical treatment of fibre strength 2.2.4 Matrices 2.3. 1 Polymer matrices 2.3.2 Metal matrices 2.3.3 Ceramic matrices Refere nces and further reading Fibre architecture (;cm; r ;11 c Oll sider;! I ion s
XIII
xiv 1 I
5 6
8
9 9 9 14 16 17 21 22 22 23 24
27 30
"130 34 35 36
39 39
Contents
VIII
3.1.1 3.1.2 3.1.3 3.2
Voids Fibre orientation during processing References and further reading
39 40 42 43 43 46 48 49 49 53 55 59 59
Long
3.2.1 3.2.2 3.2.3 3.3
Short
3.3.1 3.3.2 3.4 3.5 4
Volum e fraction and weight fraction Fibre packing arrangements Clustering of fibres and particles fibres Laminates Woven , braided and knitted fibre arrays Characterisation of fibre orientations in a plane fibres Fibre orientation distributions in three dimensions Fibre length distributions
Contents
6.2
7 7.1
Elastic deformation of long-fibre composites
60
4.1 4.2 4.3 4.4
Axial stiffness Transverse stiffness Shear stiffness Poisson contraction effects References and further reading
60 62 69 71 77
7.2
5 5.1
Elastic deformation of laminates
78
Elastic deformation of anisotropic materials 5. 1.1 Hooke's law 5.1.2 Effects of symmetry Off-axis elastic constants of laminae 5.2.1 Ca lculation procedure 5.2.2 Engin eering constants Elastic deformation of laminates 5.3.1 Loading of a stack of plies 5.3.2 Predicted behaviour Stresses and distortions 5.4.1 Balanced laminates 5.4.2 Stresses in individual plies of a laminate 5.4.3 Coupling stresses and symmetric laminates References and further reading
78 78 80 83 83 87 93 93 95
7.3
97 98 101 104
Stresses and strains in short-fibre composites
105
The shear la g model 6.1.1 Stress and strain distributions 6.1. 2 The stress tran sfe r length
105 107 109
5.2
5.3
5.4
6
6.1
H
X. I
97
8.2
x. \
IX
6.1.3 6.1.4 6.1.5
Transfer of normal stress across fibre ends Prediction of stiffness Onset of inelastic behaviour The Eshelby method 6.2.1 A misfitting ellipsoid 6.2.2 The equivalent homogeneous ellipsoid 6.2.3 The background stress 6.2.4 Composite stiffness References a nd further reading
114 115 11 8 121 123 123 126 127 131
The interface region
133
Bonding mechanisms Adsorption and wetting 7.1.1 7.1.2 Interdiffusion and chemical reaction Electrosta tic attraction 7.1.3 Mechanical keying 7. 1.4 7.1.5 Residual stresses Experimental measurement of bond strength Single-fibre pull-out test 7.2.1 7.2.2 Single-fibre push-out and push-down tests 7.2 .3 Other tests Control of bond strength Coup lin g agents and environmental effects 7.3.1 Toughness-reducing coatings 7.3.2 Interfacial chemical reaction and diffusion barrier 7.3.3 coat ings The interphase region 7.3.4 References and further reading
133 133 135 137 137 138 138 140 143 146 147 147 151
Strength of composites
158
Failure modes of long-fibre composites X.I.I Axial tensile failure Transverse tensile failure X.1.2 x.u Shear failure X.I.4 Failure in compression Failure or laminae under off-axis loads X.2.1 Ma ximum stress criterion 8.2 .2 Other railure criteria 8.2. 3 Experimental data ror single laminae St n: ngt h or la mi na tes
158 159 171 177 178 184 185 186 188 191
152 153 155
x
Contents
8.3.1 8.3.2 8.3.3
8.4
9
9.1
9.2
9.3
10
10.1
10.2
10.3
Contents
Tensile cracking lnterl aminar stresses Edge effects Failure of tubes under internal pressure 8.4.1 Pure hoop loading 8.4.2 Combined hoop and axial loading 8.4.3 Netting ana lysis References and further reading
192 194 195 197 199 201 203 205
Toughness of composites Fracture mechanics 9.1.1 Basic concepts 9.1.2 Interfacial fracture and crack deflection Contributions to work of fracture 9.2. 1 Matrix deformation 9.2.2 Fibre fracture 9.2.3 Interfacial debonding 9.2.4 Frictional sliding and fibre pull-out 9.2.5 Effects of microstructure Sub-critical crack growth 9.3.1 Fatigue 9.3.2 Stress corrosion cracking References and further reading
208 208 208 213 217 217 218 219 220 223 226 227 233 234
Thermal behaviour of composites Thermal expansion and thermal stresses 10.1.1 Thermal stresses and stra ins 10.1.2 Thermal expansivities 10.1.3 Thermal cycling of unidirectional composites 10.1.4 Thermal cycling of lamin ates Creep 10.2.1 Basics of matrix and fibre behaviour 10.2.2 Axial creep of long-fibre composites 10.2.3 Transverse creep and discontinuously reinforced com posi tes Thermal cond uction 10.3.1 Heat transfer mechanisms 10.3.2 Conductivity of composites 10.3 .3 I nterfacial thermal resi stance Rckrcnccs and further readin g
237 237 237 240 244 247 251 251 253 255 259 259 260 264 269
11 I 1.1
11.2
11 .3
12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.X 12.9
Xl
Fabrication Polymer composites I I . I. I Liquid resin impregnation routes 11.1.2 Pressurised consolidation of resin pre-pregs 11 .1.3 Consolidation of resin moulding compounds 11.1.4 Injection moulding of thermoplastics 11.1.5 Hot press moulding of thermoplastics Metal composites 11.2. 1 Squeeze infiltration 11 .2.2 Stir casting 11.2.3 Spray deposition 11 .2.4 Powder blending and consolidation 11.2.5 Diffusion bonding of foils 11.2.6 Physical vapour deposition (PVD) Ceramic composites 11.3.1 Powder-based routes 11 .3 .2 Reactive processing 11.3.3 Layered ceramic composites 11.3.4 Carbon/carbon composites References and further reading
271 271 272 274 276 278 279 280 281 282 283 285 285 286 286 288 290 291 291 293
Applications Minesweeper hull Sheet processing rolls Helicopter rotor blade Golf driving club Racing bicycle Diesel engine piston Microelectronics housi ng Gas turbine combustor can Aircraft brakes References and further reading
295 295 297 299 301 303 303 305 307 308 309
.' I fi / 1(' I/(I ix Nomenclature . llItl/ll/" int/e.Y .')lIhi('("/ il/t/ex
311 315 320
Preface
From the preface to First Edition !\ book on composite materials which is fully comprehensive would embrace large sections of materials science, metallurgy, polymer technology , fracture mechanics, applied mechanics, anisotrop ic elasticity theory, process engineering and materials engineering. It would have to cover almos t all classes of structural materials from naturally occurring solids sue h as bone and wood to a wide range of new sophisticated engineering ma te rial s including metals, ceramics and polymers. Some a ttempts have bee n made to provide such an over-view of the subject and there is no doub t that the interaction between different disciplines and different ;Ipp roaches offers a fruitful means of improving our understanding of compos ite ma te rials and deve loping new composite systems. T hi s book takes a rather narrower view of the subject since its ma in o biective is to provide for students and researchers , scienti sts and engilIeers alike, a physical understa nding of the properties of composite materials as a ba sis for the improvement of the properties, manufacturing processes and design of products made from these materials. This undersla lldin g ha s evo lved from many disciplines and , with certain li mitations, is com mo n to a ll composite materials. Although the emphasis in the book is o n th e properties of the composite materials as a whole, a knowledge is rL'q uired o r the pro pe rties of the individual components: the fibre , the IlIalrix and the inte rface between the fibre and the matrix. The esse nce of co mposite materials technology is th e ability to put slroll g slill fibres in th e ri ght place, in the right orientation with the I ig hl vo lum e rra c ti on . Implic it in this approach is the concept that in 11I ;lk ill g Ih e co mp os it e materia l o ne is a lso makin g the final product. J'll is IllL'; III S Iklt there mu st be ve ry cl ose co ll aboration between those
XIV
Preface
who design composite materials at the microscale and those who have to design and manufacture the final engineering component. Composite materi a ls can be studied at a number of different level s each of which requires a different kind of expertise. The method of approach depends on the objectives of the investigation . Thus, the development of a composite material to resist a corrosive environment, while maintaining its physica l and mechanical properties, is primarily a n exercise in se lecting fibres , resin s a nd interfaces which resist this environment a nd is within the expertise of chemi sts, physicists and materia ls scienti sts. In contrast, the engineer who has to des ign a rigid structure, such as an aerodyna mic control surface on an aircraft or a press ure pipeline, is more concerned with the macrosco pic elastic properties of the ma terial. He uses a nisotropic elasticity th eo ry a nd finite element analysis to design an optimum weight or o ptimum cost structure with the desired performance characteristics. The di sciplines in these two examples barely overlap and yet it is important for the physical scienti st to understand the nature o f the design problem a nd for the engineer to a ppreciate the subtleties of the ma teri a l he uses in design. This book goes so me way towards building th e bridge between these widely different ap proaches and should be of value to a ll scient ists and engineers concerned with eompos ite materials. Naturally, each gro up will look to other texts for an in-d epth treatment o f specific aspects of the subject.
Preface to Second Edition In the 15 years sinee the first edition was published , the subject of composite materials has become broader and of greater technological importance. In particular, composites based on metallic a nd ceramic matrices have received widespread attention, while the development of improved polymer-based systems has co ntinu ed. There have a lso been significant advances in the understand ing of how composite materials behave . F urt he rm ore, the wider range of composite types has led to greater interest in certain properties, such as those at elevated temperature. We therefore decided to produce a major revision of the book , covering a wider range of topics a nd presenting appreciably deeper treatment s in many areas. Howeve r, because the first edition ha s co ntinued to prove useful and relevant, we have retained much of its philosophy and objectives and some o r it s structure. Throughout the book. emphasis is given to the principles govcrn in g the Ix:haviour or composite m;lterials . While these principles ;Irc applic;lhk to ;i11 types 01" cO lllposilL' lIlalL'ri;i1 . eX;llllples arc
Preface
xv
given illustrating how the detai led characteristics of polymeric- , metallica nd cera mic-based systems are likely to differ. The first chapter gives a brief overview of the na ture and usage of composite materials. This is followed by two chapters covering, firstly, the types of reinforcement a nd matrix mate rial s a nd , seco ndly, geometrica l aspects of how these two constituents fit together. The next three chapters are co ncerned with the elastic deformation of composites. Cha pter 4 deals with ma terial co ntaining unidirection a ll y aligned continuous fibres , loaded parallel or transverse to the fibre axis. This is extended in C hapter 5 to la min a tes made up of bonded stacks of thin shee ts , each having the fibres a li gned in a particular direction. The following chapter covers di sco ntinuously reinforced composites, containing sho rt fibres or particles. Equations are presented in these cha pters which a llow prediction o f elastic properties, but the emphasis is on picto ria l representatio n of the concepts invol ved a nd it is not necessary to foll ow the mathematical details in o rder to understand a nd use the results. Chapter 7 is concerned with the interface between matri x a nd reinforce ment. This covers the nature of the interfacial bond in various systems a nd the measurement and control of bond strength. The interface often has a n important influence on properties related to inelastic deformation a nd failure of composites. Trea tment of this aspect is divided between the next two chapters, the first dealing with stress levels at which various defo rmation and damage processes occur and the second concerning energy absorption and quantification of the toughness of composite materia ls. The thermal behaviour of composites is described in Chapter 10, which includes thermal stresses, creep and thermal conduction. The last two chapters are largely independent of the rest of the book. The first of these gives a brief survey of the manufacturing methods used to produce components from various types of composite. T hi s aspect is particularly important, since the material and the co mpone nt are common ly made in the same operation, at least for lon g-fibre com posi tes. Th is ca ll s for close integration between the processes of material specification and component design. This requirement is a lso highli ghted in the fina l chapter, coverin g app licat ions. The inten ti o n here is to identify so me of the advantages a nd pro blems of using composites, by means of a series of illu stra tive case hi sto ri es, rather than to give a systematic survey. To aid in the use of the book , a nomenclat ure li sti ng is given as a n appendi x. Thc contents have large ly evo lved fro m undergradu ate courses we have given and. as with the first ed iti o n, the book is intended as a teaching aid at thi s level. It should also provc uscful for scientists and cngineers wo rk -
XVI
Preface
ing with composite materials and for those engaged in research in this area. At the end of each chapter, a list of references is given, many of them relevant to specific points made in the text. These references should serve as useful sources of further detailed information at the research level. They need not , in general , be consulted by undergraduates studying the subject for the first time. A further point concerning additional sources relates to computer-assisted learning. Software packages are now available which allow both interactive exploration of elementary topics and calculation of composite properties not easily obtained from analytical equations. In many cases, these can serve as both teaching and research tools. One such package, entitled 'Mechanics of Composite Materials' (Clyne & Tanovic, published by the Institute of Materials in 1995 and by Chapman and Hall, as part of the MATTER software series, in 1996), is largely based on material in this book. We would like to acknowledge the support of many colleagues in Cambridge and Liverpool Universities. Collaboration with and suggestions from W. J. Clegg, A. Kelly and P. J. Withers have been particularly useful. Stimulation and support from past and present students in our research groups, particularly in the Materials Science Department at Cambridge, have also been very helpful. In addition, we are indebted to all those who have provided us with micrographs and unpublished information. These are acknowledged in the text and figure captions. We would also like to acknowl edge the financial and moral support we have received for our own research work on composites, in particular from the Engineering and Physical Sciences Research Council , Alcan International, British Petroleum , Ford Motor Company, Imperial Chemical Industries, National Physical Laboratory, Pechiney, ORA Farnborough , Pilkington, Rolls Royce" T & N, and Scott- Bader. We have had extensive scientific contact with various people from these and other organisations, which has been of considerable benefit to us. We are also grateful to Brian Watts , our copy editor, for his painstaking work and many useful suggestions, and to the editorial staff at CUP for their cooperation and efficiency in producing this book. Finally, we would like to thank our wives, Pauline and Gail, for their invaluable support during the preparation of this book. O. Hull T. W. Clyne 11)%
1 General introduction
Composites make up a very broad and important class of engineering materials. World annual production is over 10 million tonnes and the market has in recent years been growing at 5- 10% per annum. Composites are used in a wide variety 0/ applications. Furthermore, there is considerable scopefor tailoring their structure to suit the service conditions. This concept is lI'e!! illustrated by biological materials such as lI'ood, bone, teeth and hide; these are all composites with complex internal structures designed to give mechanical properties well suited to the pel./ormance requirements. Adaptation of manufactured composite structures for different engineering purposes requires input Ji-om several branches o/science. In this introductory chapter, an overviell' is given of the types of composite that have been developed.
1.1 Types of composite material Many materials are effectively composites. This is particularly true of natural biological materials, which are often made up of at least two constituents. In many cases, a strong and stiff component is present, often in elongated form, embedded in a softer constituent forming the matrix. For example, wood is made up of fibrous chains of cellulose molecules in a matrix of lignin , while bone and teeth are both essentially composed of hard inorganic crystals (hydroxyapatite or osteones) in a matrix of a tough organic constituent called collagen (Currey 1983). Commonly, such composite materials show marked anisotropy - that is to say , their properties vary significantly when measured in different directions. This usually arises because the harder constituent is in fibrous form , with thc fibre axes preferentially aligned in particular directions. In addition , onc or more of the constituents may exhibit inherent anisotropy
2
General introduction
as a result of their crystal structure. In natural materials, such anisotropy of mechanical properties is often exploited within the structure. For example, wood is much stronger in the direction of the fibre tracheids, which are usually aligned parallel to the axis of the trunk or branch, than it is in the transverse directions . High strength is required in the axial direction, since a branch becomes loaded like a cantilevered beam by its own weight and the trunk is stressed in a similar way by the action of the wind. Such beam bending causes high stresses along its length , but not through the thickness . In making artificial composite materials, this potential for controlled anisotropy offers considerable scope for integration between the processes of material specification and component design. This is an important point about use of composites , since it represents a departure from conventional engineering practice. An engineer designing a component commonly takes material properties to be isotropic. This is often inaccurate even for conventional materials; for example, metal sheet usually has different properties in the plane of the sheet from those in the throughthickness direction , as a result of crystallographic texture (preferred orientation) produced during rolling - although such variations are in many cases relatively small. In a composite material, on the other hand , large anisotropies in stiffness and strength are possible and must be taken into account during design. Not only must variations in strength with direction be considered , but the effect of any anisotropy in stiffness on the stresses set up in the component under a given external load should al so be taken into account. The material should be produced bearing in mind the way it will be loaded when it is made into a component. Thus, the processes of material production and component manufacture must be integrated into a single operation. This, of course, is exactly what happens when biological materials are produced. There are several different types of composite. Examples of typical microstructures for the three main classes, grouped according to the nature of the matrix , are shown in Fig. 1. 1. Most composites in industrial use are based on polymeric matrices ; thermosets and thermoplastics . These are usually reinforced with aligned ceramic fibres , such as glass or carbon. They commonly exhibit marked anisotropy, since the matrix is much weaker and less stiff than the fibres. More recently, there has been considerable interest in metal matrix composites (MMCs) , such as a luminium reinforced with ceramic particles or short fibres , and titanium containing long, large-diameter fibres. The property enhancements being so ug ht by th e introduction of reinforcement are often less pronounced
I .I Types of composite material
3
II II
hII
II II I
Carbon fibre reinforced epoxy crossply laminate 1:ig. 1.1
1han
Silicon carbide particulate reinforced aluminium
Silicon carbide monofilament reinforced glass ceramic
Schematic depiction of representative polymer, metal and ceramic matrix composites .
for polymers, with improvements in high-temperature performance or tribologica l properties often of interest. While various industrial applic; ltio ns have been developed or are being explored for MMCs, their (·o ll1 mercial usage is still quite limited when compared to that of polymer l"l llllposites (PMCs). Finally, composites based on ceramic materials ( ·MCs) are also being studied. The objective here is usually to impart lo ug hness to the matrix by the introduction of other constituents, since I he st iffness and strength are unlikely to be much affected . Such materials .Ire st ill , for the most part, in the early stages of development, partly because they are rather difficult to manufacture. I n co nsidering the formulation of a composite material for a particular I vpe o f a pplication , it is important to consider the properties exhibited by lite po tential con stituents. The properties of particular interest are the , I tlTncss (Young' s modulus) , strength and toughness. Density is of great "g nilica nce in ma ny situations, since the mass of the component may be II I c ritica l importance. Thermal properties, such as expansivity and condllc tiv it y, mu st al so be ta ken into account. In particular, because comIl()s ile ma teri a ls a re s ubject to temperature changes (during manufacture .I IHI / or in servi ce), a mi sma tch between the thermal expansivities of the (() lI slit uc nt s lead s to inte rna l residua l stresses. These can have a strong (" 11 i.:cl o n thc mcc ha ni cal behavio ur. Some representa tive property data . lI l · shown in T ab le 1. 1 fo r va ri o us types o f matrix a nd reinforcement, as \Vd l ;IS ro r so me ty pi cal cnginee rin g ma te ri a ls a nd a few representative \·() llI posilcs. In spec li o n o r th esc data shows that so me attracti ve pro perty \ Il lllh illa li o ns (ril l" eX ;II11p lc. hi g h slilTness/sll"e ngl h a nd low d c nsit y) ca n
1.2 Design of composite materials
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the matrix may be modified, so that it has different properties from the bulk matrix. It is also worth noting that the matrix is often highly constrained between closely spaced fibres and that a highly uniform distribution of fibres is required if physical contact between them is to be avoided (see below).
Onc of the main consequences of non-regular packing is the difficulty "I :Ic hievi ng volume fractions greater than 0.7 and this value must be 1l'1':lrded as the practical limit for commercial materials. It follows that 1.IIIIi nae ca nnot be regarded as being homogeneous from a microstruct 111: 11 point of view, although for the prediction of laminate properties it is ,1\, lImed that each lamina has a set of characteristic properties. A nothe r point to note about fibre spaeings concerns ease of composite 1ll,llIufaeture. Most composite manufacturing operations involve penetraII()II of liquid matrix into an array of fibres (see Chapter 11). When fibres .Ill' ve ry closely spaced, initial penetration of liquid involves the genera1111 11 of sha rp meniscus curvature, which requires the application of a high 11ll'SSlI re. Furthermore, subsequent flow through the fibre array at an ,1ll'Cptable rate needs a high pressure gradient, particularly if the melt h,IS a high viscosity (as with thermoplastic polymers). The pressures 1\'lJllired during processing can therefore become prohibitively high \I hen fIbres are closely spaced, particularly if the fibres are fine.
42
3.1.3 Clustering offibres ami particles Experimental studies of the distribution of fibres in unidirectional laminae show that these ideal distributions do not occur in practice, except in small localised regions. An example is given in Fig. 3.3 of a section cut normal to the fibre direction in a lamina with a high fibre content. In some regions the packing closely approximates to an hexagonal array, but there are also matrix-rich regions with irregular packing. Some points of fibre contact are apparent. In laminae with lower fibre contents the packing is often very irregular, with fibre bunching and large matrix-rich regions. Misalignment of the fibres is also much more likely.
43
3.2 Long fibres
3.2.1 Laminates Ill gh-perfor ma nce polymer components usually consist of layers or /amislacked in a pre-determined arrangement. For the prediction of elasIll ' properties of the component as a whole, each lamina may be regarded ,1\ homogeneo us in the sense that the fibre arrangement and volume 11,1e( ion are uniform throughout. The fibres in the laminae may be cont IIlIlOllS or in short len gths and can be a ligned in one or more directions II I r:lI1do mly distributed in two or three dimensions. Two simp le arrangeIlll'lIls of laminae are illustrated in Fig. 3.4. A unidirectiona l lamina is "l lell ca lled a ply and a stack of laminae is called a laminate. The flat 1.IIIIinate in Fig. 3.4(a) consists of identical unidirectional laminae or plies sLicked with adjacent plies at 90 to each other. This construction is 1\ J11c:II, though considerab ly simplified , of the material used for high,t 11 rlless pa nel s in a ircraft. The curved laminate in Fig. 3.4(b) is part of thl' lVall of a cylindrical vessel. This laminate configuration is commonly Illlllld in applicalions such as pressure pipes a nd torsion tubes. In this n: llllplc , I he inner lamina is a layer of chopped-strand mat and the outer 1IIIIdi rec lional laminae arc arranged with the fibres oriented at ± 55 0 to I h,' :1,\ is or I he cyli nder. Some or I he faclors a rfecling t he choice of stackIll)' 'l'llllCllce arc descrihed in Chapler 5. 1/1/('
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Optical micrograph 01" :1 sectioll cut at ri ght all gles to lihres ill ulli directiollal 1:111I11l:IL' nl' '1 :lss lihre/pol yes tcr resill .
3.2 Long fibres
Fibre architecture
44
45
(h)
90' L....,."'--:....-T""7r7"7'"::l"""-'rT-o/ O' L....,."'--:....-T""7r7"7'"::l"""-'rT-o/
O'
90· ~~~~~ O· L-__________- Y (a)
Fig. 3.4 (a) Flat laminate with unidirectional laminae at 90° to each other. (b) Cylindrica l laminate with one layer of chopped-strand mat and two unidirectional laminae.
A simple convent ion is often used when describing stacking sequences. This is illustrated by the simple cross-ply laminate shown in Fig. 3.5(a). The stacking sequence, in relation to the x-direction , is written as 0° /90°/ 0°/ 0° /90°/ 0°, which can be simplified to [0/90/ 0 2 /90/ 0]' where the subscript 2 indicates that there are two plies in the 0° orientation. Since, in this case, the stacking is symmetrica l about the mid-plane, the notation is further simplified to [0/90/0]s the subscript s denoting that the stacking sequence is repeated symmetrically. Similarly, the angle-ply laminate shown in Fig. 3.5(b) is denoted by [0/ + 60/ - 60 2 / +60/0], which is abbreviated to [0/+ 60/ - 60]s or [0/ ± 60]s' When the plies do not have the same thickness, or are made of different materials, it is necessary to specify both the material and the thickness of each layer, as well as the orientation of the fibres. Thus, the notation [90/ 0/2Rc)/(2Rc/0/90)/ Rco 7s] refers to a laminate with fibres in the 0" and 90' directions, combined with layers of random mat reinforcement (Rc) which have two different thicknesses, Rc and 0.75 Rc. Similarly, the notation Kevlar TM 49/T300 carbon/ Kevlar TM 49 , [0.,/ ± 45 /90], refers to a symmetrical laminate with three plies of Kevlar™ 49 fibres, one ply of I 45 and o nc ply of 45 rwo carhon fihres and olle pl y of 9() ' Kev!;lr'l M 49 fihres. III ;ldditi o ll to specifyin g the pl y OriClll;lIioll ill
O'
_60'
L....,.--...---...-........,...........,...........,...~~
60' '---,..-,--~..........,rT"7""T"T7..,..
O· L-__________
~
(h)
' I) '
l. ~
Arrangement of plies in (a) a cro ss pl y laminate and (b) an angle-pl y laminat e sa ndwi ched betwee n 0 plies,
3.2 Long fibres
Fihrl' arclli/I'c/ure
47
relation to a rcicrence direction (x-direction in Fig. 3.5), it is also necessa ry, for non-symmetrical lamina tes, to relate the stacking sequence to th e form of th e component. Thus, for the simple example in Fig. 3.4, the random fibres are on the inside of the pipe, so tha t the stacking seq uence is: outside[+ 55 / - 55 / RcLnsidC"
3.2.2 Wovell, braided alld kllittedfibre arrays Continuous fibres can be produced in a variety of geometrical forms, in addition to stacks of unidirectional plies , using technology originally developed for textile processes: weaving, braiding and Imilling. The arrangement of fibres in a woven cloth is illustrated in Fig. 3.6. In woven cloth , the angle between the warp and weft directions is 90°. The flexibility of cloth allows draping and shaping to occur, facilitating use in non-planar structures. The angle between the warp and weft directions will depend on the extent of drape. A complete characterisa tion of woven roving composites requires detail s of weave spacing, number of fibres in each roving, angle between warp and weft directions and the rati o o f the number of fibres in these directions. W oven structures lead to pockets o f matrix a t the cross-over points (see Fig. 3.6(b)) a nd the maximum fibre content for woven roving composites is less th a n for fully aligned ma te ri a ls. The fibre arrangements produced by two-dimensional braiding are similar to woven fabrics. Braiding is commonly used for flexible tubes , with the fibre tows interlacing orthogona ll y. Stretching such a tube by increasing the lengt h o r the diameter results in rotation of the fibre tows. More comp lex shapes can be generated, with the fibre tows meeting a t different angles. Braiding is now used to produce three-dimensional fibre a rchitectures. As with woven fabric reinforcement, matrix-rich regions are un avo id a ble, so the maximum fibre co ntent is less than in lam in ates made by stackin g unidirection a l plies. Knitting is a lso used to produce fabric preforms. The fibres are usua lly in the fo rm of a sta ple yarn to facilitate knitting. M any knitting co nfi gurations are possible. The ya rn is a rranged in a repeating se ries of intermeshed loops, so that the o ri entati o n of the fibres is cha nging co ntinuou sly in threc dimension s. The volume fraction of fibrcs is rclative ly low and large matrix pockets can no t be avo ided. Novel meth ods of laying a dditional stra ight fibres in knitted structures, to increasc th c properties in specific dircction s, are bein g developed . A common ly used rorm o r rihre distribution , particula rl y ror low-cost app li cat io ns. is choppl'd stralld m at. Bundl es or reblti ve ly lOll .' rihrl's ;Irc
I
I)'
(h)
1.C1 (a) SFM micrograph o f a woven rovin g befo re infiltration w ith resin. 1'1I0\Olllicl"llgraph a poli shed secl ion throu gh a woven rov tll g la!l1t1lale
or
pa ra Ik l \ (l o m: scl
or li hn:s.
4X
Fihre architecture
assembled together with random in-plane orientations, as shown in Fig. 3.7. The material is easy to handle as a preform and the resultant com posite material has isotropic in-pl ane properties. However, the fibre volume fraction is limited to relatively low va lues.
49
3 .3 Short fibres (a )
3.2.3 Characterisation o.ffibre orientations ill a plane The orientation distributions of the fibres in assemblies such as those in Figs. 3.6 and 3.7 are simple to describe. However, there may be cases where the distribution is more complex. These can be represented using normalised histograms of the type shown in Fig. 3.8 . The p lots are obtained by recording the orientation of individual fibres , with respect to some reference direction. This can be done automatically by image analysis of a photograph, such as a simple optical or electron micrograph , or an X-ray radiograph. The directions are then divided into a convenient number of ' bins' . For the plots shown, there are 18 of these, at intervals of 10°. The span needed is only 180° since no distinction is made between the two directions along the axis of a fibre. The radius of each bin in the plot is proportional to the fraction of fibres with orientations in
F ibre fr ac tion (%)
8
x
6 8
I 11' I.X No rm a lised hi stog ram s o f th e fibre o ri ent a ti o n di stributi o ns in two dlllll'lh iona l ar rays o f fibres . (a) Co mpl etely ra nd o m (iso tro pic); a nd (b) a n • \ l'l'lI nl enla l d istri b uti o n (D a rlin gto n et al. 1976) fro m a n injecti o n m o ulded glass fibre/ po lypro pylene co mposite.
I Ill' ra nge co nce rned . The radii sum to 100 % . For the simple isotropic dl , llihutio n show n in Fi g. 3.8(a) , the radiu s of the circle is 100/1 8 ~ \ .., " o. Fo r the d istributi o n sho wn in Fig. 3.8(b), the fibres are aligned 11Il'ilTcntia ll y nea r a n a xis in the pl a ne.
3.3 S hort fibres 3.3,1 Fibre orielltatioll distributiolls ill three dimellsiolls Fi g.3.7
SE M mi c ro g ra ph o f c ho pped -s lrand ( I : mlll J); lrlill !'I OII
('I
111 ;11 he fo re inli llrali o n wilh resin . Ill. 1'J7(,) .
( )ll l'nta tion dis t rih uti o ns ,"T mo re diffi c ult to meas ure a nd cha racteri se " lIl' lI til l' fih res do li n t li e par;illel to a sin gle pl'l ne. whic h is freque ntl y
51
Fibre architecture
3.3 Short.flbres
the case with relatively short fibres. The simplest met hod (Vincent and Agassant 1986) is based o n the assumption that the fi bres arc stra ight cylinders o f circu lar section. A planar, undistorted secti o n or the composite is examined in which each fibre is clearly vis ible as an ellipse, as illustrated in Fig. 3.9. The block ABCDEFGH represen ts a thin para llel-sided slice of material , which has been cut at a pre-determined position a nd angle with respect to the reference axes of th e component. The orientation of the fibre is defi ned by the two angles (V and (1. The angle ex can be id entified on the section (e.g. ABCD) as that between the reference direction (marked as y in thi s case) a nd the directi o n of the major ax is of the ellipse - see F ig. 3.9(b). The angle f3 can be mea sured in one of two ways. The simplest method involves measuring the aspect ratio (major to minor ax is) of the section , from wh ich f3 is rea dil y obtained
However, this ratio may be difficult to measure accurately, particularly if the fibre diameter is small .lf the section is transparent (optically or by Xray radiography), it is a lso possible to measure the projected length, Lp , of the fibre. The angle f3 is then given by
50
(3.7)
IJ
(a)
c
A ~------+---4-----~~rt------~D
(;
10· Lc..::..----~-----------==z~-------Ir.1
x
(b)
Fi g.3.9 De te rmin at ion or libn: o ri c ntati o n ill ~I Ihin scc li o n. O ri e nl a tio n d elincd (a) hy a ng les (l and 11; and (h) hy sli ;lpc alld oriell la li o n or libr.: c ro ss SLoc ll(ll1.
f3 = tan - I (~J
(3.8)
where t is the thickness of the section. Neither of these methods fully characterises the orientation of the fibre , beca use there are two possible positions for a fibre having angles ex and f3. T he same aspect ratio and projected length would be obtained from a fibre lying at an angle (7f - f3). It may be possible when examining transpa rent sections to establish which end of the fibre emerges at the top surface, perhaps by comparing optical and X-ray photographs, but this in hibits the a utomatic acquisition of data by image ana lysis. There are other method s of characterising fibre orientation distributio ns, although their usefulness is rather limited. For example, if an image in which the fibres are opaque and the ma trix tran sparent is derived from a conventional microgra ph , then a Fourier transform ca n be obtained by the diffraction of light passing through this image (Ovla nd and Kristian sen 1988). If this is repeated for a series of sections , then a full characterisation of the di stribution can be obtained . Another possible technique (Juul Jensen et al. 1988), ap plicable only to singlecrysta l fibres with a known crystallographic direction along the fibre axis (s uch as SiC whiskers) , invo lves study of diffracti on pa tterns from the co mponent. In many cases, X-rays are not su ita ble in view of their limited penetration depth (particul a rly in MM Cs) and neutron diffractio n is preferable. Orientation distributions in three dimensions are commonly represe nted on a stereographic projection (stereogram). Thus , texture information for polycrysta ls is presented as pole .flgures, which depict the relative rreq uencies of the o ri enta tion of specified crysta llographic directions, rela tive to the externa l frame of reference (Bunge 1982, Bunge 1989). Represe ntation of fibre distributions is si mpler than for the texture of J1olyc rys ta ls, since on ly the orientation of the fibre axis is req uired . The orient a tion o f each fibre axis is represented as a point on the stereogram. On a stereographic projection , a random (isotropic) threedimensiona l distribution of orientations does not plot as a uniform densit y or points; the points are clu stered nea r the centre and a re spa rse low:ml s the edgcs. Th is is illustratcd in Fig. 3. 10, which shows (a) how
3.3 Short fibres
Fibre architecture
52
3.3.2 Fibre length distributions
Specimen
~
./'" /'" Dirc-
20 10
(a) 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
69
Idea of the errors likely to be introduced in real cases by use of simple ana lytical expressions, as compared with the Eshelby method , which sho uld be more reliable than those from the simpler models. It can be see n that the equal stress assumption gives a significant underestimate ror both PMCs and MMCs, which have large and small modulus mismatch res pectively. The Halpin- Tsai equation, on the other hand , is quite n:lia ble. I n practice, the behaviour may be influenced by other factors which are difficult to incorporate into simple models. These include the dTects of a degree of fibre misalignment, elastic anisotropy of the rib re (or of the matrix - e.g. for a textured polycrystalline metal) or t he ea rly onset of a non-elastic response. Nevertheless, it should be no ted that, even in the absence of any such complications, use of the eq ual stress model introduces significant errors: this should be borne in min d , for example, if it is being used in laminate elasticity analysis (see ('h apter 5).
Fibre volume fraction,! 400
4.3 Shear stiffness
350 ~ 0...
8
..... Equal stress ......... Halpin-Tsai
300
kl ","
--Eshelby
250
.2 ::l -0 0
E
'"
'''0
c:
200 150
::l 0
>-
lOO 50
(b)
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Fibre volume fraction,! Fig. 4.6 Predicted dependence on fibre volume fra ction of the transverse Young's Illoduli of conlinuous-iibre composiles, according to the equal slress, Eqn (4.6). Ilalpin Tsai, Eqn (4.7) and hhelby model s for (a) glass fibres in epoxy :lnd (h) silico n ca rhide libres in tilaniulll.
rhe shear moduli of composites can be predicted in a similar way to the ax ial and transverse stiffnesses, using the slab model. This is done by eva luating the net shear strain induced when a shear stress is applied to I he co mposite, in terms of the individual displacement contributions from I he two constituents. It is important to understand the nomenclature co nvention which is used. A shear stress designated Tij (i i- j) refers to :1 stress acting in the i-direction on the plane with a normal in the jdirec tion. Similarly, a shear strain lij is a rotation towards the i-direction or the j-axis. The shear modulus Gij is the ratio of Tij to lij. As the l·o ll1posite body is not rotating, the condition Tij = Tji must hold. In addit ion , Gij = G ji so that lij = Iji . Since the 2- and 3-directions are eq uivalent in the aligned fibre composite, it follows that there are two shea r moduli, because G l 2 = G 2l = Gl3 = G 3 l i- G23 = G32 · There are a lso two shear moduli for the slab model (Fig. 4.7), but these arc unlikely to co rrespond closely with the values for the fibre composite. rhe stresscs Tl2 and T21 are assumed to operate equally within both of the l"IlIlstituents. The derivation is simi lar to the equal stress treatment IeadIll)!. 10 Fqn (4.6) for transverse st iffness
4.4 Poisson contraction effects
Elastic deformation of long~fi:bre composites
70
SLAB MODEL
ACTUAL
wh ich is similar to Eqn (4.3). It may be noted that neither the equal stress condition nor the equal strain condition are close to the ,it uatio n during shearing of the fibre composite, in which the strain p~ lrtitio ns unevenly within the matrix. Therefore neither of the above eq uatio ns is expected to be very reliable, particularly the equal strain ex rreSSlO n. I t is not obvious just how poor the approximation represented by Eqn H.8) is likely to be, nor even which of the two actual shear moduli it will a prroach more closely. In fact more rigorous methods predict that the va lues of C I2 and C n are rather close to each other, with C I 2 slightly 1~lrge r in magnitude. Equation (4.8) gives a significant underestimate rela tive to both of them, while Eqn (4.9) is a gross overestimate. In view of this , the semi-empirica l expressions of Halpin and Tsai (1967), me ntioned in the last section, are frequently employed. In this case, the ;I prropriate equation is
(a)
G, 2 = G ' 3 = G21 = G 31
Ir~(~~i~ ======-=::7/
G , 2 = G 32 = G 21 = G23
Mixed
L./
Equal stress
Equal strain
Mixed
C
Fig. 4.7 Schematic illustration of how the shear moduli are defined for a rea l fibre composite and for the slab mod el representation , indicating how stress and strain partition between the two cons titu ents in each case.
where 'Y m and 'Y12111 are the individual shear strains in the two constituents. The total shear strain is found by summing the two contributions to the total shear displacement in the I-direction
+ Ulm ) . ( ') + (I -f) =,hm + I - I 'Y12m
(Ulr
=f
.C ..
.
- Cm(l 12 -
(b)
'Y12
_ 12 -
I.e . C I2
712 _
'Y12
7m
- f'Ym
[f
+ ( I -fhl2m
-f)]-I
= - +(I- - Cr
Cm
71
( I - fh2m] - 1 [L+ C 7m r
(4.8 )
The other shear modulus shown by the slab model, C I3 = C 31 in Fig. 4.7 , corresponds to an eq ual shear strain condition and is analogous to the axial tensile modulus case. It is readily shown that (..J.
(»
111
+ ~Tif)
( I - Tif)
(4.10)
which
;I nd the parameter ~ is again often taken to have a value of around lInity . This has been done for the curves in Fig. 4.8 , which shows co mparisons between the predictions of Eqn (4.10) and those of the eq ual stress (Eqn (4.8)) and Eshelby models for both polymer and Illeta l matrix composites. It can be seen that the Halpin- Tsai expression l'l:p resents a fairly good approximation to the axial shear modulus (C/d . A striking feature of both the transverse and the shear moduli ror polymer matrix composites (Figs. 4 .6(a) and 4.8(a)) is that they are c lose to the matrix values up to relatively high fibre volume fractions, ;iltilough in both cases the true modulus is not as low as the prediction (lr the eq ual stress model.
4.4 Poisson contraction effects The Poisson's ratio //ii describes the contraction in the .i-direction on :Ipply in g a stress in th e i-d irec tion and is defined by th e equation
11
I
72
Elastic deformation of long~fibre composites
4.4 Poisson contraction effects
73
20 18
c; 0...
8 ~
'" ::l ::l
"0
16
. . . . . C 12 Eq ual stress ........ ·C I 2 Halpin-Tsai
14
I ' , '
,
- - C I 2 Eshelby
,:
- . - . -C2l Eshelby
12
,f " ,'::
:' ,:
,
.:
10
,
I .
'
~i
E
....
..r::
C/l
b
d--
'
V 12
=V
13
V21
=V
31
V 23
=V
32
' '
"1
0
o:l [ S] as cp ---> O. The behaviour of the
I1 will be seen lamina , Idl ru ll y described by four independent ela stic con stants, since these six I 1"lllcnt s ca n all be expressed in terms of SI I , S1 2, S22 and S66' A similar 1'1 llL'cd urc can be used to derive the elements of [C], the tral/sformed '(lllilc.n tel/sor 1.
c\ = C II C4 + C22 S4 + (2C 12 + 4C66)c2S2 + (C II + C n - 4C66 )c2s2 = C II ,s.4 + C 22 C4 + (2C 12 + 4C66 )C 2S2
(' 12 = C 12 (C 4 + S4) ('22 --;
3
Finally, the ori ginal tran sfo rm matrix of Eqn (5.12) can be used to express these stresses ill term s o r those bein g ex ternally appli ed . to give the res ult
3
( 16 = (Cl I - C I2 - 2C66 )C S - (Cn - C I2 - 2C66)CT 3
( 5.20 )
3
( 26 = (Cl I - C I2 - 2C66)CS - (C n - C I2 - 2C66)C S ('66
Now, the strains rel a tive to the fibre direction can be expressed in terms of the stresses in those directions via the on-axis stress- strain relationship for the lamina , Eqn (5.9), giving
(5. 19)
= (4S 11
~
in which
(5.1 8)
5 11 = SII C4 + S22S4 + (2S 12 + S66)c 2S2 5 12 = Sd c4 + s4) + (SI I + Sn - S66)c 2S2 5 22 = SIIS4 + S22 c4 + (2S 12 + S66) c2s2 3 3 Sl6 = (2S 11 - 2S 12 - S66)C S - (2Sn - 2S 12 - S66) CS 3 3 S26 = (2S 11 - 2S 12 - S66)CS - (2S22 - 2S 12 - S66)C S
in which
[~~ ~~
~ I TT ' [SII T] [ ;: 1~ Is] [;;]
111 (' ele me nts of [S] are obtained by cOl/catel/atiol/ (the equivalent of lll1dt iplica tion) of the matrices [T' r l , [ S] and [ T] . The following I \ pn:ssio ns are obtained
(5. I 5)
[T'] =
87
5.2 Ofraxis elastic constants of laminae
=
(Cl I
+ Cn
- 2C I2 - 2C66)c2S2 + C66 (C 4 + S4)
5.2.2 EI/gil/eeril/g cOl/stal/ts I I1 hL'!' o r thcsc matrices fully defines the elastic response of the material. I I(l\\,c ve r. it is often more convenient to represent these cha racteristics in I, IIIl S o r th e co nventional engineering constants. These can be obtained 11, ' Ill I he sti ITncss or compliance tensors by inspection of the rela tionships I'"',c nt cd a s Eqn s (5.9) and (5.10). The relationships are simpler if the I Il ll1p li a ll ce te nso r is used. Thus
(5.21 )
88
Elastic deformation of laminates ( 5.22) 35
(5.23) V .H
= - E,SI2
( 5.24)
'"2
v\'.r
=
( 5.25)
S
These engineering constants can therefore be found once the compliance tensor has been evaluated. Some examples of the behaviour predicted by Eqns (5.19) for two different composites are illustrated in Figs. 5.4, 5.5 and 5.7. The dependence of the Young' s and shear moduli of the lamina on the value of cp is shown in Fig. 5.4(a) for a polymer matrix composite, using both the equal stress (Eqns (4.6) and (4.8)) and Halpin- Tsai (Eqns (4.7) and (4.10) with ~ = 1) expressions for the transverse Young's modulus (cp = 90°) of the composite. The equal stress assumption introduces quite significant errors over a wide range of loading angle, although the predictions do not differ in qualitative terms. The tensile stiffness (Young's modulus) remains close to the theoretical maximum if the stress axis is within a few degrees of the fibre axis, but if cp is more than about 5° then it decreases rapidly. The reduction is less pronounced for the metal matrix composite (Fig. 5.4(b)). These predictions have been confirmed by experiments. The shear stiffness is less sensitive than the Young's modulus to cp, but a pronounced peak is always exhibited at 45 °. This efficiency of stiff diagonal (45°) members in resisting shear forces is important in many engineering situations - see, for example, the discussions in GOI'don ( 1978). As mentioned earlier, an important feature of the off-axis loading of unidirectional laminae is the appearance of non-zero 'interaction' terms (5 16 and 5 26 ) , indicating that normal stresses produce shear strains and shear stresses produce normal strains. It is convenient to introduce two other engineering constants to characterise the strength of this interaction effect rl.,T.r = E"SI6
(5.26)
= E,.S26
( 5.27)
71.rrr
The parameter 'I )rr.r therefore represents the ra tio of the shear strain h \I')' induced by the application 01' a normal stress (rT\), to the normal strain (E J induced by the S;lIlle norlll;ti stress . It indicates the n;ltllrl' 01' the
0...
- - - - - Young's modulus, E, (Equal stress used for E2
)
- - Young's modulus, E, (Halpin-Tsai used for E2
)
- -0 - -
30
- E"SI2
89
5.2 Orf-axis elastic constants of laminae
Shear modulus, G
---.-- Shear modulus, G
xy xy
(Equal stress used for E, ) -
(Halpin-Tsai used forE,) -
25 20 15 IQ
5
o
~~~~~~~~~~~~~~~~~~
o
10
20
30
40
50
Loading angle, IP
60
70
80
90
n
(b) 250
'"2 200 0...
S '"::s
"3
- - Young's modulus, E,
150
---.-- Shear modulus, G x y
":::E o
50
00L~~~~~~~~~~~~~~~~~~ 80 ~~ 90 10 20 30 40 50 60 70
Loading angle, IP (') I:ig. 5.4 Variation with loading angle cp of the Young's modulus Er and shear lIlodulus G\I' for laminae of (a) epoxy/ 50% glass and (b) titanium/ 50% SiC 1\1011Olilamenl. The transverse Young's moduli were obtained by using the equal stress (Eqn (4.6» and Halpin Tsai (Eqn (4.7» models in (a) and the Halpin Tsai model only in (b).
~
91
5.2 OfFaxis elastic constants of laminae
Elastic deformation of laminates
90
0.5
~.
0
e c::
0
0
tl .... =k [
El"
E)"
1
( 5.32)
'"(n
'"( 12k
c:
.S: U OJ .... 0)
.5
The stresses in the ply are then obtained from these stra ins, using the (onaxis) stiffness matrix for the kth ply
0.5 J " . .1
0
,
,
'"
-0.5
O" lk [ 0"2k
,
,
IQ
20
30
40
50
Loading ang le,
60
__ ...
70
80
O" lk [ 0"2k
90
tP n
F ig,5. l0 Variation with load ing a ngle (p of the interaction ratio 1/"1",\ for a sin gle lam ina and for three laminates with different stack in g scquences, composed o f epoxy/ 50% glass fibre s. (The eq ual stress model was used for the tran sve rse Young's modulus of a la min a.)
balanced la minate. In a ll cases, the stacking orde r in which the plies are assembled does not enter into these ca lculations, although it may be important in determining the interlaminar co upling st resses (see bel ow).
[ O"X 0")"
~u
So me results fro m suc h a calcu latio n are shown in Fig. 5.11, which gives the variation of O" lk, as a ratio to the applied stress, with the a ngle tP 3 - - Single ply (0')
---
--
I;)~
......... Crossply laminate (0'/90' )
2
1;)"
- - - - - 0115/30/45/60175/90' lam inate
1.5
,
,
, j
0)
1::
U)
The internal stresses may be subdivided into ill-plalle stresses, wh ich can be calculated by the method s o utlined below, and ;nteriam;lIar or through-thickness stresses, which arise as a result of co nstraint effects and are more difficult to quantify. The approach to establishing illpl a ne stresses follows directly from the preceding trea tments. Refer rin g to Fig. 5.8, and assuming the stack of laminae to be subject to a stress state 0".0 0")" a nd T n " the laminate strains are esta blished from the transformed compliance tensor of the laminate.
T, ,.
(5.33)
Tn
'"'"
5.4.2 Stresses ill illdh'idual plies of a laminate
[SJ [ ::,]
[( 5. 10)1
1= [Cld T'] =JSg] 1
cS 'iil ....
,"( , "
E lk E2k
'"( 12k
2.5
[ :: ]
k
Thc stresses in the kth ply are rel a ted directly to the applied stresses by
-I
0
=
TI2k
I
...
1 [Cl [ 1
(S,] I )
0.5 0 -0.5 -I
0
10
20
30
40
50
Loading angle, tP
60
70
80
90
n
hg. 5.1.1 Variation with loadin g angle cP fo r a single lami na and fo r two la miflates 0 1 e poxy/ 50% g lass fibres , of the stress alk para llel to th e fibre axis in a p ly Ifl lllall y ol"le n ted ; 11 () 10 Ihe st ress ax is. T he stress is p lo tted a s a rati o to the ;q'pl led slress n, . (The eq ual slress mod el was used for the tran sve rse Young's Illodu lu s o r ;1 la lllina .)
100
Elastic deformation of laminates
5.4 Stresses and distortions
101
- - Along fibre axis (alk ) 1.5
------- -- Normal to fibre axis (au ) - - - - - Shear ('1"12)
•
••
o _
0.30"x
•• • -0.070"tJl
•
-0.5
Loading angle, cp
n
• •• •• •• ••
J
Fig.5.12 Variation with loading angle cP of the stresses alb a Zk and TI2k within the ply orien ted at 00 to the stress axis, for an epoxy/50% glass fibre 0/90 (erossply) laminate. The stresses are plotted as a ratIO to the applied stress . (The equal stress model was used for the transverse Young's modulus of a lamina.)
between the loading direction and the fibre direction in the 00 ply. This is shown for a single lamina and for two laminates. When more plies are present , so that the 00 ply being considered presents a smaller relative section , it bears a proportionately larger stress at cP = O. This is because the 00 ply is much stiffer than those at other orientations. Note also that the ply can be put into compression when it is oriented at a large angle to the loading direction. This is the result of a Poisson contraction effect. It can also be seen in Fig. 5.12, which shows all the stresses present in the 00 ply for a crossply (0/90) laminate. The compressive stress parallel to the fibres (in the I-direction), which has a magnitude of about 0.07 times the applied stress at cP = 90 0 , arises because the ply has a small natural Poisson contraction parallel to the fibres , but is being stressed by the larger natural contraction of the other ply (which is being loaded along its own fibre axis for q) = 90°). The stresses in the two plies are illustrated schematically in Fig. 5. 1:l for (/) () . (Those shown for the l)() ply arc the S;lllle ;I S Ihl' (Llta in
l'ig. 5.13 Schematic representation of the stresses alk and a2k within both plies of a 0/90 (crossply) epoxy/50% glass fibre lam inate, oriented so that the fibres are normal and parallel to an applied tensile stress ay.
F ig. 5. 12 for the 00 ply at cP = 90 0.) It is clear from Fig. 5.11 that the co mpressive stresses generated in this way within individual plies can in SO ll1e cases be surprisingly large. The details are sensitive to the Poisson 's ra tio of fibre and matrix, but - since (ceramic) fibres tend to have low v; dues (relative to both polymers and metals) - the composite Poisson's ra tio for contraction parallel to the fibre axis of a ply will always be less Ih;1I1 that in a transverse direction and hence an effect of this type is quite ge neral in composites based on these matrices.
5.4.3 COllplillK stresses alld .~ymmetric lamillates I"hrou g h- thickness (or 'coupling') stresses hetween the laminae are diffinill In (\escrilw ri!'ololl sly. Ilowever, they ;Ire important in practice and
102
Elastic deformation of laminates
can lead to significant distortions of the laminate. The general nature of the distortions can be illustrated by two examples. Consider the simple crossply laminate illustrated in Fig. 5.14. If thi s is loaded in uniaxial tension, as in (a), the difference in natural Poisson contractions of the two plies will cause the laminate to distort in the manner shown, and outof-plane stresses are needed to maintain the assembly flat. In addition to this, the transverse ply also exhibits a large through-thickness contraction as can be seen from the data in Fig. 4.IO(a). A similar effect is shown in Fig. 5.14(b), for a crossply laminate which has been heated. Because the thermal ex pansion coefficients are different parallel and normal to the fibre axis (see § I 0.1.2), the laminate is deformed and becomes saddleshaped. In thi s case it is assumed that Q2 > Q I , which is expected in view of the low thermal expansion coefficients ex hibited by (ceramic) fibres. The stresses which arise within such a laminate on changing the tempera ture can also cause microstructural damage - see § I 0.1.4. Distortions such as these can be reduced considerably if the arrangement of the plies is symmetric about the mid-plane of the laminate, i.e. if it has a mirror plane lying in the plane of the laminate. In symmetric laminates , the coupling forces large ly cancel out and the la minate as a whole will not distort, although there are still local stresses across the interlaminar boundaries. In addition, the use of many thin laminae rather than a few thick ones minimises the distortions and leads to a reduction of the local interlaminar stresses. The classification of laminae according to whether or nor the stacking sequence is balanced and / or symmetric is illustrated in Fig. 5.15 with some examples. There are many advantages in using balal/ced symmetric stacking sequences and this is common commercial practice. However, it should be noted that a laminate is often designed in the light of information about the expected in-service stress state. For example, with tubes to be subjected to internal or external pressure, unequal biaxial tension or compression will be imposed and ply angle sequences will be chosen with this in mind. The probable mode of failure , as well as the elastic deflections , may also need to be considered (see Chapter 8). Furthermore, the type and magnitude of permissible deflections and distortions will vary widely between different applications. It is therefore rather difficult to specify an optimum stacking sequence without detailed information about the performance requirem ents. This highlights the important concept o f designing the material and the compone nt simultaneollsly a recurrent theme when working with composites.
5.4 Stresses and distortions
103
expansions
contraction s
000 0
(b) (a)
Fig. 5. 14 Schematic illustration of how a crossply laminate will tend to distort as a result of through-thickness coupling stresses when subjected to (a) an external load and (b) a change in temperature. Unbalanced Asymmetric
0 90 -30 +30 -30 +30
l-"i g. ). 1)
Unbalanced Symmetric
m 90 0
-30 +30 +30 -30
Balanced Asymmetric
o 60 120 0 60 120 0 60 120
Balanced Symmetric
0 60 120 120 60 0 0 135 90 45 45 90 135 0
1·:.\: llIlpk, of slacking sequences whi c h result in laminat es c lassi fi ed \\' hcl hn Ihey :Ire halanced :Ind / o r symmet ri c.
: 1, '''1 1110
0
0. 1
0
0.2
0.3
0.5
0.4
0 .6
0 .7
Fibre volume fracti o n , f
12
~
. . . . . Fibre aspect ratio, s
(b)
r
10 f-
- - Fibre aspect ratio, S = 100
'2 0..
S
kl
=I
.. .... ... Fibre aspect ratio, S = 5
8 '-
'" :::I
:; "0 0
E
6
r
VJ
-co C :::I
0
>2
0 0
0.1
0.2
0. 3
0 .4
0 .5
Fibre vo lume frac ti o n,
0 .6
0 .7
f
Fi g. 6. 13 Es helby pred icti o ns of th e Y o un g' s m od ~t1u s a s a fun c ti o n o f li brc vo lum e fr ac ti o n fo r glass fibres w it h as pect rati os 0 1 I, 5 a nd 100, III ;I n e pox y m a tri x fo r (a) a xi;l l and (h) tr;ln svc rse load in g .
Cshelb), m odelling Bro wn , L. M . a nd C la rk e, D. R . ( 1975) W o rk ha rd enin g du e to intern a l stresses in co mp osite materi a ls, Acta Me tall., 23 82 1- 30 C lyne, T. W. a nd With ers, P. J. ( 1993) An Introductioll to Me tal M atrix Composites. Ca mbrid ge U nive rsit y Press : Ca mbrid ge Es he lby, J. D . ( 1957) The d etermin a ti o n o f th e elas ti c fi eld o f a n ellipsoid a l inclusio n , a nd rela ted pro blem s, Proc. R oy. Soc ., A241 376- 96 Es he lby, J. D. ( 1959) The elas ti c fi eld o uts ide a n elli pso ida l inclusio n , Proc. Roy . Soc ., A252 56 1- 9 M ura , T. ( 1982) Microm echanics of Defects in Solids . M a rtinu s Nijh o ff Pcderse n, O . B. ( 1983) Therm oelas ti cit y a nd plasti cit y o f co mposites - I. M ea n fie ld t heo ry, Acta M etall. , 31 1795- 808 Ta na ka, K. a nd M o ri , T. ( 1970) The ha rd enin g o f crysta ls by no n-d efo rmin g pa rticl es a nd fibres, Acta M etall., 18 93 1- 9 Taya , M. ( 1988) M od elling o f ph ysica l pro perti es o f m eta llic a nd ce ra mic co mp osites; ge nera lised Es helby m od el, in Mechanical and Physical Behavio ur 0/ Me tallic and Ceram ic Composites. S. I. A nde rse n et al. (ed s.) Ri so Na t. La b .: Ros kilde, D enm a rk pp. 20 1- 3 1 W it hers, P. J ., Smith , A. N ., Ciy ne, T. W . a nd Stob bs, W . M . ( 1990) A p ho tog ra p hi c exam in a ti o n o f th e va lid it y o f the Eshelby app roac h to th e mod ellin g o f M M Cs, in Fi ll/(II/IJ/ellwl Relatiollships hetll"('ell Mic rostructural 111111 A/('cl/((I/im l I'mlll'rties A/etal Matrix CO /ll posites. M . N . Gungor ;lIHI i'. K . I i;l lV (l·d , . ) TM S pp . ~~) 40
or
132
S tresses and strains in
short~flb re
composites
7
General Carrara, A. S. and McGarry, F. l. (1968) Matri x and interfac ia l stresses in a di sco ntinuou s fibre co mposite model , 1. Comp. Mat ., 2 222~4 3 Galioti s, C, Youn g, R . l ., Ye un g, P. H . J. a nd Batchelder, D . N. ( 1984) The stud y of mod el pol ydiacetyl enejepoxy composites . Part I: The axia l strain in the fibre , 1. Mat. Sci., 19 3640~8 McDanels, D. L. ( 1985) Analysis o f stress~s tra in , fracture , a nd ductility of a luminium matrix composites co nt a inin g discontinuous silicon carbide reinforcement , Metall. TraIlS. , 16A II0 5~ 15 Termonia , Y. ( 1987) Theoretica l study of the stress tran sfer in single fibre co mposites, J . Mat. Sci., 22 504~8
The interface region
The preceding three chapters ha ve dealt lI'ith the elastic behaviour 0/ composites. Amollg the asslImptio/l.l' made ill IIIOst o/ these treatlllellts is that the illter/acial bond is 'perFect '. This means that there is no debonding, cracking or sliding
0/ allY
in/act , no elastic or illelastic processes
description. In practice , manl' importallt phenomella may take
place at the inter/ace, depending all its structure and the stresses gellerated there. These processes tend to promote plastic def ormation 0/ the matrix and can also inf7uence the onset alld nature of/ailllre. Before treating the strength andfi'acture beha viour o/composites ( Chapters 8 and 9), it is necessary to consider the illter/ace and examine hOIl' its response call be characterised and illfluell ced. III the present chapter, the meaning and meaSUrel1lell t
0/ bond streng th are described. 0/ inter/acial bOllds ill
fo llowed by an outline a/ the fo rmation
This is various
systems and a sllml1lary a/the techniques used to influence the bonding characteristics.
7.1 Bonding mechanisms 7.1.1 Adsorptioll alld wettillg
II' the s urfaces of two bod ies spo ntaneously come into intimate (atomic "call:) co ntact when they are brought close to each ot her (common ly with (ll 1l': of the bodies in liquid form) , then 'wetting' is sa id to have take n pla ce. Adhes ion is primarily caused by van der Waals forces , a lthoug h ot her types of bondin g may reinforce these . The occurrence of wetting ('a ll he trea ted lI sin g simple th ermod ynami cs, but in practice there ma y be (' hc lllical c han ges taki ng p la ce whieh arc tim e-dependent. Fig. 7. 1 illu str:t\cs so lid /so lid :rlld solid / liquid int e rfa ces . The so lid / solid con tac t area
In
7. J Bonding mechanisms
The interface region
134
a nd the interface surface energy . Interface surface energies are difficult to o btain (and may be innuenced by chemical reactions) , but they are freque ntly sma ller than the values for the phases being exposed to a ir . The surface energies of fibres and (liquid) matrices are generally known and systems where the former greatly exceeds the latter are likely to wet very easily. For example, glass hsv = 560 mJ m - 2 ) a nd graphite h sv = 70 mJ 111 - 2 ) are readily wetted by polyester hLV = 35mJ m - 2 ) and epoxy b LV = 43 mJ m - 2) resins, but polyethylene fibres hsv = 31 mJ m - 2 ) a re not. Lack of wetting is a problem for certa in metal matrix composites ~ Ind coatings on the fibres are used to improve this (see §7.3. 1).
(a)
(b)
135
'YLV
7.1.2 Interdijfilsioll alld chemical reactioll Fig. 7.1 (a) Isolated contact points leadin g to weak ad hesio n between tw o rigid ro ugh surfaces. (b) Contact a ngle a nd surface energies I for a liquid drop o n a so lid surface.
e
is limited to those regio ns where as perities to uch (Fig . 7.1 (a)) a nd the effective bo nd stre ngt h is very low unless extensive deformation is promoted to rem ove the as perities . Surface contamination ca n a lso rest rict the a rea of effective contact. For the liquid /so lid case , intimate co ntact ca n be establi shed providing the liquid is no t too viscous a nd a thermodynamic driving force exists. This is comm only expressed in terms o f surface energies, "'f , so that the 1V0rk of adhesioll , Wa , is a simple net sum , often termed the Dupre equation
Wa = "'fsv
+ "'fLV
- "'fSL
(7. 1)
The subscripts S, L and V refer to so lid , liquid and vapo ur, respectively . The vapour phase is com m on ly a ir. According to this eq uatio n, wetting is strongly favoured if the surface energies of th e two co nstituents are large and their interfacial surface energy is sma ll. In practice, however, a la rge va lue of the liquid surface energy inhibits the sprea ding of a liquid droplet. The eq uilibrium wetting o r COli tact allKle is dictated by the YOUIIK equatioll , obtained by a balance of hori zo nt a l forces , Fig. 7. I(b),
e
"'fsv
=
"'fSI.
+ "'f I.V cos 0
(7.2 )
It follow s that co mplet e wetting (0 0' ) occllrs ir th e slIri';lce e nergy or th e so li d is equ;!1 to or "re;iler th ;1I1 th e sum or th e liquid Si ll i';Il'l' e nCl'gy
Various types of diffusiona l process which promote adhes ion can take place at the interface. For example, Fig. 7.2(a) shows the diffusion of free c ha in ends at the interface between two polymers, which leads to cha in e nta nglements and a rise in the adhesive strength. This effect is employed in some coup lin g agents used on fibres in thermoplastic matrices (see ~i 7 .3.1) . Interdiffusion can also take place in non-polymeric systems, particu larly if it is accompan ied by a chemica l reaction. The adhesive stre ngth is dependent on the nature of the resultant interatomic bonds (and also on the stresses generated by the reaction - see below). Va rious types of chemical reaction may occur at the interface, either de liberately promoted or inadvertent. These can be represented , as in Fig. 7.2(d), by new A- B bonds being formed as a result of interfacial chem ica l reactio ns. These bonds may be cova lent, ionic, metallic, etc., and in many cases a re very strong. There are many examp les of the interfacial bond stre ngth being raised by loca li sed chem ica l reactions, but it is often observed that a progressive reaction occurs which results in the formation of a brittle reaction product. Carbo n fibres are prone to surface reactions with organic groups; the de la il s depend o n the manufacturing method s (e .g. see Scola 1974). An im po rta nt fea ture is the a ngle at which the ba sa l planes meet the free ';urface (see §2.1.1), as many reactions take pl ace preferentia ll y at th e edgcs of these pla nes. For example, the high-modulus PAN -based fibres h;!ve a thick sk in with ba sa l planes predominantly parallel to the surface; reaction takes place less readily tha n in carbon fibres with ba sa l pla nes Ilorma l to the surface a nd the fibres a re prone to co hesive failure as a res ult o r weak int er-plan e bonding. Heat treatme nt s pri or 10 co mposite
7.1 Bonding mechanisms
The interlace region
136
~/
("'~
(b)
///J/J'iJ//J//J/J///J'///' +++++++++++ -
-
-
-
-
-
-
-
-
-
If/T/T/T///T///7//77/7//
137
l"
e
.2
;.§
Experimental data for Cu/W (Kelly 1966)
20
(b)
/ 15
600
'" '"
..J
200
00
/.'
6
400
/' 0.2
0.4
(l-j) O"mu
~.,
10
Ul
0.6
0.8
1.0
/.
Fig. 8. 11 Ax ia l tensil e testing of metal matrix laminae. (a) Idcalised stress- strai n plots for fibre , matrix and composite, a nd (b) a compa ri son between theory a nd experiment (Kelly and Macmillan 1986) for the dependence of fa ilure stress o n fibre vo lume fraction.
. )(
.'
f"
/'
5
Fibre volume fraction , f
'
..'
.' .' .' B
(.-"
b
(b)
..' ..
/
0..
c
'"
/
'2
~
.§
Ar
800
.
./'
/'
~
00
0.05
0 .1
0.15
0.2
0.25
0.3
Strain (0/0) I I)'. X. 12 Stress- strai n curves for (a) three unreinforced polyeste r resin s and (b) I.lIll inac bascd o n these resins, with 48 % glass fibre , tested in transverse tensi o n (Legg 1980) .
strength is less than that of the unreinforced m a trix , often sign ifi cant ly so, and the strain to failure can be eve n more dramatically red uced. A consequence of this is that the transverse plies in a c rossp ly laminate us uall y start to crack belore the parallel plies, even though th ey are less stilT and so carry less load sce }i lL~ .
l'h e influence of fibres on the transverse strength is illustrated by the npe rilllental data shown in Fig. 8.1 2, which compares transverse tensile ' tll'SS s tr;lin plot s ror laminae based on three polyester resins with the hl' lt :lviollr or tltl'Sl' 111:ltl'l"i :tl s ill the ullreillroreed rorm . Both the strengt h
174
8. J Failure modes of long~fibre composiles
Slrenglh of composites
175
and the stra in to failure have been markedly reduced by the presence of the fibres. This is largely due to the inherent tendency for high local stresses and strains to develop in the matrix (see Fig. 4 .3(b)). The fibrcs make little contribution to the strength. If the interfacial bonding is weak , then cracks tend to form at the interface and link up through highly stressed sections of matrix . A process of this type is illustrated in the micrographs of Fig. 8.13. If, on the other hand , there is strong resistance to interfacial decohesion , cracks will tend to form in the matrix close to the interface - where there is a concentration of stress and a high degree of triaxial constraint, so that matrix plasticity is inhibited. Alternatively, some fibres (such as carbon fibres) with a layered structure have little transverse strength and may fail internally. With a metallic matrix , broadly similar characteristics are exhibited . Plots are shown in Fig. 8.14 which illustrate the effect of interfacial bond strength in a titanium composite. These are PO;SSOIl plots, in which th e strain transverse to the loading direction is shown as a function of that parallel to the applied load . The gradient gives the Poisson ratio. The plots are for axial and transverse loading, before and after a heat treatment which raised the interfacial bond strength. Under axia l loading, the Poisson 's ratio ri ses slightly as inelas tic behaviour starts; this is due to plastic flow in the matrix (with an associated Poisson's ratio of 0.5) . Under transverse loading, however, there is a tendency for the Poisson's ratio to fall; this is a result of the interface opening up , which allows extension in the loading direction with little lateral contraction . After the heat treatment , this effect is very limited and failure occu rs at (I much reduced stra in . An estimate of the effect of the presence of the fibres on the transverse strength can be obtained by treating the fibres in the composite as a se t of cylindrica l ho les and consideri ng the reduction in load-bearing cross-secti on thus introduced. (This is not accurate, since the presence of evc n completely de bonded fibres would lead to a different stress distribution in the matrix than would be the case for holes, but th e approach is useful as a guide.) For a simple sq uare a rray of holes, consideration of the maximum reduction in matrix cross-sectional area leads to the following expression for the transverse strength of a lamina having a volume fraction f of fibres
0"211
=
0"11111
[I - 2 (;f") 1/2]
I:ig. !i.U
(R.5)
SEM microgra phs illustrating the propa gation of a transverse crack in a pol yes te r/gla ss lamin a (J o nes 1981).
Strength of composites
176 -2
i
:!
·1.6
~
-,A
1 l 1 1, l
.~ ·1.2
;" ~
-,
S
.5 -0.4
0...
~ ·1.6 gc -'A
S t>~
1
"::;; -0.6 ~
c
~
=-1 V
II
~ -0.2
O\f..-'---'-'---'-'---'-'---'-"-,-"-,-"-,-"-,-"-,-.LL.-'-'-l
-2 ',~~~~~~~~~~~~
~ ·1.8 ~
'"c
~ -0 .4
~
~ -0.2
'"~ '">~
( b) -
0
300
200
o 100
r:'"
-2 ~~~~~~~~~~~~
-1.8
.ll-'·6 l
Fibre vo lume fraction , f (%)
~ -'A ~
J"'~~ r~
400
~
= 0.03
;; (a)
Experimental (Prewo & Krieder 1972) o 6061/ BORSIC (As-Fab) • 6061 / BORSIC (T6)"
0'0
-,
:s -0.8
500
..c
.~ -1 .2
~
J
§ -0.6
-;C' -1.8
~
@ -0 .8
177
-2
~~~~~~~~~~~~
- 1.8
8.1 Failure modes of long:/ibre composites
{J
VI '
I Ig. H. IS Experimental data (Prewo and Kreid er 1972) for th e tran sverse tensile '.In: ngth of Al j BORSI C laminae as a function of fibre volume fra ction , compared with predictions from Eqn (8.5).
= 0.34
~ -0 .8
~
-0.6
~
~ -0.4 ~ ~
~ -0.2
o
r~
( d)
(c) .
8.1.3 Shear failure
L ·~~~~~~~~~~~W
o
10
LongilUdinal strain (m illistrai n)
12
10
12
Longitudinal strain (millistrain)
Fig.8.14 Experimental data (Wa tson a nd Clync 1993) fr om ax ia l and transverse tensile testin g of Ti 6AI 4VjSiC mo no filam ent laminae, plotted in th e form 01" latera l contraction as a function of extension in the load in g direc ti o n . Plots are for (a) ax ia l and (b) transverse load ing of as-fabricated composite, and for (c) axia l and (d) transverse loading a ft er a heat trea tme nt which rem oved the g rap hitic coa tin g o n the fibre s.
A comparison is shown in Fig. 8.15 between predictions from this equation and experimental data for AI(6061)/ Borsic composites. In this case. the model gives good agreement with experiment. There is interest in improving the transverse properties of laminae. particularly the failure st rain. Among the possibilities that have becn considered is the provision of a very compliant (e.g. rubber) la ye r on the fibre surface, so as to red uce the stra in loca li sat io n and co nstraint imposed on the matrix. Unfortunate ly. a layer suffi cient ly thi ck to increase sign ifi can tl y the transverse failure strain tends to have an adverse clTcct on ot her properlies. slIch as the shea r stiITIl l:ss.
\s with tensile fracture, shea r failure tends to occur on pla nes determined (he fibre direction. The six possible combinations of plane and shearIllg direct ion , and their indices, are depicted in Fig. 8.16. There are three "l'tS of equiva lent pairs. Normally, th ere is considerable resist a nce to the ilacture of fibres, so that the pa ir of modes denoted 72 1 and 73 1 are 1IIl like ly to occur. Of the other two pairs, involving sliding of fibres IIVl: r o ne a nother ei ther axially (712) or la terall y (7)2), it is not obvious \\ hcther one is inherently more likely than the other. However, when "o ll sidering the stressing of a thin lamina in the 1- 2 plane, stresses of llit: 712 type do not arise and only the magnitude of 712u is important. l\road ly speaking, this is affected by the same factors as the tran sve rse Il'lls il e st rength , because shear stresses and strain s become concentrated 111 thl: matrix betwee n fibres in a manner similar to that outlined above lor tens ile stresses and strain s. However, the details of thi s dependence ,11 e different. There is mo re scope for local matrix deformation to take 111;tcl: (wi th o ut cracking) under this type of stress and local stress concen11 ;I t ions a re relaxed more readi ly. No simple ;tll;il yli c; il l:x pression is available (0 predict the effect of fibre '() Ili ellt Oil TI']]" 1\t\ ;llll S ;llId DOrller (1967) have lIsl:d linite difTerence 11)
178
8.1 Failure modes of long-fibre composites
Strength of composites
179
10
.... 0
u
~
c
8
.~
§
=6 Q)
u
c 0
u Vl Vl Q)
4
b
Vl
.... o:S Q)
..c:
CI1
2
00
0.2
0.8
0.6
0.4
Fibre volume fraction, f I Ig. X.17 Shear stress concentration factor as a function of fibre volulllc fraepredicted by finite difference modelling for a square array of fibres (Adam s and Domer 1967).
11. 1I1,
Table 8.2 Typical experimental failure data for laminae based on therll/o.\·('1 malrices Composite 1"2 1
Fig. 8.16
1"3 1
Nomenclature and orientation of shear stresses acting within a n aligned fibre cOIllPosite.
methods to deduce how the shear stress concentration factor should vary with fibre volume fraction. The results are shown in Fig. 8.17 . Unless the fibre volume fraction is very high (when constraint on matrix deformation becomes severe) , this factor is quite close to unity and TI 2u is expected to have a value close to Tu for the matrix. This is broadly confirmed by the experimental data summarised in Table 8.2. It may be noted that there are both practical and theoretical difficulties to be overcome ill obtaining such data. These are outlined in §8.2.3.
8.1.4 Failure ill compressioll Failure in comp"es,\'ioll is dependent o n the wa y that thc IO ;ldin g is applied and , in parti c lll ;lr , on th e d eg ree of lateral eon s tr;linl. l lnd e r ;l xi;Ii
1'., lycster/ 50% glass I poxy/50% carbon WM) I poxy/50% KevlarT
Axial Transverse Shear strength strength strength al u alu Tl l u (MPa) (MPa) (MPa) 700 1000 1200
20 35 20
50 70 50
Axial Transverse failure I'ailun.: strain strain flu (,X» ( 2 11 ('Y. ,) 2.0 0.5 2.0
03 0.3 04
,,) m pression , there is a tendency for the fibres to huckle. Excepl at low Ilh re volume fractions, neighbouring fibres are constrained to bllckk: in Il hase, as shown in Fig. 8.18. Buckling results in compressive and tellsil' , tn.:sses across different parts of the fibre section, leading either to rra e IlIrc o r (if the fibre is one, such as Kevlar™, which can derorm s ig nili • ;lIlt ly) to local distortion. If buckling becomcs extensive, thell it will I .llIse general collapse, i.e . failure, of the specimen . A m o re common ty pe or railure occ urs fr o m the on set of' a loe;Ii bllck lIn g in s tability . A 1.;111. IWllt! or Illi sori e nted fibres Illa y rorm , a s illu str;lll'd II1 Jo'i g . X. II) . h)'III " X 10 s hows a rr;l e tllred c lrhon lihn: rl'inrorn'd
1I
180
Strength
0/ composites
8.1 Failure modes o/Iong:/ibre composites
181
I ig. 8. 19 Optical micrograph of a poli shed section of a carbon fibre/epoxy resin Jlu ltr uded specimen , showing a kink band formed in the compression zo ne of a four-point bend test specimen (Parry and Wronski 1981).
c/). Argon (1972) proposed that the compressive failure stress could be ex pressed as (8.6)
Fi g. 8.18 (a) T ensile and compressive stresses in a fibre due to in-pha se buck ling, leading to a kink zo ne. (b) Two planes offracturc formcd with brittlc carbo ll fibres . (c) Unfractured kink zo ne form cd with Kevla r™ 49 fibre s.
composite which has failed in thi s way in th e compression zonc 01" ;1 specimen loaded in four point bcndin g. Jclf and Flcck (1992) have shown that most failures und er axial co mpressio n arc o f thi s type . which they refer to as plastic micro/mc/dillg. Plastic dcformation or the matri x is neccssa ry for th c mcchani slll to initi a tc. The main ra ctors whieh inlluence the onset 0 (" this type 01" instahilit y. ; 1\) ~lrt rrom I"ihre co nt ent , ~ 1I"l: malri x shear yield slress. T YIIl' alld (;lver;l gc ) lihrc IlIi s; lli )' llIlI l' lll ;In gk ,
whcre 6. cjJ is in radians. It is assumed that the volume fraction of fibres is hig h enough for this type of failure to be likely. In this regime, the failure , t rcss is pred icted to be independent of fibre content. It is also assumed tha t the interfacial bond strength is high enough to ensure that debonding docs not initiate failure . T he data shown in Fig. 8.21, taken from a number of different studies, co nfirm that there is a strong correlation between matrix shear yield stress and composite fai lure stress in compression. The gradient of the bcst-fit line in this plot corresponds, via Eqn (8.6), to a value for 6.cjJ Il l" abo ut 3". This is physically reasonable, in that measured misalignIlle nts in nominally unidirectional co mposites often range up to about this lig ure. Errors in specime n grippin g geo mctry mi ght typically IlIvo lve l1li s~ di g nl1l l' lIt lip 10 '" I " . Furlhcrl1lore, th ere is sO lll e ev id ence
182
8. J Failure modes of long~flbre composites
Strength of composites
183
on on
~on ~
.2 ~
100
Q)
>
on
i3
0..
10
E
o
u
I
L-~~~~~~~~L-~~~~~~~~
0.1
10
Matrix shear yield stress,
100 TYm
1000
(MPa)
I'ig. 8.21 Compressive failure stress for a variety of unia xial composites, taken fro m several different studies, plotted against the shear yield stress of th e mat ri x (Jelf and Fleck 1992).
Fig. 8.20 SEM micrograph of the fracture surface of a carbon fibre/epoxy res in lamina a ft er a fibre buck lin g mode failure due to a lo ngitudinal compress ive stress. (a) Low ma gnifica tion view showing smoo th fra cture surfa ce. (h) Ili ghma gni fi ca t io n view show ing tensio n and com pressive fr,lct 1I re in , I singlc fi hrc . (I :win s ;Ind Potter Il) X() .
that composites showing particularly good alignment have excellent co mpressive strengths. It is, however, difficult to be precise about the reliability of Eqn (8.6), since it is unclear how large a group of fibres needs to be misa ligned by 6.q; in order for kink-band formation to in itia te . This is an area requiring further resea rch . A composite can also fail under axia l compression by macroscopic shear o n certain planes. This must involve fra cture or gross deformation of li bres, since no shear stresses a re developed on a ny planes parallel to the J"i bre axis. Thi s usually occurs at applied load s similar to those necessary to ca use axia l tensile failure , although modellin g of the mechanisms involved is di fficult. These compressive failure load s can be significantly reduced if fihre huckling occurs. This is genera lly favoured by measures which red uce the stiffness orthe matrix, such as heatin g or, with some polymer matri ces, prolo nged exposure to water. Reduction s in th e interfacial bond strength Ui 7.3) a lso tend to facilitate this. Fin a ll y, there is a significant depend cnce ' 1Il the fibre diameter. Large-diameter fibres a re much more rcs istant to huck lin g than fine fibres. This point was made in §2.2.2. The se nsiti vity to d i;ltlle ter can be inferred from the Eul er buckling formula given as Eqn (2 .1) and thc J"ihn: flexih ilit y data in Tabl e 2.4. An exa mple ofcxploitation o J" the cxce ll enl Il'sist:lnCl' oJ" largc-d iam cter fihrcs to buckling is givcn in :: 12.4, rei:! Iill ) ', 11 ) Ill ,' 11 \ , ' I ) i' horon 1110nofil:ll11cnts in go lJ" cluhs.
Strength of composites
8.2 Failure of laminae under o/raxis loads
In general, the stress- strain plot of a composite loaded under ax ia l compression is rather sim ilar to the corresponding tensile plot. Common ly, the initial gradient is slightly reduced and the failure stress somewhat lower under compression. These changes reflect the stra inin g and damage development which can occur under compression when fibres become mi sa li gned. These compression tests become meaningless if macroscopic (E uler) buckling of the specimen is a ll owed to occur. It is therefore necessary to ensure that the specimen has a low aspect ratio (length/diameter) and /or that suitab le anti -buckling guides are used. Application of the technique to thin lam in ates is described by Lagace and Vizzini (1988). Compression testing of MMCs has been used to obta in information, not only about damage development and failure mechanisms, but also co ncerning residual stresses in the matrix. Differences in yielding behaviour under tensile and compressive loading can be related to these residual stress levels. Some of the experimental aspects of such testing have been described by Kennedy (1989) . Further information can be obtained by load reversal tests, in which a specimen is plastically deformed in tension and then subjected to compressive loading (or vice versa). M MCs often exhibit a pronounced Bauscltillger eflect (easier yield ing after prior reversed plastic flow). Interest has centred mainly on discontinuously reinforced material. Interpretation of experimental data requires some care - see, for example, Taya et al. (1990). Under some circumstances, failure may occur under trallSI'erse compressioll, involving shear on planes parallel to the fibre axis . This is expected when a shear stress of the 732 type (see Fig. 8.16) reaches a critical value - which should be broadly similar in magnitude to 712u' It follows that this type of failure is expected at an applied normal compressive stress of about 271 2u, on planes inclined at 45° to the loading direction and parallel to the fibre axis. Experimental measurements are broadly consistent with this, although there is sometimes a dependence on interracial bond strength; for example, if a high bond strength leads to failure by shear yielding within a polymeric matrix , then thi s usually occurs less readily under compression than in tension .
\ Ive loads and through-thickness stresses are not present.) A number of /ililure criteria have been proposed. The main issue is whether or not the nitica l stress to trigger one mechanism is affected by the stresses tending In ca use the others - i.e. whether there is any interaction between the Illodes of failure.
184
8.2.1 Maximum stress criterioll
111 the simple maximum stress criterion , it is assumed that failure occurs \\ hen a stress parallel or normal to the fibre ax is reaches the appropriate nit ica l value, that is when one of the following is satisfied (ll 2: (llu
(8.7)
2: (l2u 712 2: 71 2u (l2
hH any stress system ((lx, (l, and 7,,0) applied to the lamina , evaluation of Ihese stresses can be carried out using Eqn (5.12)
[(5. 12)] 111 which [T] is given by Eqn (5 . 13) ?
[T] =
)
[, e
s-
s-
e
-es
cs
)
- 2" 2es ) e - s-?
1
[( 5.13)]
(e = cos c/>, s = sin c/» Monitoring of (ll , (l2 and 712 as the applied st ress is increased , allows the onset of failure to be identified as the point when one of the ineq ualIlies in Eqn (8.7) is satisfied. Noting the form of [ T ], and considering ap plied uniaxi al tension , the magnitude of (l,. necessary to cause failure CII1 be plotted as a function of loading angle c/> between stress axis and Ilbre axis, for each of the three failure modes. (ll u cos- c/>
a .nl
== --)-
(T
=--
8.2 Failure of laminae under off-axis loads
Failure of laminae subjected to arbitrary (in-plane) stress states can bc understood in terms of the three railure mechani sms (wilh dcJ'il1 e(\ va lu cs or (T I" . rr.,,, ; 111(\ 7 1 ~11 ) sho wn in Fi g. X. I. (It is ;ISS IIIlIUIIIl ;11 1;II I'l' L'Olllprcs-
185
(l 2u
xu
(T \ 11
sin 2 c/>
sin (/1cos rll
(8.8) (8. 9)
(R. IO )
Strength
186
0/ composites
8.2 Failure a/laminae under off-axis loads
The three curves are plotted in Fig. 8.22, using values of (Jll" (J2u and TI2u appropriate for a polyester/ 50% glass lamina (see Table 8.2). The solid line indicates the predicted variation of the failure stress as q; is increased , according to the maximum stress criterion. Typically, axia l failure is expected only for very small loading angles, but the predicted transition from shear to transverse failure may occur anywhere between 20° and 50°, depending on the exact values of TI2u and (J2u'
whe re (Jp, (Jq and (Jr are the principal stresses and (Jy is the yield stress tinde r uniaxial loading. I n plane stress ((Jr = 0) Eqn (8.11) red uces to (8.12) f'he von Mises criterion corresponds to yield occurring when the distortio nal (shape-changing) strain energy stored in the material reaches a cri tical value. This may be expressed ((Jp - (Jq)2
Various other attempts have been made to predict the failure of longfibre composites under combined stresses, particularly for the plane stress conditions applicable to individual plies in a laminate. A comprehensive review of the approaches adopted has been published by Rowlands (1985). Most trea tmen ts a re ba sed on ada pta tions of yield cri teria deve loped for metals. The most common yield criteria are those of Tresca and von Mises. The Tresca criterion corresponds to yield occurring when a critical value of the maximum shear stress is reached. This may be written as (8 .1 I)
I~
'2
6
....
,
on '"
~
Fig. 8.31 Optical micrograph o r a n interlaminar cra ck on th e cdgc r:lce (!\B( 'I) in Fig. X.29) o r a gla ss lihre/ po lycstc r rl:sin angk-pl y Ianlill:ll l' (.Ioncs I')X I).
,
,
VJ V>
,
0
o
0
t
0
0 0 ---0--
_
0
Onset of transverse cracking Complete fracture
0 .5
I
1.5
,I = 2
50"! 2 .5
Width of laminate, 2b (mm) I Ig. X.32 I:fl i.:c t (lr iL'st spcc im en width o n tcnsil e stress for transverse crackin g .llId co mpkiL' I'l:1 r lll rl' ill :ln gk -ply laminat es (cl) SO) o f polyester/SO'Y-
~
Ql
c
llJ
Crack length c
Total energy of the system
2
U=_allC
2
E
F ig. 9. 1 Schemat ic plot o r th e two cont ribu ti o ns to the energy a ssociat ed wi th th e prese nce o r a cra ck in a brittle mate ri al, as a runctio n o r c ra c k le ng th . /\ c rack or le ng th c, o r large r wi ll grow spo ntan eo usly, with a redu e ti o ll in the to t;1I e ne rgy.
I.Ilr1y easy to obta in experimenta ll y. For exa mple, the work done in a 1(,llsion or bending test is given by the a rea und er a load-d isp lacement plo t a nd , provided this energy is all permanently absorbed in the speci111l:n, the fract ure energy is then found by simply dividing by the sectional ,m:a thro ugh which failure has occurred. The specimen is commonly prelI() tc hed so as to ensure that crack propagation occurs . Typical va lues of (;, are given in Table 9.1 for various materia ls. Tough (soft) meta ls have Irac ture energies of 100kJm - 2 or more, whereas a brittle materia l, such . IS gla ss, ca n have a value as low as 0.0 1 kJ m - 2 . Rea rranging Eqn (9.4), Iltc strcss necessary to cause spo nta neo us fracture in a component with a prc-ex isting crack of size e (2e if interna l) ca n be written as
rr ,
(9.5)
Toughness of composites
9.1 Fracture mechanics
This approach is particularly useful in practical terms, because atten tion is diverted from the complex problem of the precise nature of Ihe stress field close to the tip of a crack to a more global approach involvin ' macroscopic quantities which are measurable experimentally. However , there is still interest in the phenomena occurring locally near the crack tip. A useful link is provided between the energy and stress fie ld approaches by the concept of a stress illtensity factor, K. This parametc r, which largely evolved from the work of Irwin in the 1950s, can be expressed as
9.1.2 Interfacial fracture and crack deflection
212
K = CJvnc
(9.6 )
It therefore encompasses the effects of both the applied load and the preexisting crack size, with the relative weighting that these two parametcrs have in determining the value of G, the energy release rate (see Eqn (9.4)) . It characterises the severity of the stress field around the crack tip . A critical value can be identified, corresponding to the case where the associated value of G reaches Gc
Kc = CJ * V'nC Jl.(; = V!£G LV c
(9.7 )
This critical stress illfensity factor is often known as a Factllre toughness. Values are given in Table 9.1 for various materials. For tough materia ls, the fracture toughness can exceed 100 MPa JiTI, while a brittle materia l might typically have a value around I MPaJiTI. The usefulness of the stress intensity factor lies largely in the way it can be related to local crack tip features. For example, it can be shown that the si ze of the pla~, tic lOll/' ahead of the crack tip is related to the yield stress of the material by
ry : : :; ~ (~) 2 211: CJy
Similarly, the crack openillg displacemellt , 8, can be expressed as
8:::::;
(~) CJyE
(9.9 )
Such parameters are useful wh en considering how energy-absorbing processes might be stimulated in composite material s, sincc Ih cy a llow Ih L' scale of features of the cra c k lip 10 be relal cd 10 Ihe sca k or Ih e micr(lstru cl urc.
213
I "hk 9. 1 shows that a composite made from glass fibres and epoxy resin 11.1 \ a fracture energy comparable with those of metals (Gc rv 50 kJ m - 2 ) , , \ I'll though the constituents are both brittle (Gc rv 0.01-0.1 kJ m - 2). I illS high toughness of composites, which is very important in practica l il-llllS, is closely linked with interfacial effects. A first step in exploring Ill" is to analyse the conditions under which interfacial debonding, i.c . , 1,lck propagation along an interface between two different materials, '" L·urs . For a given loading configuration , the propagation of a crack ,d"llg a n interface between two constituents gives rise to an energy rclcasc 1,11l", G;, in much the same way as for the case when the crack is in a IlIllllogeneous material. Also , there is a critical value , G;c , an interfacial / fIIl'f llre energy, which G; must reach for the crack to propagate. Va lues of G;c are not as readily available as Gc values for homogeI H'OUS materials. There are several reasons for this. Firstly, the toughness "I an interface is sensitive to the way in which the interface was man IIlact ured , rather than being unique to the pair of constituents on cither '.lIk. A second reason is slightly more complex. Interfacial cracks oftc n I" opa gate under mixed mode loading conditions. This is in contrasl 10 a I Iack in a homogeneous material , which will always tend to advancc in a dlll:ct ion such that the stress field at the crack tip is purely tensile (mode I) A n interfacial crack , however, is constrained to follow a predelerm ined path. Depending on the loading configuration, thc stress IIl'id a t the crack tip may include a significant shear stress componenl .1\"Iing o n the plane of the interface (mode 11). In general , thc energy npe nded in debonding the interface is greater when there is a mode II IOlll po ne nt than for the case of pure mode I loading. Thi s compli cal es I ilL' experimental measurement of G;c . Not only can it bc diffi e ult 10 ('s la bli sh the exact stress field at the crack tip, but it may vary wilh posi lio n in the specimen , particularly for fibre / matrix intcrfaees . Th L' "llu;ll io n is further complicated if any residual strcsscs (e.g. see :: 10. 1. 1) are present. T hc proportion of opening and shearing modes al Ihe cra c k tip is oi"l e ll I IIa rac tc rised by means of the phase allgle, '1/) (psi). This is dc fined ill le rlll S Ill' Ihe mode I and mode II stress intensity factors, sho wn sehemali call y ill 1112.. 9.2.
,I,
214
9. 1 Fracture mechanics
Toughness of composites 10
(a)
~
N
E 0 u
cS ;:.. 0Jl .... f·~.e
/ /
~"f"'"
~
~ 0...
6
................... .................. .... . .........
1000 K
OE 800
....
'" IU '"
b
'"
E ::I E .;( ro
600 400
::E
-
'"
-
- S-glass/epoxy
- - A I alloy (2024-T3)
""
-
- - - - - E-glass/epoxy --------- Boron/epoxy - - Carbon/epoxy
200 0
10 3 5
10
15
!';K(MPa . .J m)
Fig.9.10 Schematic depiction of fati gue crack growth rat e as a fun ction ,)1 applied stress intensit y factor 6.K, fo r a ty pi cal particle- reinforced MMC ;llld the co rrespondin g unreinforccd all oy, illu stratin g th e etTee t 0 1' reinl'orcemc nt (I ll th e I'ati guc res pon se.
10 ' Number of cyc les to failure , N,
1'1' '>.1 1 Ex perim ental .'> / N, plot s (!\garwa l and Broulm ;ln I ll' jl(l ly tll er cO lllposilL's. a ~ a 1'IIIlL'lio n 0 1' Ihe pe; lk ;Ippli ed l(lad . Th e stress r;ltl (l li was 0 . 1 ill ; llI e; l ~ l's /\ 1' (1 , It (lWIl IS a plo t I'or a ty pi c; ti IIllreinl'o reed ;tilllll i llllllll ;tll(l Y·
-230
Toughness of composites
9.3 Sub-critical crack growth
boron and carbon, show excellent fatigue resistance, being able to wilh stand alternating loads of around I GPa for very large numbers of cyck: ~ The fatigue performance of these materials is markedly superior to th; 11 of a typical aluminium alloy. With glass fibres , on the other hand, til l" lower stiffness of the fibre leads to reduced stress transfer, exposing till" matrix to larger stresses and strains. This causes progressive damage ;11 considerably lower applied loads than for the stiffer fibres. While the axial fatigue resistance of long-fibre composites tends to I l' very good, particularly with high stiffness fibres , performance is usua ll y inferior for laminates or under off-axis loading. This is illustrated by tl,.· plots in Fig. 9.12, which are for glass-reinforced polymer. The crossr ly and woven cloth laminates fail at appreciably lower loads than the uni directional material and show little evidence of a fatigue limit stress va lm' being identifiable. Damage to the transversely oriented regions starts ;11 low applied loads (see §8.1.2), transferring extra load and event ua ll y causing cracks to propagate into the axial regions. Nevertheless, I Ill' fatigue resistance of such materials compares quite well with that 0 1 many metals. Finally, the chopped strand mat (CSM) and dou. 1I
'llou lding compound (DMC) show relatively poor fatigue resistance. In 11 1(;se materials, fibres are misaligned and have relatively low aspect latios, particularly for the DMC. Broadly similar behaviour is exhibited by MMC laminates. Data in the lorm of S I Nr plots are shown in Fig. 9. 13(a). The best performance is shown by the unidirectional material, having the fibres parallel to the ,Ipp lied load. The performance of the other laminates can be rationalised hy calculating the range of stress to which the 0° ply (parallel to the ,Ipplied load) is subjected during loading. When this is plotted against IlIe number of cycles to failure (Fig. 9.13(b)), then the data for the difInent laminates fall on a common curve. This highlights the point that Ihe laminate does not fail until the fibres in the 0° ply become fractured. I'he fatigue properties can , however, become badly degraded if matrix nacks are not deflected at the fibre /matrix interface (Johnson 1993). A further point worthy of note with respect to the fatigue of composi tes is that the behaviour is often sensitive to the absolute values of the st resses being applied , rather than just the !::;'K range. In particular, the Int roduction of compressive stresses usually reduces the resistance to I"at igue. This is largely due to the axially aligned fibres having poor res istance to buckling (see §2.2.2). This results in damage to the fibres ;I nd the surrounding matrix and also allows larger stresses to bear on neighbouring, transversely oriented regions , accelerating their degradalio n. Aramid (e .g. Kevlar™) fibres are particularly prone to this effect , si nce they have poor resistance to compression. This is illustra ted by the data in Fig. 9.14, which show that the fatigue resistance of Kevlar™ com posites becomes poor for negative R values . (It should , however, he no ted that the effect is exaggerated by plotting the peak stress rather tha n the stress difference, which is larger for the lower R values.) Largedia meter monofilaments, on the other hand , tend to be resistant to buckling, leading to improved performance at lower R values. A final point concerns the frequency of cycling. For metals , this usually has little effect, but in polymer composites a higher frequency often has tens failure. Thi s is partly because of the viscoelastic response of po lymers. Matrix damage is more likely if the strain is imposed rapidly, :dlowin g no tim e for creep and stress relaxation . A second effect arises I"ro m the lo w thermal conductivity of polymers , particularly if the fibres are a lso poo r co nducto rs (gla ss, Kevlar™ , etc.) . Such composites tend to inc rease in tempe ra ture durin g fati gue loadin g, as a result of difficulties in diss ipalin· Ih e hl'a l 5 ne rated locall y by dama ge a nd vi scoe las ti c defo rIll ati o n. Thi s is ;'" "\' III II;ll l'd a l hi g h cyclin g I"reque nc ies. Sin cc Ih e streng th
__ 0°
- - - [W 1W )51s - - [(±45°,(00»)2 1s
-
- - - - - Woven cloth laminate --------- Chopped strand ma t - - - - - Dough moulding compound
~ 1000
6
""
--- --,
500
[
) -I
"-
""
--._- . . "-
"-
....
--
--- - ---
~,-- ....
-
" ....
...
.. - .......... ....... -...... - ... -. -.. _- ..... -- .. -. -.... - ..... - ..... _......... -. .... - .......... . , - , - -7 - - 1- - - - -r - - - - .. --,.
o
2
3
- ..i - - -- _ ........... _~ _ _... L~_...l...-_
4
5
6
7
Log (N ,) Fi g. 9.1 2 Ex perim enta l SIN, plo ts (Ha rri s 1994). show in g th e num he r o i" eYl' lL-, to failurc durin g fati guc loadin g o r gla ss fibre/ po lyes ter co mpos it es with v; lri o ll s librc di stributi o ns. as a rUll cti o n o r th e peak appli ed IO; ld . T il e slress r; lti o I< (
"""""/""",,,,) IV;IS
0. 1 in:lll
':1 ' "
231
9.3 Sub-critical crock growth
Toughness of composites
232
-{)-W18 -
~ ~ -0
.~
-0---
[(0 ' )/±45' l,
_
[ 0 ' /90 ' 12, [0 ' / ±45 ' /90 ' 1,
233
800
1500
Q..
-o---R = 0.1
a. Ol
.>
'Vi
( 10 .7 )
a m( 1 - f)E Ill
(I -
~
Co 40
f
Er (cv m - ar) a c = am - ( I - f ) E111 + f Er
( 10.9)
Since the ax ial force bal a nce is reli a ble fo r the sla b m od el (§4.1 ), this predicti o n should be quite accura te. (It is no t entirely ri go ro Lls, beca use differenti a l Poi sso n co ntracti o n stra ins a re neglected .) The expansivity in the tran sve rse directi o n, a nd the va lues fo r sho rtfibre a nd pa rti culate co mpos ites, a re mo re di ffi c ult to esta bli sh , SII1C
244
Thermal behaviour
0/ composites
where the stiffness, C, and expansivity, et, are here both tensors, as are the Eshelby tensor, S, (which depends on the aspect ratio of the fibre) and the identity tensor, f. Several features of the curves in Fig. lOA are worthy of note. Firstly, the force balance (Eqn (10.7» and Sehapery (Eqn (10.8» predictions agree well with the Eshelby model, confirming that they are quite reliable. Secondly, the case of spherical particles is quite well represented by a rule of mixtures (linear variation between the expansivities of the consti tu ents). Finally, the transverse expansivity of a (long-fibre) composite tends to rise initially as the fibre content increases. This occurs because, on heating the composite, axial expansion of the matrix is strongly inhibited by the presence of the fibres and the resultant axial compression of the matrix generates a Poisson expansion in the transverse direction , which more than compensates for the reduction effected in the normal way by the presence of the fibres, at least for low fibre contents. Plots such as those in Fig. lOA are of interest to engineers, since they allow the tailoring of expansivity via selection of constituents and reinforcement contents. However, it is important to note that these values are based on elastic behaviour. The associated internal stresses may become large, particularly if the temperature changes involved are substant ial, and under these circumstances the matrix is likely to undergo plastic now, or creep, which will alter the dimensional changes exhibited by the composite and make them difficult to predict.
10.1.3 Thermal cyclillg of ullidirectiollal composites
Large internal stresses can be generated when the temperature of a co mposite is changed. This often occurs during service, since temperature nuctuations of at least severa l tens of QC are likely even with compone nt s which arc not designed for high- (or low-) temperature use. The beh;l viour of composites during such thermal excursions is therefore of practical importance. Composites may respond to the associated intern;J1 stress changes in an inelastic manner. For example. dilatometry (length) measurements made on composites often exhibit significant hysteresis (i.e. the heating and cooling curves do not coincide). A schematic representation of the clTects or thermal cyclin g is presented in Fig. 10.5. This shows changes in axial matri x stress and COIl1 posite strain over a relati vely large temperature ran ge. r(lr ,I matrix pru ll l' to yieldin g (e.g. a ll1etal or;1 therll1opla stic) . Th e Illatri x is initi ;J1l y (pOillt A) t;lk ell ;IS h;IVill !-!- c_ ! !::i~
which is closely analogous to Eqn (6.34) for stiffness. Hatta and Taya (1986) have shown that, for the transverse conductivity of a long-fibre composite, this reduces to the expression
: ~IC
-;> ~0(}\~: , " 1r 1-,- ,- , ...;.,____ :1-;> ..;.....;.I
,
I
I
,
I
,
I
2c
Fig. 10.17 Dcrivation of exprcssio ns for axial and transversc conductivity. SchematiC depiction of (a) thc slab modcl for lo ng-fibre composites, (b) axial heat now and (c) transve rse heat now.
The transverse conductivity, based on the slab model, is obtained by equatin g the heat nuxes through the two constit uents (Fig. 10.17(c))
Q2c
= K2c T: =
Q2f
= KrT( = Q2m = Km Tt~,
( 10 .2 1)
The thermal gradients in the two constituents are related to the overa ll average value by the expression
T:
=I
T(
+ ( I - I ) Tt~,
leadin g to the following express ion for the transvcrse conductivity
K2c =
1-I)-I
I +-(Kr
Km
( 10.22 )
This is analogous to the expression for the tr,lnsverse st illn ess, derived in ~l4.2. As with that derivation, the assumption that th e two ul nslilllcnl s li c ' in scrics' with e; lch olher ic;ld s to thi s ex press ion h -ill !' Il l' ptltlI ;lL·c lIr 1000 "e) durin g most procedures a lso co ntributes to thc difficulties. Thcre is a limited n um bel' of processes which arc feasi blc for prod Ll et ion of ( ' M ( 's, and very few of th ese a rc in COJl1ll1cre i ~ JI Ll se. Th e oVLrv inv PI\'s,' lllLd in
Fig. 11 . 10 (a) A SiC mo nofi lament with a 351lm vapour-deposited laye r o r TiSA l 5V and (b) A Ti SA l 5V/80 vol. % Si C co mposite produced by HIPlI1g ora bundlc o r Ill o nori lamcnts with 8 1lm thi ck coatings (Ward-Close a nd Partridge 1990) .
Fi g. 11 . 11 rellcct s the limit ed cho ice ava il a bl e, a lth ough production de tail s ma y vary wide ly for differe nt materials and a pplica tions. Mo st proeetilll' 's ill vo lve startin ' materia l in th e form of ceram ic powders and thL' iirsl SL' ,tillll h 'Inw t'\lVl'I'S 'L'n c ral aspects o f how these a re handled.
2XX
F(fiJrica t ion
11.3 Ceramic composites
vapour infiltration Fig. 1l.11
Schematic overv iew of the approachcs employcd In fabrication of ceramic matrix composites.
Sections are then devoted to reactive processing methods and to layered composites, neither of which necessarily involve the presence of fibres. Finally, the fabrication of carbon/carbon composites is covered in a separate section, since this case diFFers from most other CMCs and the process is of commercial significance.
11.3.1 Powder-based routes Production of ceramic artefacts by powder-based routes is very well established in industrial practice. Green bodies are produced by cold compaction of fine powders, often with a binder of some type, and these are then sintered or hot pressed so that voids are eliminated by diffusive processes. In some cases a liquid is present during the consolidation, in which case void elimination is assisted by cap illary action and consolidation is much Faster. The problems arise when an attempt is made to introduce fibres into such operations . These difficulties are covered in detail by Phillips (1983) and Chawla (1993) . Fibres can be mixed with powder particles, For examp le by blending or by dragging a fibre tow through a suitab le slurry. However, subsequent conso lid a ti on is then strongly inhibited as the fibres resist the volume contraction or the matrix as it consolidates. Severe matrix cracking, of th e type shown in Fig. 11.12, usually results. In some cases, these con tra c ti oll strcsses can he at leas t partly olTsd by the imposition or a 1;11")',\ ' lJ \' dl(l ~ t ; ltic
1
289
CIn.
Fig. 11 .12 Photograph (Clegg 1992) of a composite made by sintering a powder compact containing dense Zr02- 3% Y 20 3 fibres in a matrix of the same material. Large c racks ha ve formed transverse to th e fibre direction, a long which tensile stresses developed in the matrix as consolidation occurred.
compressive stress, as in the hot isostatic pressing (H IP) process. However, this adds substantially to the processing costs and may not elimin ate cracking entirely. A possible way to resolve this problem is to employ a matrix which is partly , or completely, liquid at the consolidation temperature. This constrains the choice of matrix to those which are likely to show re la ti vely poor properties at elevated temperatures. Nevertheless , there has been interest in making CMCs in this way, using glass or glasscera m ic ma trices. Borosi Iica te glasses and cordieri le (glass-ceramic) have attracted particular attention. However, even when the consolidation can be achi eved without severe matrix crack in g, problems ofte n arise from differential thermal contraction. The misfit strain (see ~i 10.1.1) is often large for systems in which the matrix is fluid at high temperatures , since in such cases it is common for it to exhibit an appreciably highcr thermal expansivity than the fibres. An example of the co nsequences or such diFFerential thermal contraction is shown in Fig. 11 . l l . III .'cllcral , the diFFiculties and const raints on the manur;lctllrC o r rihll' ll' illi'orl'cd ccramics have strongly inhihited commercia l dcvcl()PlIlI'llt
2l)O
Fabricat ion
J J.3 Ceramic composites
291
reinforced MoSi 2 composite made in this way has been shown (Suzuki et al. 1993) to exhibit good creep resistance.
11.3.3 Layered ceramic composites
F ig. 11.13 Optical micrograph (Philiips 1983) of a composite made up of short carbon fibre s in a matrix of magnesia . Matrix cracking has occurred as a result of differential thermal contraction during cooling a fter fabrication.
//.3.2 Reactive processillg Several simil a r processes have been developed in which constituents are brought together under conditions such that a chemical reaction occurs while the mixture consolidates. In several such processes, liquid metal is introduced and progressively oxidises. For example, the directional oxi dation of aluminium is exploited in several processes patented under the 'X O' trade name. An attraction of such procedures is that, by makin g a suitable powder compact into which liquid metal is infiltrated , near-netshape forming is possible. Levels of internal stresses and porosity can be kept low by control over reaction kinetics, thermal gradients and liquid infiltra tion rates . In many cases, there is residual unreacted metal , but this can often be tolerated and may help to raise the toughness. Various composite systems have been developed , including several ba scd on intermetallic matrices (Stoloff and Alman 1990). The oxidation reaction s exploited by the Lanxide corporation have been covered by Newk irk 1' / al. (1987) and a n overview of th e materials produccd by thi s type or processing ha s been presen ted by U rq lIha rt (1991). SOllle good comb inati ons o r properties can be ac hi eved. For L·X; llll pk-. ;1 Si( '-
An attractively simple method of making relatively tough ceramic composites involves stacking thin sheets or tapes in the green state and consolidating these by a sintering operation. The procedures involved have been developed for SiC composites by Clegg and co-workers (Clegg et al. 1990, Phillips et al. 1994). Fine ceramic powder is blended with viscous polymer solutions and then rolled to produce tapes, typically about 200 ~1I1l thick. These tapes are stacked and sintered, after coating with thin (cv 5 J..lm) layers designed to provide weak interfaces which cause crack deflection (see §9. 1.2) and hence raise the toughness. Graphitic layers have proved effective, although they suffer from the disadvantage of very poor oxidation resistance at high temperature. The volume contraction on sintering, and subsequent cooling, ta kes place uniformly and does not res ult in significant internal stresses. Although the graphitic layers have a different expansivity from the SiC, they have a low modulu s and are apparently able to accommodate the shear associated with contraction without becoming damaged. The material is anisotropic, but this is acceptable for many applications (e.g. see § 12.8). The microstructure, shown in Fig. 11.14(a), is very similar to that of certain mollusc shells - see F ig. 11.14(b). The production process is relatively quick and cheap, since it does not involve either handling of fibres or application of pressure.
11.3.4 Carboll/carboll composites Carbon is an excellent high-temperature material , provided it is not exposed to oxidising environments. The excell ent mechanical stability of carbon at high temperature , particularly when suitable internal interfaces are present, has led to its use in several important applications (F itzer 1987), notably aircraft brakes (§ 12.9). Another consequence of th is sta bility, however, is that it cannot be sintered. There are two basic approaches to production of carbon /carbon composites. Both in volve the infiltrat io n o f a carbon-bearing fluid into the interstices between an array of carbon fIbre s. In both cases, the main concern is with achieving co mplete in III t ra t ion ill a rea so na bly sho rt time . F ull technical details ;m : ,ivcn hy MeAlli stcr ;Ind La chman ( 19lSJ). The two routes arc shown se ll 'nl ;lti e; tll y ill h g . 11 . 1 . Dllrin g liquid impreg nati o n. a pitch or resin
F(/hric({liOIl
References and further reading
293
is injected and then heated so that it decomposes to leave a carbon deposit. Chemical vapour impregnation (CVI), which can also be app lied to various other composite systems (Chawla 1993), involves injection of a suitable hydrocarbon gas, such as methane, together with hydrogen and nitrogen, which decomposes at the infiltration temperature to deposit carbon on the fibres. For both liquid and gaseous impregnation, severa l cycles of heating and cooling are necessary to complete the operation. Furthermore, it is common to set up a thermal gradient across the component, in order to encourage complete infiltration before the supply of fluid becomes choked off by closing of channels near to the source of fluid. For these reasons, processing is timeconsuming and costly.
F ig. 11.14 SEM micrographs (Clegg el al. 1995) of (a) a layered SiC/graphite composite, with the SIC layers about 200 ~lm thick and (b) a layered ca lcium ca rbonate! protell1 composite in the mollusc she ll pinctada margaritifera.
Liquid impregnation - thermosetting resin - pitch
Chemical vapour deposition - hydrocarbon gas (1000-1200 "C) ; repeat 1-3 times 1-5 times
composite I :ig. I I . I::;
Sc iJ e mal ic ove rvi ew (M c A lIi sle r 1994) o r mcthods oi" pr(ldllc l iOI1 o i" ca rh()l1 /c~ 1 rbu n co III posi tes.
References and further reading Becker, W. E. ( 1979) Reaclioll Injection Moulding. Van Nostrand Reinhold: New York Blake, J. (1989) Composite Materials. Hobsons Publishing: Cambridge Chawla , K. K. (1993) Ceramic Matrix Composiles. Chapman & Hall: London Clegg, W. J. (1992) The fabrication and failure of laminar ceramic composites, Acta Metall ., 40 3085- 93 C legg, W. J. , Kendall, K. , Alford , N. M. , Birchall , D. and Button , T. W. ( 1990) A simple way to make tough ceramics, Nature 347 455- 7 C lyne, T. W. and Mason , J. F. (1987) The squeeze infiltration process for fabrication of metal matrix composites, M etall. Trans. , 18A 1519- 30 Clyne, T. W. and Roberts, K. A. (1995) The influence of process parameters on consol id ation efficiency when forming titanium composites by spraying onto monofilaments, Acta Metall. Mat er., 43 254 1 50 Clyne, T. W. and Withers, P. J. (1993) All Introduction 10 Metal Matrix Composiles. Cambridge University Press: Cambridge Everett , R. K. ( 1991) Deposition technologies for MMC fabr ication , in Metal Matrix Composites: Processing and Intel/aces. R. K. Everett and R. J. Arsenau lt (eds.) Academic Press: Boston pp. 103 19 Feest , E. A. ( 1988) Exploitation of the metal matrix composites concept, M etals and Materials , 4 273- 8 Fitze r, E. (1987) The future of carbon-carbon composites, Carbon , 25 163- 90 Folkes, M. J. and Russell , D. A. M. (1980) Orientation effects during the flow of short fibre reinforced thermoplastics, Polymer, 21 1252- 8 G o tch , T. M . (1994) Spray deposition , in Handbook 0/ Polymer Fibre COlllflosites. F. R. Joncs (cd .) Longman: Harlow pp. 205- 9 Iloo ver. W . R . (1991) Di e ca stin g of Duralcan™ composites, in M etal Matrix COIII/}().\"it!'.\" /'roc('.\"sillg. Microstrllctllre alld Properties . N. Han sc n el al. (ed s.), RI '" N: lli o l1 :Ii I.aho rat o ry: D c nmark pp. 3X7 92 .I o nl's, I: I{ (1 ')1).1) A 11I Ol'I:IVl: mo uldin g, in /Ill/If/hook of'l'oll 'lIler Fi/m' ( '(/ III/ ,(/"t", I , I{ l" lll" (l' d .) I. o l1 g m:llJ: 1larlu w pp . !.I X 4.1
294
Fabrication
Klier, E. M ., M ortensen, A. , Co rnie , J. A. a nd F lemin gs, M. C. (199 1) Fabrication of cas t pa rticle-reinfo rced m etal s via press ure infiltration , J. Mat. Sci. , 26 2519~26 L1oyd , D. 1. (1989) The solidifica ti o n mi cros tructures o f particulate reinforced AI /Si C composites, Comp. Sci. & Tech. , 35 159~80 L1oyd , D. J. (1991) Factors influencin g the properties of particulate reinfo rced composites pro duced by m o lten metal mi xin g, in Metal Matrix Composites ~ Processing, Microstructure and Properties. N. Hanse n et al. (eds.) Ri s0 Nationa l Laborato ry: Denmark pp. 8 1 ~99 Martineau , P. , Lahaye, M. , Pa iller, R. , Naslain, R ., Co uzi, M. a nd C ruege, F. ( 1984) SiC filament / tita nium matrix comp osites rega rded as m odel co mposites. Part 2 : Fibre/ matri x chemical interact ions at hi gh temperatures, J. Mat . Sci., 19 27 49~7 0 McAllister , L. E. (1994) Ca rbon-carbo n co mposites, in Concise Encyclopaedia 0/ Composite Materials. A . Kelly (ed.) Pergamo n: Oxford McAllister, L. E. a nd Lachman , W. L. ( 1983) Multi-directio nal ca rbo n-carbon composites, in Fabrication 0/ Composites. A. Kell y and S. T . Mileiko (eds.) N o rth-Holl a nd: Amsterdam pp. 10 9~76 Middleton , V. (1994) F ilament winding, in Handb ook 0/ Polymer Fibre Composites. F. R. Jon es (ed.) Longman: H a rl ow pp . 154-60 M o rtense n, A. a nd Corn ie, J . A. ( 1987) On th e infiltra ti o n o f m etal matri x composites, Metall. Trans. , 18A 11 60~3 Newkirk , M. S. , Lesher, H. D., White, D. R. , Kennedy , C. R., U rquhart, A. W. and C laar, T. D. ( 1987) Preparation of Lanxide ceramic composite mate ri a ls: m a tri x formation by th e directed ox idat io n of m o lten m eta ls, Ceram. Eng. Sci. Proc. 8 879~95 Phillipps, A. J., C legg, W. J. and Clyne, T. W. ( 1994) The failure o f laye red ce ra mics in bending and tension, Composites 25 52 4~ 33 Phillips, D. C. ( 1983) F ibre-reinforced ce ra mics, in Fabrication 0/ Composites. A. K ell y and S. T. Mileiko (eds.) North-Holland: Amsterdam pp. 373--428 Skibo, M. , Morris, P. L. a nd L1oyd , D. J. (1988) Structure and properties of liquid m eta l processed SiC reinfo rced a luminium , in Cas t Reinforced Metal Composites. S. G. F ishm a n a nd A. K . Dhingra (eds.) ASM pp. 257~6 1 Smith , C. S. ( 1990) Design 0/ Marin e Structures in Composite Materials. E lsevie r: London Smith, P. R. a nd Froes, F. H. (1984) Developments in tit a nium met a l m a tri x co mpo sites, J . Metals , 36 1 9~26 Stoloff, N. S. a nd Alman, D. E. ( 1990) Inn ova tive processin g tec hniqu es for intermeta llic matri x composites, M RS Bulletin , 15 47~ 53 Suzuki, M. , Nut! , S. R. and Aiken , R. M . (1993) C reep behaviour of an SiCreinforced XD MoSi 2 co mposite, Mat. Sci. & Eng. , AI62 73~82 Upadhyaya, G. S. ( 1989) Powder metallurgy m etal matri x compositcs : a n ove rvi ew, Met. Mater. Process, I 2 1 7~28 Urquhart, A. W. (1991) N ovel reinforced ceramics a nd met a ls: a rev iew o f Lanxide's co mposite techno logies, Mat. Sci. & Eng. , A 144 75 82 Ward- C lose, C. M. and Partridge, P. G. ( 1990) A fibre coa tin g proccss for advanced metal matrix co mp osites, 1. Mat. Sc i., 2543 15 23 W ells, G . M. and M cA nult y, K. F . ( 1987) Co mputer-a id cd fil amc nt wi nd in g usin g no n-geodesic trajectorics, in hoc. ICCM6, Vo l.! . F . L. Matlh cws I't al. (eds .) Elsevier: London pp. 16 1 73 Willis, T. C. (1988) Spray dcpositi o n proccss fo r Illctailll ;ll rix cO lllposilc manufaclurc, MI'/ols olld MO/l'I'iol.l' , 44X 5 X
12 Applications
Composite materials are used in a very wide range 0/ industrial applications. In this chapter, the objective is to identify some 0/ the considerations in volved in commercial exploitation 0/ composites. This is done by means o/a/ew case studies and there is no attempt to present a systematic survey. The examples given cover a range o/composite type, engineering complexity, manu/acturing route, market si::e and competitive position relative to conve11lional materials. A t the beginning 0/ each case study, a list is given identifying the reasons/or preferring a composite to more conven tional engineering materials. Although the examples are spread over the .lidl range 0/ matrix types, the bulk 0/ the annual composite production 0/ around 10 million tonnes is currently inthe/OIm o/PMCs. At the start o/each example, a list is given
0/ the requirements 0/ the application. 12.1 Minesweeper hull • • • • •
low density ease of moulding to complex shape non-mag netic good resistance to corrosion and marine fouling good resista nce to fatigue and stress corrosion crack ing
Glass-reinforced plastic (GRP) is now very popul a r for various land and sea transport applications. While la rge ships are usuall y co nstructed in stee l, over 80 % of marine hull s less than abo ut 40 m in length are m ade ofGRP (Sm ith 1990). This is partly because fabricatio n in GRP is more econom ic for relatively smal l craft. Also of impo rtance, however, is the sco pe for ;1l' hi L'vin)2, weight reductions and eas ier maintenance. Addi li oll ;ili y, Ih t'Il' ; ll'l' l'L'I' i;lin app li cal ions in which the ma g netic,
296
Applications
Applications
~j -' . - -. ~;:;-~~ "' - ---. --.. - ... . .
~- .
-J:. '.
,
p
N ~.-
297
electrical or thermal properties of GRP are preferable to those of steel. An example is provided by minesweepers, which need to be non-magnetic in order to avoid activation of magnetic mines. A hull of this type is usually fabricated by contact moulding, using cold curing polyester resin and E-glass fibre , against an open female steel mould. The mould face is prepared by facing with epoxy, polishing and coating with a release agent. The glass fibre is placed against the mould , commonly in the form of a sequence of plies of chopped strand mat, woven rovings and unidirectional laminae (see §3.2.2). For a fairly large ship, such as a 40-m long minesweeper, the thickness of the layup is ~ 30-50 mm. This is too thick for placement and impregnation with resin to be carried out easily by manual methods. A semi-automated arrangement along the lines illustrated in Fig. 12.1 is normally uscd. Draping of the fibre lay-ups, mixing of resin and catalyst and pumpin g of the mixture to roller- impregnators is carried out on moveable gantries. Lay-up weights are typically ~ 2 kg m- 2 ; these can be quickly and fully wetted-out using this procedure. Production of a hull with these dimcnsions is completed in about 10 weeks (Smith 1990).
12.2 Sheet processing rolls • • • • •
(c) F ig. 12. 1 A ut o m a ted lay -up o f a la rge m a rin e hull in G RP (S mith 1990). (a) Secti o n thro ug h hull , sho win g ga ntry fo r place ment a nd wet-o ut o f glass libre m a ts. (b) Stiffe nin g ribs, fo rm ed ove r cores o f ex pa nded po lym e r fo am . (c l Sc hem a ti c pe rspec ti ve view of a min esweepe r hull un de r con stru ct io n .
high beam stiffness (ex: Young's modulus) high torsional stiffness (ex: shear modulus) low density good thermal stability good surface finish
High-performance rolls are needed for many processes involving the handling of thin sheets such as newsprint, plastic sheets, etc. In many cases, the rolls need to be relatively wide and so they need a high beam stifflless (= moment of inertia of section x Young' s modulus of material) in order to avoid excessive bending. A further requirement is that they can be rotated at high speed. This presents difficulties, since rolls with sufficient beam stiffness tend to be so heavy that they become unstable at high rotational speeds. Furthermore, roll speed cannot bc changcd quickly. In the past, steel rolls were employed , but the abovc rcquiremc nt s for li ght , stiff structures have Icd to thcir rcplacmcnt hy carhon fibrc /c po xy co mpos it es, produccd by filam c nt windin g Oi 11 . 1. 1) . A prohlc1l1 with Ih ' m;lnuf"a cture of suc h roll s I"rom tlhn.: co mposil cs ari ses I"rolll Ih l' I IlT d Ip l ho lh he ndin g and lo rsiollal slillll L'ss. T o rsioll ;iI
298
Applications
Applications
stiffness is needed to ensure that the rolls do not distort excessively when a torque is applied to make them rotate . Torsional stiffness is dependent on the shear modulus of the material. The dependence of (axial) Young's modulus, E , and shear modulus , G, on the winding angle, rP, for an angleply epoxy/65% carbon -fibre composite is shown in Fig. 12.2. A very low winding a ngle would result in both moduli being low. Peak shear stiffness occurs at rP = 45°, whereas the maximum in Young's modulus is at rP = 90°. At an angle of about 60°, values of E and G are about 70 GPa and 50 GPa respectively , which compare very favourably with steel (E '" 210 GPa , G '" 80 GPa) when account is taken of the fact that the composite has a density which is about one-fifth that of the steel. In industrial usage, weight savings of 75% have been achieved when replacing steel rolls. Rolls up to 9 m long and 0.35 m in diameter have been manufactured. The excellent surface finish required is obtained for the composite rolls by coating them with a thin layer of metal or rubber.
12.3 Helicopter rotor blade
• • • •
299
high beam stiffness (ex: Young's modulus) high torsional stiffness (ex: shear modulus) Iow density good fatigue resistance
The rotor blade of a helicopter provides a good example of a component requiring excellent specific stiffness. The blades act as aerofoils which generate lift. A typical rotor blade shape and rotor hub assembly configuration can be seen in Fig. 12.3. Composites have been used for rotor blades, and for other helicopter components, since the 1960s. Initial attractions of using composites included good fatigue resistance as well as specific stiffness. Full use has also been made of the scope for tailoring the elastic properties via control of the fibre arch itecture and improved aerodynamic blade designs have emerged by stress and fluid
300 - - Young's modulus (HM fibre) ,---.
250
. . . . . Young's modulus (HS fibre)
~
0.
8
.•..•... - Shear modulus (HM fibre)
'"
200
""E
ISO
:l
-a 0
.~
AD
'" ~
\il
100
SO .....
.... .. '
..............
.......
10
20
30
40
SO
Winding angle, cp
60
70
80
90
n
Fig. 12.2 Predicted dependence of Young' s m odu lus and shear m o dulu s o n the wind in g angle, for a tube of angle-pl y epoxy/65% ca rbon (!-I M) IIbre composite, loaded in bending or torsion. A Y o un g's m od ulu s pl o t is also s hown for usa ge of high-stren g th (!-IS) carbon IIbres. The plots were ob tain ed by the method s out lin ed in ~i 5.3. 1 . usin g property data g iven in Tahles 2.2 :Ind 2.5. The IO:ldi ll' :llI g lc for this gCO ll1cl ry is g iven hy (l)O' 'M .
I:ig . 12 ..1
I'IHlto g r:lpli 01':1 Wes tland !\gusta E lflOI helicopter. (Courtesy or Wes t 1:lnd Ilclicoptns) .
300
Applications
Applications
dyn a mics modelling, utilising the anisotropic properties of the material (Holt 1994). A particular problem arises with helicopter blades from the combination of forward and rotational motion. Since the forward velocity of the aircraft may be up to about 100 m S- I and the linear speed of the rotating blade, even at its tip, is often little more than 200 ms - I, the airspeed of the blade during the advancing part of the rotational cycle is often substantially greater than that during the retreating phase. If the pitch angle of the blade were the same during each part of the cycle, then the uplift would vary substantially on the two sides of the aircraft and it would be tipped over. Compensation for this effect is achieved by altering the pitch angle of each blade during every rotation. Further changes in pitch angle are used to alter direction during manoeuvring. It is therefore very important that the blades have adequate torsional stiffness, since they must respond quickly and faithfully to pitch-angle changes imposed at the rotor hub. The beam stiffness of the blade must a lso be high , to ensure that the tip does not lag behind during rotation or flap under its own weight excessively. From this point of view, the requirements are similar to the rolls in § 12.2, but the blade presents much greater complexity in terms of section al shape, loading configuration and fatigue performance. The construction of a typical blade section is shown in Fig. 12.4. The necessary torsional stiffness is provided by the carbon fibres at rv ± 45° to the blade axis (see §12.2). The carbon and glass fibres aligned parallel to the blade axis provide the beam stiffness necessary to minimise lag and flap. This construction also confers exce llent fatigue resistance.
12.4 Golf driving club
± 45 ' carbon
Titanium erosion shield
Elecnical heater mat
fibre/epoxy ~
± 45 ' carbon fibre/epoxy
Fig. 12.4
/
'NomexTM' (epoxy) honeycomb
Unidirectional glass-carbon/epoxy hybrid
Schematic section through a typical composite construction for a heli copter rotor blade. (Courtesy of Westlancl Helicopters .)
• • • •
301
high beam stiffness (ex Young's modulus) high torsional stiffness (ex shear modulus) Iow density high strength
There are many applications in sports goods with a requirement for stiff, slender beams. These include fishing rods, tennis racquets, skis, surfboards and go lf clubs. Polymer-based composites hold a dominant share in all such markets. The sports goods market is one in which small improvements in component performance often justify significant increases in material or manufacturing costs. The golf club (driver) provides a good example of a competitive market with a high premium on performance. As with the previous two case studies, there is a need for the golf club shaft to have good stiffness both in bending and in torsion. High torsional stiffness is very important, since this ensures that the shaft does not rotate significantly under the torque imposed when the club head strikes the ball; any such rotation would introduce an error in the direction of flight of the ball. The requirements for bending stiffness are slight ly more complex; some bending of the shaft on impact with the ball may be beneficial, since subsequent straightening can increase the contact time between club head and ball and hence increase the momentum transfer. Designs with a massive club head and slender shaft (see Fig. 12 .5(a» favour increased length of drive. However, in a shaft of low beam stiffness, the axial stresses induced during contact with the ball will be higher and the danger of damage or fracture correspondingly greater. The axia l strength of the shaft therefore becomes a key issue. In view of these requirements, hybrid fibre architectures (i.e. involving more than one type of fibre) have been developed. An example of a typical construction is shown in Fig. 12.5(b). In this case, the club shaft has several layers of carbon fibre laminae at relatively high angles to the shaft axis. These confer high torsional stiffness. Among the axial laminae are some reinforced with boroll monofilaments . These have a similar stiffness to carbon (HM), but higher strength (see Table 2.2). In particular, they have a high compressive strength , and are more resistant to bucklin g than most fibres because of their large diameter (rv 100pm). Th ese libres improve the fracture strength on the tensile side of the shal"i :Ind , parli clll:lrl y, redu ce the dan ger of failure by kink-band formalion ()Il Ih c cOlllprcss ivc sid e. Thi s o\"\"set s the di sadvanta ges of hi gher dc nsil y ;111(\ ("1l , 1 I II 11I l" hlll"O n lihrt.:s (Bu c k 1992 ).
302
Applications
A ppiic(f / ions
303
12.5 Racing bicycle • • •
high stiffness good fatigue resistance low density
Both DURALCAN and Aerospace Metal Composites (AMC) have developed bicycle frames for commerci a l sale. The DURALCAN AI(6061)/ I 0%A1 2 0 3p composite material is used in the ' Stumpjumper M2 ' mountain bike manufactured by Specialized Bicycle Components Inc. , while AMC AI(2124) /20%SiC p material is used for the frame of Raleigh racing bikes. Both models have been successfully tested in extensive sports trials. In the former case, tubing of cv I .S-mm wall thickness is extruded and rejoined under pressure a round the tube mandrel. The tube sections are then MIG fusion welded , using conventional techniques. In the case of the AMC frame , the material is made by a powder route and then the tubing is adhesively joined. The application of both types of joining procedure to MMCs is described by Ellis et al. (1994) . In addition to improved specific stiffness, both frames have exceptionally good fatigue endurance, as a result of the enhanced value of 6.K th (see §9.3.1) compared with unreinforced material. F a ti gue data for welded tubes have confirmed that the performance of particulate MMCs is superior to that of corresponding unreinforced aluminium (Harrigan 1994). A photograph of the Stumpjumper bicycle in action is shown in Fig. 12.6. Some of the manufacturing procedures involved in producing this bicycle a re given by Klimowicz (1994).
12.6 Diesel engine piston • • • •
good wear resistance high thermal stability high-temperature strength go od thermal conductivity
Thi s appli cation represents a major early s uccess in the industrial use
or MM Cs. Production in Japan has been increasing steadily over the past Fig. 12.5 (a) Photograph of the head of a golf club driver. (b) Schematic secti o n throu gh a hybrid carbon fibre/ boron monofilament construction for a golf club sha ft. (Co urtesy of Textron Specia lity Materials).
se veral years a nd no w runs to millions of units annually. Originally, a Ni ca st iro n (Ni -res ist™) insert wa s used in the ring area of alumin ium pi ston s in o rd e r to preve nt seizure of the pi s ton ring with the top ring g roove 65 %), and machining and brazing distortion minimised « ± 50 ~Lm) . In add ition , if the housing is cast it is possible to leave an unreinforced region on top of the side walls to aid
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