Mechanical testing of advanced fibre composites

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Mechanical testing of advanced fibre composites

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Mechanical testing of advanced fibre composites Edited by J M Hodgkinson

Cambridge England

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Published by Woodhead Publishing Limited, Abington Hall, Abington Cambridge CB1 6AH, England www.woodhead-publishing.com Published in North and South America by CRC Press LLC, 2000 Corporate Blvd, NW Boca Raton FL 33431, USA First published 2000, Woodhead Publishing Ltd and CRC Press LLC © 2000, Woodhead Publishing Ltd, except chapters 6, 8, 11 and 15, Crown copyright. The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publishers cannot assume responsibility for the validity of all materials. Neither the authors nor the publishers, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from the publishers. The consent of Woodhead Publishing and CRC Press does not extend to copying for general distribution, for promotion, for creating new works or for resale. Specific permission must be obtained in writing from Woodhead Publishing or CRC Press for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress. Woodhead Publishing ISBN 1 85573 312 9 CRC Press ISBN 0-8493-0845-3 CRC Press order number: WP0845 Cover design by the ColourStudio Typeset by Best-set Typesetter Ltd., Hong Kong Printed by TJ International, Cornwall, England

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Contents

Preface List of contributors

1

xi xiii

Introduction j m hodgkinson

1

References

3

2

General principles and perspectives s turner

4

2.1 2.2 2.3 2.4 2.5 2.6

Mechanical testing in perspective Formal framework for mechanical test methods Special features of the mechanical testing of composites Nature and quality of test data Mechanical tests for long-fibre composites Concluding comments References Bibliography

4 10 13 19 24 33 34 35

3

Specimen preparation f l m atthews

36

3.1 3.2 3.3 3.4 3.5 3.6

Introduction Laminate production Quality checking Specimen preparation Strain gauging Summary References

36 36 39 39 41 42 42 v

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Contents

4

Tension e w godwin

43

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

Introduction Testing equipment Specimen details Test procedure Data reduction Material and sample preparation Practical example Future developments References

43 50 56 62 64 67 70 71 73

5

Compression f l m atthews

75

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

Introduction Types of test Standards Specimen preparation Specimen configurations Execution and problems Typical results Conclusions References

75 76 82 83 85 87 89 97 97

6

Shear w r broughton

100

6.1 6.2 6.3 6.4 6.5

Introduction Test methods Summary of test methods Comparison of data Recommendations and concluding remarks Acknowledgements References

100 101 118 118 118 122 122

7

Flexure j m hodgkinson

124

7.1 7.2 7.3 7.4 7.5 7.6

Introduction Three-point and four-point flexure tests Comparison of recommended test methods Failure modes Typical data Steel versus soft lined rollers

124 125 128 133 133 138

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Contents

vii

7.7 7.8

Through-thickness flexure Conclusions References

140 141 141

8

Through-thickness testing w r broughton

143

8.1 8.2 8.3 8.4 8.5 8.6

Introduction General issues Tensile test methods Compression test methods Shear test methods Concluding remarks Acknowledgements References

143 144 146 156 160 167 167 168

9

Interlaminar fracture toughness p robinson and j m hodgkinson

170

9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8

Introduction Terminology and typical values Overview of test methods and standards Mode I testing Mode II testing Mixed mode I/II Multidirectional laminates Conclusions References

170 170 173 178 194 200 204 206 207

10

Impact and damage tolerance p j hogg and g a bibo

211

10.1 10.2 10.3 10.4 10.5 10.6 10.7

Introduction Impact testing Damage tolerance – compression after impact (CAI) tests Boeing test methods and related variants Data interpretation Standardisation status Future trends References

211 211 228 229 235 241 243 244

11

Fatigue p t curtis

248

11.1 11.2

Introduction Basic test philosophy

248 249

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Contents

11.3 11.4 11.5 11.6 11.7 11.8

Machines and control modes Presentation of data Monitoring fatigue damage growth Potential problems Fatigue life prediction Post-fatigue residual strength References

254 256 256 261 264 266 266

12

Environmental testing of organic matrix composites g pritchard

269

12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 12.12

Introduction Why environmental testing? Environmental threats to composites Standard tests Sample conditioning Experimental approaches Determination of sorption behaviour Lowering of Tg by absorbed liquids How do composites perform in adverse environments? Diffusion of liquids into composites Classification of absorption categories Edge corrections References

269 269 270 271 275 276 278 279 280 284 288 289 291

13

Scaling effects in laminated composites c soutis

293

13.1 13.2 13.3 13.4 13.5 13.6

Introduction Background Investigation of failure Practical application examples Specialised scaling techniques in composites Concluding remarks References

293 294 294 304 308 311 312

14

Statistical modelling and testing of data variability l c wolstenholme

314

14.1 14.2 14.3 14.4 14.5

Introduction Importance of looking at data plots Basic statistics Distribution of sample statistics Testing for differences between samples

314 314 316 317 317

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ix

14.6 14.7

Comparing several samples simultaneously General linear model (GLM) References

325 331 339

15

Development and use of standard test methods g d sims

340

15.1 15.2 15.3 15.4 15.5 15.6

Introduction Development of test methods Validation of test methods Sources of standards and test methods Harmonisation of composite test methods Recommended mechanical test methods References Bibliography – selected ISO standards Appendix – contact details for standards organisations

340 341 343 347 352 355 355 356 357

Index

359

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Preface

Mechanical property data are essential in the design process if structures are to perform as intended – reliably and cost-effectively for their full life. However, there are no data without testing at some stage. But what tests should be carried out to give the required data? How, precisely, should the tests be conducted, and who says so? What does the data actually mean? How reliable are the data produced? Are data obtained from small test specimens meaningful when large structures are being designed? What effect will the operating environment have? Fortunately most, if not all of these questions have been answered in the case of isotropic solids, giving a starting point for the development of mechanical test methods for more complex materials such as advanced fibre composites. This book attempts to set out the current position with regard to these potentially highly anisotropic materials, which are finding repidly increasing applications despite their complexity. The expression ‘advanced fibre composites’ probably means different things to different people. To many it might encompass only carbon and a small group of thermoplastic fibres including aramid and polyethylene, to the exclusion of glass fibres. However, in some industrial applications, glass fibres, whilst not necessarily being deemed as advanced in any particular sense, are the only fibres which can fulfil the specific design and environmental requirements. So perhaps the term ‘advanced’ in this context is really application driven. As far as this book is concerned much of the discourse surrounds high modulus, high strength fibre/plastic matrix composites, but not exclusively so, it is high performance which is the key. It has been left to the author(s) of each chapter to judge for themselves, from their own interests and experience, precisely what to include. It is in any case quite clear that, for most of the mechanical test methods described, relatively minor modifications allow perfectly good results to be obtained across the whole range of fibre/matrix combinations, from the most exotic to the most humble. This book has developed out of a short course of the same title which xi

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Preface

has normally run on a yearly basis at Imperial College (London University) since 1989. The course has now seen over 250 delegates ‘graduate’; they have come from a wide variety of industry sectors and from all over the world. The course has been supported by experts in their field from Queen Mary and Westfield College (London University), the National Physical Laboratory, the Defence and Evaluation Research Agency and City University. I am indebted to these colleagues, and those from Imperial College, who have not only taught on the course but have also given up a great deal of valuable leisure time providing their copy for the book. A special thankyou goes to Professor Geof Pritchard, the only contributor to the book who hasn’t taught on the course, which has a section on Environmental Effects but, in comparison to the book chapter, is probably woefully inadequate. In recognition that not everybody has the same interests in life, this book is organised in chapters dealing with particular types of test (tension, compression, shear, etc.), allowing the reader to ‘dip in and out’ as he/she wishes. It is my hope that the reader finds the book both informative and interesting and that it encourages best practice as it is currently known, across the various industrial sectors making use of fibre-reinforced plastic matrix composites. It is as well to remember that a bad test is not worth doing and that even the best test can be done badly. It is all in the detail. JM Hodgkinson

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List of contributors

Dr G A Bibo British Aerospace Australia 41-45 Burnley Street Richmond Victoria, 3121 Australia Dr W R Broughton National Physical Laboratory Teddington Middlesex TW11 0LW Professor P T Curtis Structural Materials Centre Building A7, Room 2008 Farnborough Hampshire GU14 6TD E W Godwin Centre for Advanced Composite Materials Imperial College Prince Consort Road London SW7 2BY Dr J M Hodgkinson Centre for Advanced Composite Materials Imperial College Prince Consort Road xiii

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xiv

List of contributors

London SW7 2BY Professor P J Hogg Department of Materials Queen Mary & Westfield College University of London 327 Mile End Road London E1 4NS Professor F L Matthews Centre for Composite Materials Imperial College Prince Consort Road London SW7 2BY Professor G Pritchard York House Moseley Road Hallow Worcestershire WR2 6NH Dr Paul Robinson Department of Aeronautics Imperial College Prince Consort Road London SW7 2BY Dr G D Sims National Physical Laboratory Teddington Middlesex TW11 0LW Dr C Soutis Department of Aeronautics Imperial College Prince Consort Road

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List of contributors London SW7 2BY Dr S Turner Department of Materials Queen Mary & Westfield College University of London 327 Mile End Road London E1 4NS Professor L C Wolstenholme School of Mathematics City University Northampton Square London EC1V 0HB

xv

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1 Introduction J M HODGKINSON

In the mind of the general public the term ‘composite materials’ is largely either misunderstood or not understood at all. There is a reasonable idea of what might be expected of some other materials and what they might be used for. Steel is used for fabricating the skeleton of many buildings (or inside the concrete) and for most automobile body shells; copper is used for electrical wiring; aluminium is used a lot in aeroplanes; plastics (of whatever colour) are used for almost everything. However, even with these isotropic homogeneous materials there is little real understanding of why they are used for particular applications. This is not an unreasonable situation. Most people have more to concern themselves about in their lives than why a specific screw could be made from steel, brass or a plastic. It does not matter whether people understand, or not. Quite rightly the expectation is that the goods that they purchase, or make use of in some way, are fit for purpose. This is where the mechanical and other types of materials testing comes in. In order to design a structure or component so that it is efficient and fit for purpose, the shape of each subcomponent needs to be decided upon, taking into account the material it is to be made from. This means that careful consideration must be given to the intimate relationship between how the component is supposed to perform in service and the properties of the material from which it is made. This can be a tricky balancing act even with isotropic homogeneous materials but substantially more difficult when attempting to make use of materials which are not isotropic and not homogeneous. How does one go about deciding what a material is capable of, mechanically speaking? Well, first one needs to know what the beast one is dealing with is made of, and in this book we are concerned with what are generally termed advanced fibres in a plastic matrix. The fibres involved in the discussion are carbon, aramid and glass, normally continuous rather than short fibres. The resins considered are epoxies and a variety of thermoplastics. For the most part, but not exclusively, we are concerned with laminates of 1

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these fibres and resins. Given any knowledge of the way that homogeneous materials react to the application of loads of varying types, it does not take much thought to come to the conclusion that these fibre-reinforced plastics are an entirely different breed, and that considerable thought and experimentation might be needed to describe, adequately well, their mechanical properties. This is what this book is all about. We need to be able to establish how these materials react to all types of loading, be they tensile, compressive or shear, of short-term or long-term duration, or cyclic, in the presence of high or low temperatures, or other environments which might significantly modify their behaviour, in the same way that we can for homogeneous materials. Designers can then make use of the information to create structures which perform within the design requirements. These structures include large parts of military and civil aircraft, racing cars, automobiles, buses, coaches, lorries, railway and military vehicles, boats, ships and other marine vehicles, a wide variety of sports, home, office, recreational and other leisure goods and, increasingly, civil engineering structures. The tests which can be carried out to ascertain the behaviour of these materials depend on testing machines which have been designed and built, not necessarily with this particular range of materials in mind, but are generally adequate for the purpose. Quite frequently it is the subtesting equipment (i.e. testing jig), specimen design and other experimental arrangements which address the special reqirements of these materials. Subsequent chapters in this book describe the specimen design and how the tests might be carried out, as far as possible to best practice, under different loading regimes, with due regard given to the statistical analysis of the data produced and progress in the development of test methods from initial conception to full international acceptance. During the period of this book’s development there have been numerous initiatives by standards organisations worldwide to update existing methods and produce new standard test methods to satisfy (or at least to attempt to satisfy) the particular requirements of advanced fibre-reinforced plastic matrix composite materials. The ‘push’ for these better, or new, test methods to be developed, refined, written into standardised form and finally adopted, preferably at international level, has come from the ‘grass roots’, largely (but not exclusively) driven by the aerospace industry. Although it is clear that many other organisations were involved in these developments in the 1980s and 1990s (and might have been equally concerned about the dearth of appropriate standardisation for this class of materials), a key catalyst appears to have been the Composites Research Advisory Group (CRAG), which set about in the early 1980s to attempt to define what the best practice should be over a range of test methods. The

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Introduction

3

Group reported the results of its preliminary deliberations in 1985 and in a final report1 in 1988, but by this time numerous sections of industry, research organisations and university researchers (primarily but not exclusively in the UK) were making use of the recommendations. The CRAG recommendations were proposed to the British Standards Institution and subsequently had a considerable effect in the development of new international standards. From start to finish the process has taken the best part of 20 years to establish a fairly coherent and comprehensive body of standards at international level. One is tempted to suggest that this is an extraordinarily long time. It is also a time during which the influence of the aerospace industry on the future of composite materials has diminished somewhat. At least we are left with the legacy of the standards.

References 1. P T Curtis (ed.), CRAG Test Methods for the Measurement of the Engineering Properties of Fibre Reinforced Plastics, Royal Aircraft Establishment, Technical Report 88012, February 1988.

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2 General principles and perspectives S TURNER

2.1

Mechanical testing in perspective

2.1.1 Overall objectives of mechanical testing Humanity’s utilization of materials has always been supported by testing activities, which have developed over the centuries from crude tests of the fitness-for-purpose of service items to the modern science-based procedures that support all aspects of the science and technology of materials and their utilization. There is now a mutual dependency between advances in scientific knowledge and test method development, with first one and then the other providing an enabling facility for further progress in the development of versatile evaluation programmes capable of supporting various essential industrial operations. In the particular case of mechanical tests those operations include: • • • • • • •

quality control quality assurance comparisons between materials and selection design calculations predictions of performance under conditions other than those of the test indicators in materials development programmes starting points in the formulation of theories.

This list is a simplification, in that some of the functions overlap and several are linked by lateral connections which become effective at various stages in the conversion of materials into end-products. But, in isolation, these functions make different demands on the data, and therefore, the resources that are deployed need to be matched carefully to the demands of particular circumstances. For instance, quality control can usually be achieved by the use of simple test procedures provided that they reflect relevant mechanical characteristics of the product; the simplicity of the test procedure and precision of the data are usually deemed far more 4

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General principles and perspectives

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important than scientific rigour and accuracy whereas, in contrast, the priorities would be reversed for a procedure used to generate data for a design calculation. Some test methods are multipurpose via a variety of operating procedures. Thus, a conventional tensile test operated under fixed conditions may serve a quality control function whereas, operated with controlled variation of influential factors such as temperature and straining rate, it may provide a first-order estimate of load-bearing capability. On the other hand, some test methods are uniquely dedicated to a single purpose and the data they yield could be misleading if used in a wider context. There is another complication in materials testing. The property value derived from a mechanical test varies with the state of internal order of the tested item, which for many classes of material is sensitive to the production route and other factors. Each sample or test specimen is then unique, and derived data must be regarded as relating just to it, rather than to the material in general. The corresponding properties of the latter, or of other samples, have to be inferred. There are, therefore, far-reaching ramifications for the scope of test programmes, evaluation strategies, the mode of utilization of the data, design procedures and so on. The variations in material state are commonly in the molecular or atomic orders which, after the processing stage, slowly change towards a state of greater order. In a fibre composite the molecular reordering process generally occurs in the matrix and at the fibre–matrix interfaces. However, the dominating source of variation is the spatial distribution of the fibres, which may change inadvertently during the manufacturing stage, or may be changed deliberately by the fabricator to induce a particular mechanical effect. Thus the trains of inference that, for a simple class of material, lead from test specimens, to sample, to material and finally to end-product, are more tenuous and less reliable and may even be inappropriate for longfibre composite systems.This occurs to the point where ‘test specimen’ tends to be replaced by ‘test coupon’, the concept of sample is largely discarded in favour of items such as subelements and substructures and ‘material’ is replaced by ‘structure’.1 These changes are functional rather than cosmetic, signifying a testing strategy linked more closely to engineering than to physics, though the testing of structures, substructures and so on supplements rather than replaces the testing of coupons. The suite of tests used for the evaluation of the mechanical properties or attributes of a material expand in range and complexity with the severity of the anticipated service but also as the class of material changes from isotropic to anisotropic and from homogeneous to heterogeneous. Thus, numerous methods are deployed to measure the mechanical properties of long-fibre composites. In most cases they are elaborated variants of the tests that have traditionally been used for other classes of material, for example,

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metals and plastics, and they are described in standard test methods, the scope of which is variously international, national, industrial sector and company. However, whilst the technical details of such standard test methods are always explicit, the underlying rationale is generally unstated there; and in the absence of such statements, the special stipulations on test configurations and procedures can seem to be demanding, costly and irksome. In comparison, other classes of material may seem to be simpler in general characteristics and more amenable to rational evaluation but those classes may well have seemed correspondingly difficult to evaluate during their novelty and development phases. For example, the testing of thermoplastics during the period 1940 to 1970 was fraught with misleading test data and imperfect rationale. It finally transpired that the initial confusing multiplicity of test methods could be reduced and rationalised through the agency of refinements to the theories of mechanics and through the testing of ‘critical basic shapes’ that function as a formal set of substructures. There is some evidence that the same rationalisation process is taking place in the field of long-fibre composites, but a reliable comparison is elusive because the market environment for thermoplastics was, and remains, very different from that in which long-fibre composites exist. There is, of course, an extensive literature on the manufacture, properties and service performance of composites, but only a small proportion of it relates either directly or peripherally to mechanical testing. A short bibliography at the end of this chapter cites a number of text books which are intended to complement the present work. The list includes one text (Brownlee) which sheds precomputer light on the subject of practical statistics.

2.1.2 Service-pertinent mechanical properties of long-fibre composites Long-fibre composites are generally required to function as load-bearing structures. It follows that elastic modulus, strength, ductility and fracture toughness are particularly important properties. The property values and general chartacteristics manifested by long-fibre composites and other, similar materials are the resultants, via various combination rules, of the properties of the separate constituents. However, the realities of practical situations may violate the rules, so that a datum derived from a particular test procedure may be a biased or invalid indicator of the property, or attribute, that the test ostensibly measures. The apparent interlaminar shear strength of a long-fibre composite derived via flexure of a short beam is one such vulnerable quantity, because the beams often fail by a combination of several fracture/rupture processes that frustrate any attempt to assign a proper value to the postulated property. There is, also,

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a more fundamental issue. The polymeric nature of most matrix materials introduces viscoelastic characteristics into the mechanical behaviour of composites such that, depending on local circumstances, the concepts of elastic modulus, strength and ductility may have to be expanded to embrace phenomena such as creep, stress relaxation, creep rupture and fatigue, and attributes such as impact resistance. Any modern textbook discussion of the mechanical properties of the matrix materials (i.e. plastics) is likely to include this extended range of topics. Corresponding treatments, including this one, of long-fibre composites tend to concentrate on the four primary properties and pay less attention to ‘time-dependent’ or ‘ratedependent’ aspects of those properties – except for fatigue, which has been studied comprehensively. The relative neglect of some features of the mechanical behaviour may have arisen mainly because viscoelastic characteristics are reflected in only some composite structures in some stress fields whereas, in contrast, anisotropy is a dominant feature of many structures, with modulus and strength often varying much more with stress axis than with elapsed time or straining rate. Additionally, the superposition of viscoelasticity on to anisotropy introduces formidable analytical difficulties and increases the testing burden two-fold or three-fold, so the long-standing tendency for long-fibre composites to be regarded as anisotropically elastic rather than anisotropically viscoelastic is explicable as a pragmatic compromise. However, that compromise offers no universally safe solution to loadbearing calculations, since a large composite structure might creep to an unacceptable degree because of unpredicted creep in a single element. At the present time the vast majority of applications for long-fibre composites have little reason to consider time-dependent effects; this situation may change when such materials are used more extensively in, for example, heavy civil engineering applications, where design lives of 50 years or more are required. Little is known about the time-dependent behaviour of longfibre composites, although it is generally recognised that any effects are likely to manifest themselves when the materials are subjected to shear or through-thickness loading. It is highly likely that new test methods will need to be developed to tackle measurement of the viscoelastic properties of this class of materials, because those presently available appear to be inadequate in a number of ways.2 Strength is often loosely related to the elastic modulus, both being similarly sensitive to the volume fraction of the fibres and their alignment relative to the stress field. Ductility, or toughness if the item is a substructure or a structural element, is a more complex matter. For a homogeneous material it is inversely related to modulus; a rough working rule is that steps taken to enhance the modulus, for example, by modification of the composition, tend to diminish the toughness and vice versa; and similar

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correlations arise for long-fibre composites, but the simple inverse relationship is distorted and partly obscured. This is primarily because the rationale breaks down when the dimensions of the stress field irregularity near the crack tip are similar in magnitude to the scale of the heterogeneity. This particular detail exemplifies a general point that the mechanical evaluation of composite samples does not lie exclusively within the formal framework defined by continuum mechanics; their heterogeneity and their anisotropy dictate a larger repertoire of tests than would suffice for a sample of a more conventional material. Thus, for example, for long-fibre composites, modulus and strength measurements in flexure and uniaxial compression are as important as, and sometimes more important than, tests in tension and can be regarded as complementary to them, whereas for homogeneous samples they often play only a supplementary role. The mechanical properties depend on several variables of the composition: • • • • • • •

properties of the fibre surface character of the fibre properties of the matrix material properties of any other phase volume fraction of the second phase (and of any other phase) spatial distribution and alignment of the second phase (including fabric weave) nature of the interfaces.

Mechanical properties also depend on the many details of the processing stage, particularly those affecting the degree of adhesion between fibre and matrix and the physical integrity and overall quality of the final structure. If the mechanical properties of the fibre and the matrix are known, mathematical models enable the corresponding properties of samples with particular fibre volume fractions and fibre spatial arrangements to be calculated, but the models are imperfect. The fibre alignments in test coupons and service items generally deviate from the ideal states assumed for the models, and the properties deviate correspondingly from the calculated predictions. The effectiveness of the coupling between the phases in a composite is also an influential factor. It is neither fully quantified nor properly understood. Good coupling seems to be desirable where a composite with high moduli is the objective and also, in many cases, where high strengths are required. The lines of reasoning are less clear where toughness is the objective. Poor coupling is advantageous in that local decoupling between fibre and matrix can arrest, or deflect, a growing crack and extensive decoupling is an effective mechanism for energy absorption. On the other hand, a decoupled fibre may act as a stress concentrator and promote failure.

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2.1.3 Mechanical testing strategy for long-fibre composites Despite the complications of heterogeneity, interfaces and anisotropy, the property data for long-fibre composite test coupons conform in many respects to the conventional definitions for homogeneous isotropic materials, apart, that is, from additional subsidiary definitions and nomenclature to accommodate the anisotropy and special property definitions, where there is no homogeneous isotropic counterpart, for example, the interlaminar shear strength. Even so, the almost infinite variety of possible spatial arrangements of the fibres and fibre volume fractions raises doubts about whether any particular combination of matrix and fibre should be regarded as a typical and characterising material state. The different fibre–matrix assemblies are each unique, so that, even more so than for processingsensitive homogeneous materials, a tabulation of property values derived from one structural assembly has a restricted field of relevance. On the other hand, since the mechanical testing of a long-fibre composite is a costly process, there usually has to be a pragmatic compromise between the desirability of test data for several different structures and the need for testing economy. Evaluation programmes are therefore often constrained by financial considerations, although the potentially harmful effects of such constrains may be offset by the adoption of a different testing strategy.1 The spatial distribution and alignment of the reinforcing phase are often so arranged as to satisfy a particular service requirement, and sometimes to attain an unusual combination of attributes in an end-product. Data derived either from test coupons cut judiciously from such structures, or from special subelements tested in their entirety,1 may reflect the loadbearing capability of the complete structure. Such data are unlikely to have any claim to generality but, in addition to their direct relevance to a particular structure, they should give an insight into the range of values of the ‘property’ that could be manifest in service and thereby provide quantitative options in design calculations. On the other hand, conventional data from specimens consisting of uniaxial arrays of fibres, and from lamellae with specific fibre alignments, have some general downstream utility via the mathematical models mentioned previously. Preferential alignment of fibres in one direction tends to confer property deficiencies such as low strength and modulus in a transverse direction. Similarly, stacks of lamellae with different fibre alignments are prone to out-of-plane distortions.Test programmes for such specimens, or samples, should include checks on the possible deteriorations and imperfections. Additionally, deficiencies in the production processes may give rise to inadvertent variations in fibre alignment, and so on, and the behaviour of the test coupon, or end-product, may therefore deviate from what might be expected and/or may vary from item to item.

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2.2

Formal framework for mechanical test methods

The foundation of satisfactory test methods for the measurement of mechanical properties is the theory of mechanics. That theory became well entrenched for homogeneous isotropic elastic materials during the nineteenth century and was progressively extended later to accommodate inhomogeneity, anisotropy and anelasticity, all of which are characteristic features of long-fibre composites. If the material under investigation is viscoelastic, it is convenient for a mechanical test to be regarded as consisting of the application of an excitation and the observance of the response of the test piece, with the relationship between the two defining a property. This seemingly cumbersome approach, or something similar, is an inescapable consequence of the nature of viscoelasticity; it requires that the simple elastic constitutive equations relating stress to strain be replaced by convolution integrals but, when the viscoelasticity is not dominant, some of those integrals can be replaced by simple weakly time-dependent coefficients. Irrespective of the types of excitation and response, in most mechanical tests, forces are applied and displacements ensue. In a few, the displacements are imposed, athough that necessarily requires the prior application of forces. Mechanical properties derived from such tests have to be defined in terms of the relationships between the stresses and the strains. Translation from force to stress, and from displacement to strain, is relatively straightforward if the tested item is homogeneous and isotropic, but more complex if it is heterogeneous and/or anisotropic. The basic assumption of linear elasticity theory is that the response to an excitation is a linear function of all the components of the excitation tensor, Equation [2.1]: sij = cijklekl

[2.1]

where sij and ekl are the stress and strain tensors, respectively, with cijkl being the stiffness coefficients. Each suffix has possible integral values 1, 2 or 3. Alternatively (Equation [2.2]), e = sijklskl

[2.2]

where sijkl represents the compliance coefficients. Because of symmetry in the stress and strain tensors, only 21 of the 81 stiffnesses and compliances are independent, and that number is reduced further if there are symmetries in the material (i.e. if the material is not fully anisotropic), see Table 2.1. The most general case, with 21 independent elastic coefficients, is so complex as to be virtually unmanageable in both the analytical and experimental aspects. However, this extreme situation rarely arises in practice

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Table 2.1. Classes of symmetry. Type of material symmetry

Number of independent elastic coefficients

None (triclinic) One plane of symmetry (monoclinic) Three planes of symmetry (orthotropic) Transversely isotropic (one plane of isotropy) Isotropic

21 13 9 5 2

because the fabrication processes impose some order, either from deliberate intent or inadvertently. If the material is isotropic the relationships between the stress and the strain are relatively simple and the coefficients reduce to the two moduli of isotropic elasticity theory. Elasticity theory relates to a continuum but composites are heterogeneous and therefore the equations are an imperfect representation. However, they suffice in many cases provided that the scale of the interphase discontinuities is small relative to the size of the test specimen. Stipulations on the size of test specimens in the standard test methods covering modulus and strength ensure that the heterogeneity does not distort the derived data, but there are difficulties at the micromechanical level, for instance in estimates of the stress field at the tip of a crack. The case usually considered analytically is orthotropy, which is conferred approximately by a uniaxial array of fibres in long-fibre composites, by uniaxial drawing of fibres and films and by other directional processing of thermoplastics. The stress–strain relationship for an orthotropic system is given by Equation [2.3]: s 11 c11 s 22 c 21 s 33 c31 = t 23 0 t 31 0 t 12 0

c12 c 22 c32 0 0 0

c13 c 23 c33 0 0 0

0 0 0 c44 0 0

0 0 0 0 c 55 0

0 0 0 0 0 c66

e 11 e 22 e 33 g 23 g 31 g 12

[2.3]

where the cij are the stiffness coefficients, the first suffix denotes the direction of the normal to the surface to which the stress or strain relates and the second suffix denotes the strain axis or the line of action of the stress; g is the shear strain, t is the shear stress, s is the tensile stress and e is the tensile strain. See Fig. 2.1 for clarification. The strain–stress relationship is similar and is expressed as Equation [2.4]:

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12

Mechanical testing of advanced fibre composites 3

2

s33 1

t31

t32

3

t23

t13

2

s22

t21 t12 1

s11

2.1 Principal directions and stress components for an orthotropic material.

e 11 s11 e 22 s 21 e 33 s31 = g 23 0 g 31 0 g 12 0

s12 s 22 s32 0 0 0

s13 s 23 s33 0 0 0

0 0 0 s44 0 0

0 0 0 0 s 55 0

0 0 0 0 0 s66

s 11 s 22 s 33 t 23 t 31 t 12

[2.4]

where the sij are the compliance coefficients. In Equations [2.3] and [2.4], e11, e22 and e33 are the principal strains and s11,s22 and s33 are the principal stresses. The compliance matrix can be rewritten in terms of the more familiar engineering/physical constants Eii, nij and Gij, Equation [2.5]: 1 E11 -n12 E11 -n13 E11 0 0 0

-n 21 E22 1 E22 -n 23 E22 0 0 0

-n31 E33 -n32 E33 1 E33 0 0 0

0 0 0 1 G32 0 0

0 0 0 0 0 0 0 0 1 G31 0 0 1 G12

[2.5]

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where G12 is the in-plane shear modulus (see plane number 3 in Fig. 2.1) and nij is Poisson’s ratio for transverse strain in the j direction when the specimen is stressed in the i direction. Because the matrix materials are viscoelastic, those stiffness and compliance coefficients that relate to deformations in the matrix vary with rate of straining, duration of loading and so on, and are therefore viscoelastic functions similar to those that describe the mechanical behaviour of plastics and on which there is an extensive literature. In contrast, there is a relative dearth of information on the time dependence of the stiffness and compliance coefficients relating to long-fibre composites and a general ignorance about the nature of the interactions between them. Despite its imperfections, the existing formal framework contains justifications for the various constraints and stipulations that have been imposed on test configurations and test procedures for long-fibre composites.

2.3

Special features of the mechanical testing of composites

2.3.1 Features arising from the theory of anisotropic elasticity The principal precautions that are necessary during the mechanical testing of long-fibre composites are in relation to: • • • • •

generation of a uniform stress field in the critical reference volume avoidance of overwhelming ‘end-effects’ attainment of adequate loading levels without damage or failure near the loading points appropriate specimen dimensions related to the scale of structural inhomogeneities tension–shear coupling.

The first four precautions apply similarly to the testing of homogeneous isotropic materials and give rise to various stipulations about specimen dimensions, test configurations and machine specifications, although heterogeneity and anisotropy entail more severe constraints and introduce additional considerations. Some of these complications reflect a greater stringency in Saint Venant’s Principle when the specimen is a composite. In its original form, for isotropic materials, it states that any differences in the stress states produced by different but statically equivalent load systems decrease with increasing distance from the loading points, the differences becoming insignificant at distances greater than the largest linear dimension of the area over which the loads are acting. In an anisotropic

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specimen, the region of uniform stress is approached much more gradually. It has been shown that the decay length, l, is of the order: 1

Ê E11 ˆ 2 b Ë G12 ¯

[2.6]

where b is the maximum dimension of the cross-section. For rectangular strips subjected to traction at their ends, Equation [2.7]: 1

b Ê E11 ˆ 2 lª 2p Ë G12 ¯

[2.7]

where l is the distance over which a self-equilibrated stress applied at the ends decays to 1/e of its end-value. The ratio E11/G12 may have a value lying between 40 and 50 for a unidirectional composite with a carbon-fibre volume fraction of 0.6. The value would be about 3 for an isotropic specimen and if Equation [2.7] is valid for the anisotropic case, as it should be, the respective decay lengths are in the ratio of about 3.5 : 1. Other difficulties arise when the test configuration is such that the principal directions of the stress and strain tensors do not coincide with the symmetry axes of the specimen. This can easily be shown for a thin laminate (e.g. a single lamella) for which a state of plane stress can be assumed, such that: s33 = 0, t23 = 0, t31 = 0

[2.8]

e33 = s33s11 + s32s22

[2.9]

and

which is therefore not an independent coefficient, in which case, Equation [2.4] reduces to Equation [2.10]: e 11 s11 e 22 = s 21 g 12 0

s12 s 22 0

0 s 11 0 s 22 s66 t 12

[2.10]

An important feature of Equations [2.3], [2.4] and [2.10] is that the normal and shear components are uncoupled; in other words, normal stresses do not induce shear strains and shear stresses do not induce normal strains, but this situation prevails only when the coordinate system for the stress field coincides with the symmetry axes. For a lamella whose material axes are aligned at an angle q in the 1–2 plane to the stress axis, the relationship in Equation [2.10] becomes:

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General principles and perspectives ex s11 e y = s 21 g xy s61

s12 s 22 s 26

s16 s x s 26 s y s66 t xy

15

[2.11]

where s11 = m 4 s11 + m 2 n 2 (2 s12 + s66 ) + n 4 s22

[2.12]

in which m and n are cos q and sin q, respectively. The other terms have a similar form. The normal and shear modes are now coupled. That is, a tensile stress induces some shear and a shear stress induces some tensile strain. The expression for s11 may be rearranged into Equation [2.13]: 1 cos 4 q Ê 4 1 1 ˆ sin 4 q = + sin 2 q cos 2 q + Ë E45 E90 E0 ¯ E0 E0 E90

[2.13]

to give the in-plane variation of tensile modulus for this simple system of anisotropy. The consequences of Equation [2.11] and similar relationships are important: •

•

if the principal axes of the stress field do not coincide with the symmetry axes of the specimen, extraneous forces and deformations will arise; e.g. flexed coupons may additionally twist and tensioned coupons may exhibit in-plane shear. if a laminate consists of unidirectional lamellae lying at various angles to each other, deformation mismatches occur at the interfaces because of the different degrees of tension/shear coupling in the various lamellae. The severity of the effects will depend on the stacking sequence, the degree of asymmetry, the test modes, the clamping arrangements and so on, and may be sufficient to cause delamination, especially at the edges. In summary, the principal practical consequences of anisotropy are:

1 2 3

4

severe ‘end-effects’, which extend in the direction of higher stiffness (a function of both the specimen geometry and the anisotropy) premature failure in grips or at other loading points premature delamination at free edges, or other unintended failure modes.They tend to arise from the interactions between the macrostructure of the composite and even the simplest system of external forces. property imbalances between, say, a tensile modulus (or strength) dominated by the properties of the fibre and a shear modulus (or strength) governed largely by the properties of the matrix.

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These consequences entail special constraints on test configurations, specimen geometries and stacking sequences in laminates. They also sometimes induce behaviour in subelements, substructures and structures that is unique to anisotropic systems.

2.3.2 Features arising from practical realities The results from experimentation are sometimes erroneous because the requirements to ensure accurate data are onerous and not always achievable. Additionally, errors arise from imperfections originating in the fabrication stage. The possible defects include imperfect alignment and dispersion of the fibres, broken and kinked fibres, incompletely wetted fibres, voids and general mismatches between the constituents. The tensile modulus along the fibre direction of a composite containing a unidirectional, parallel array of fibres provides a simple example of the effect that fabrication defects can have on properties. The modulus can be estimated using the ‘Rule of Mixtures’ equation: Ec = jEf + (1 - j )Em

[2.14]

where Ec is the Young’s modulus of the composite, Ef the Young’s modulus of the fibre and Em the Young’s modulus of the matrix, with j being the volume fraction of the fibres. In practice the simple Equation [2.14] usually has to be modified to: Ec = hohljEf + (1 - j )Em

[2.15]

where ho is the efficiency factor for fibre orientation and hl the efficiency factor for fibre integrity (length and effective length). Usually Ef >> Em so that: Ec hohljEf

[2.16]

the upper bound of which is: Ec = jEf

[2.17]

and lower values of Ec reflect the fabrication deficiencies mentioned above. Research indicates that the properties of the fibres can be utilized with an efficiency of about 85% for modulus and about 70% for strength. With this as an upper bound, the simple tensile test procedure on this type of coupon provides a first-order assessment index of the quality of composite attainable from a particular fibre–matrix combination. The situation is much more complex for other stress fields and/or other fibre–matrix assemblies, where the matrix and the interface may be sources of weakness. The interlaminar shear strength, the shear modulus, the properties in the transverse direction and those under uniaxial compression are

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all sensitive to the properties of the matrix and reflect the potential deficiencies of fibre composites. For such situations a third efficiency factor has to be incorporated into any analogue of Equation [2.15], to quantify the effectiveness of the fibre–matrix coupling. It follows, therefore, that the firstorder assessment by tensile testing is insufficient for many purposes and anything other than the most elementary evaluation programme should include tests in at least one additional and fundamentally different deformation mode. A popular test procedure which utilizes a different deformation mode purports to measure the interlaminar shear strength, by three-point flexure of a short beam. The span/depth ratio of the beam is so chosen that the beam should fail by interlaminar shearing rather than by tensile failure. In practice, failure is often mixed mode because the properties vary from point to point and therefore critical stresses may arise simultaneously at several positions; it is not unusual for evidence of tensile failure in the tension face of the beam, fibre buckling in the compression face of the beam and interlaminar shear at a mid-plane, all to be found in one specimen. Additionally, the configuration dimensions favourable for shear failure are such that the shear stress prevailing at the instant of failure cannot be calculated with high precision or accuracy. Even so, in principle the failure should be either at a fibre–matrix interface or in the matrix, and hence the measured value should not exceed about 60 MN m-2 for any of the plastics–matrix composites currently available. When higher values than this are reported, it is probable that some fibres were misaligned and had an orientation component out of the plane of the laminate, so that the measured breaking force was partly attributable to the stretching and possible fracture of some fibres. In such cases the tensile properties should correspondingly be lower than normal for the particular fibre volume fraction and fibre disposition. A similar role can be played by uniaxial compression tests, but they are fraught with practical difficulties associated with the transfer of force from the actuator to the test specimen. Irrespective of whether the ends of the specimen are clamped or free, a compromise has to be found between the ideal long slender specimen which tends to buckle under axial loading and the short wide specimen that is mechanically stable but yields data distorted by frictional or mechanical constraints at the thrust plates. Apart from the associated inaccuracies and imprecisions, the lateral strains are tensile in character and can cause phase separation in some composite structures when the coupling is weak; axially aligned fibres may become unsupported columns which then tend to buckle with damage developing progressively, whereas under tensile stress the fibres would contribute fully to the strength and modulus along that axis. Irrespective of the deformation mode and the anisotropy, elastic modulus is a bulk property and, provided the dimensions of the specimen are much

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greater than the scale of the inhomogeneity, it is amenable to measurement and calculation. Strength and ductility, to some degree, are ‘local’ properties and therefore susceptible to structural discontinuities; consequently, the property values tend to be more variable and the test methods less soundly based than those for modulus. In particular, the methods used for the measurement of fracture toughness are not entirely satisfactory, mainly because the fractures seldom progress as a single crack and the critical region (i.e. the crack tip) is of the same order of magnitude as the scale of the heterogeneity.

2.3.3 Samples and specimens for mechanical tests The samples from which specimens are taken for test purposes are usually in one of three forms: pultrusions, filament-wound tubes and flat sheets, all of which may be tested in their entirety, or used as a source of smaller test pieces. The first two forms were chosen partly for fabrication convenience and partly for their correspondence to important industrial production processes. In pultrusions, the fibres are mainly aligned along the pultrusion axis; in filament-wound tubes the fibres may be aligned circumferentially or along spirals (often opposed, balanced spirals), and in other filament wound shapes the fibres can be placed to optimum effect. Also, these fabrication processes facilitate good consolidation of the structure and relatively voidfree end-products. Commercially produced flat sheets fall into four classes, with radically different fibre dispositions: • • • •

randomly oriented fibres (mainly random in the plane of the sheet rather than three-dimensionally random) layers of uniaxially oriented fibres variously aligned with respect to a reference axis layers of woven fabric variously aligned with respect to a reference axis sandwich structures.

The four classes of sheet, the pultrusions and the filament-wound structures offer various anisotropy options, ranging from isotropic in the plane to severely anisotropic and even some reinforcement in the third direction, which relate to a range of downstream composite structures. It is obviously imperative that any quoted properties data be qualified by a clear description of the volume fraction and spatial arrangement of the fibres in the structure, substructure, element, subelement or coupon that is tested. For the singular case of laminates consisting of unidirectional laminae arranged with their fibre-alignment axis varying from layer to layer, which are

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Table 2.2. Laminate code. Guide to the notation Orientation of each lamella is expressed in degrees between the filament axis and the x-axis Positive angle is clockwise looking towards the layup tool surface Lamellae are listed in sequence, starting from layup tool surface Successive layers of different orientation are separated by/ Subscripts denote repeat lamella orientation The beginning and end of a code are marked by brackets, after which subcript T indicates that total laminate is shown and subscript S indicates that only one half of a symmetric laminate is shown

Examples of stacking sequence code

+45,-45,0,90 = +45/-45/0/90 +45,-45,0,0,90 = +45/-45/02/90 +45,-45,0,90 = (+45/-45/0/90)T 90,0,45,45,0,90 = (90/0/45)S ¯)S 90,0,45,0,90 = (90/0/45

popular for research purposes, there is an agreed notation which describes the stacking sequence, see Table 2.2. The properties of coupons cut from laminates vary with the stacking sequence, the alignment of the specimen axis in relation to the pattern of fibre orientation and, to a lesser degree, the in-plane position of the specimen. Some companies (e.g. in the automotive and aircraft industries) have in-house sheet cutting patterns designed so as to minimize the cost of specimen preparation and simultaneously to maximize the information derivable from each sheet. Local agreements on collaboration sometimes result in a group of companies adopting the same lamination and sheet cutting patterns. Similarly, the properties of pultrusions, filament-wound structures and coupons cut from both sources depend on the fibre disposition, but the testing emphasis is on structures (e.g. tubes, small pressure vessels, etc) for which there are special standard tests, rather than coupons, although filament-wound rings are tested in several standardised configurations such as diametral compression of an intact ring, flexure of a curved segment cut from the ring, torsion of a cut but otherwise complete ring and so on.

2.4

Nature and quality of test data

The factors that have to be considered in assessing the quality of mechanical properties data include the following:

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Mechanical testing of advanced fibre composites precision accuracy authenticity and typicality relevance to the test objectives physical significance.

Precision and accuracy are easily amenable to statistical analysis but are not unambiguously separable in a small set of data. The last three factors are not so readily quantifiable because of the possible uniqueness of each test coupon, or service item, although experimentation dedicated to particular issues can circumvent that difficulty in principle, if not always in practice. Similar values of a notional property are generated by replicate tests, but there is usually some scatter. The resultant distribution of values in a set is compounded of varabilities related to: • • •

precision of the measurements accuracy of the measurements variations in the structure of the test coupons in the set.

Overall, the interspecimen variability is an indicator of the quality of the data, but it cannot identify the separate causes unless the test programme has been specifically designed to do so. The mean value and a measure of the width of the distribution (e.g. the standard deviation) characterise the distribution of values in a set of independent measurements. They constitute only estimates of the mean value, and so on, of the distribution for all members of the population. Alternative characterising indicators are the median and the range. The median gives less weight to extreme values than the mean does and is thereby a superior measure in some circumstances; the range is less quantitatively justifiable than the standard deviation as a measure of the variability. The standard deviation is the square root of the variance, and that is given by Equation [2.18]:

(Â xi ) 1 È 2 s = ÍÂ xi n - 1 ÍÎ n 2

2

˘ ˙ ˙˚

[2.18]

where s is the standard deviation of a set of results, n the number of specimens in the set and xi the individual values. The symbol s denotes the standard deviation of the data from the tests on a set of specimens, and the standard deviation of the entire population is usually denoted by s. Apart from their direct role as a measure of the variability in a set of data, the variance and the standard deviation enable inferences to be drawn about:

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General principles and perspectives • • • • •

21

confidence limits for a set of data reliability of apparent differences between sets of data combined uncertainty of measurements when there are several sources of variability separate variabilities when several factors have affected a set of data goodness of fit when correlation between a dependent and an independent variable is derived.

Variance and standard deviation say nothing about the physical significance of a set of data, the difference between sets, correlations and so on, and in isolation they are likely to be misleading if the distribution of property values is multimodal, because what may then actually be variation would be presented as variability. They are also ineffectual if the criterion of acceptability is a boundary value rather than a mean value, because the number of requisite test results increases disproportionately as the probability level approaches the upper or lower limit of unity or zero. Some experimental and service situations are fraught with both extreme value and multimodality difficulties, as explained later in this section. Multimodality arises when the individual specimens in a set do not all respond similarly to the imposed excitation. This is commonly encountered in certain types of strength test, where the failure may be variously due to shear at an interface, tensile failure in fibres, compression buckling of fibres and so on. The overlapping distributions of strength values associated with the different processes can be identified and quantified by several techniques ranging from the construction of simple histograms to elaborate numerical manipulation, but ideally any such analysis should be supported by visual evidence of the different modes of behaviour. The standard deviation may be converted into confidence limits on the mean value via the expression: ±L = s e

t n

[2.19]

where L is the confidence limit for some specified probability level (usually 95%), se is the estimated true standard deviation (i.e. s above), n is the number of specimens and t is the Student’s t. t/ n decreases as n increases, as shown in Table 2.3 for 95% confidence limits. Thus, for example, if the mean value, x , has been derived from a set of ten specimens there is a 95% probability that the true mean value (i.e. from an infinite set of specimens) will lie within the range x = 0.715 se.

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Mechanical testing of advanced fibre composites Table 2.3. Variation of t / n with n.

n

t n

n

t n

n

t n

5 6 7

1.24 1.05 0.93

8 9 10

0.84 0.77 0.715

15 20 30

0.555 0.47 0.37

Similarly, judgements can be made as to whether an observed difference between the mean values from two sets of data are statistically significant via the calculation of t from the expression: t=

x1 - x2 se

n1 n2 n1 + n2

[2.20]

where 2

2

se =

(n1 - 1) s1 + (n2 - 1) s 2 n1 + n2 - 2

2

[2.21]

and the suffixes 1 and 2 denote the two sets. Reference to the standard tabulation of Student’s t then gives the level of significance of the observed difference. The identification of individual variances when several are affecting the overall variability in a set of data relies on a procedure referred to, unsurprisingly, as the analysis of variance.Where there are several influential variables, which may not be completely uncoupled, and where the effects of each one cannot be varied methodically and independently of the others (i.e. in the usual industrial situation), it is necessary in the interests of testing economy and statistical efficiency that the test programme be appropriately designed. Correlation coefficients are also limited in what they signify unless they are supported by physical evidence. Lifetime curves (e.g. fatigue and creep rupture data) are particularly challenging because the regression curve is often nearly horizontal. At any particular level of severity the number of cycles or the time to failure is highly variable, typically two decades on a logarithmic scale. A shallow slope tends to worsen the variability because a small variation in the applied severity converts into a large change in lifetime. The practical concerns are the severity level below which no failures occur, the investment in testing that will enable that limiting level to be determined with a high degree of confidence and the

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risks entailed in extrapolating experimental data to times significantly longer than the duration of the tests. A nearly flat, featureless regression curve based on unimodal sets of lifetimes observed at different severity levels may suddenly change slope as a second failure mode suddenly intervenes. Statistical analysis of data embraces techniques ranging from simple estimates that entail nothing more that mental arithmetic to elaborate calculations requiring modern computing power. The latter are now much in vogue as a support for scientific experimentation, but they should be regarded with some circumspection because their superiority over the elementary methods rests mainly on their ability to extract more information from scattered data and not on an enhanced ability to provide a rationale. Thus, enhanced confidence limits on a set of data do not in themselves endow the result with a physical significance, justify an extrapolation beyond the range of the data, signify that an observed correlation is evidence of a causal relationship or imply that other inferences may be drawn from the data. That reservation is not intended to discredit statistical analysis nor is it an endorsement of the view of a very famous physicist who said, ‘If your experiment needs statistics, then you should have done a better experiment.’ With regard to the latter, it is undoubtedly true that an elaborate statistical analysis cannot improve the data derived from a poorly conducted or poorly designed experiment. However, in some instances impeccable experimentation nevertheless yields high variability and statistical analysis may then be the only route to the extraction of information from the data. The value of such analysis varies with the circumstances. Commercial benefits can accrue from minor differences in the properties of competing materials but, on the other hand, an observed difference may be statistically significant but physically unimportant and even a perfect correlation does not alone signify a causal relationship. Overriding all other considerations, however, is the fact that the penalties for malfunction in service may be severe. Therefore, validation test programmes for service items or prospective service are necessarily cautious and expensive. Apart from the precautions that have to be taken to ensure that tests are properly conducted, any data that indicate the enhancement of a property must be interpreted with caution because the advantage of a favourable trend in one property with respect to some independent variable may be completely offset by the disadvantage of a simultaneous unfavourable trend in another property. For example, precise uniaxial alignment of fibres maximises the attainable tensile modulus in that direction but the modulus in a transverse direction, the transverse strength, the torsional rigidity and the interlaminar shear strength are all adversely affected; the implications for testing strategy and evaluation costs are obvious.

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2.5

Mechanical tests for long-fibre composites

2.5.1 Primary properties An extensive infrastructure of test methods and procedures has had to be developed to support the composites business, but the great variety of composite structures, the complexities of the properties, the diversity of service applications and the immediacy of particular commercial pressures have resulted in the developments often being arbitrary and narrowly specific rather than interconnected elements of a coherent evaluation system. Thus, the particular role of any one test method as part of the testing infrastructure is often obscure, and the test may seem to be merely one of an agglomeration of methods rather than one of a coherent system. Even a cursory inspection of the established standard test methods reveals that there are conflicting recommendations for some test procedures, coexisting minor variants of some methods and some owing more to expediency than to science. There are also some major omissions from the repertoire of commonly used tests. Even so, a logical pattern of test procedures and inferential steps can be discerned under the conflicts and confusions of the fine detail, which provides a unifying framework against which any inconsistencies and deficiencies can be set in proper perspective. This chapter seeks to set that perspective. It is generally agreed that a minimum requirement for the assessment of the three primary properties of a long-fibre composite (modulus, strength and ductility) are those parameters listed in Table 2.4, or other, very similar parameters. Table 2.4 quite properly stipulates moduli in tension, flexure and uniaxial compression, which would provide a superfluity of tests for an isotropic homogeneous sample, but which are necessary for a long-fibre composite sample for the reasons touched upon earlier. On the other hand, the minimum requirement falls far short of comprehensively quantifying the stiffness and strength tensors, and it neglects the viscoelastic aspects of behaviour. In fact, despite the list giving the minimum requirement, no single investigating body is likely to carry out all of those tests as a general routine procedure because various sectors of the industry have different objectives for their evaluation programmes. With some oversimplification it can be said that manufacturers of fibres are mainly interested in the mechanical properties manifest in fibre-dominated situations (e.g. the properties in tension and flexure of samples containing uniaxial arrays of fibres). Manufacturers of resins tend to rely mainly on those tests that entail compression and shear modes of deformation, which are sensitive to the quality of the fibre–matrix coupling. The downstream industries need to supplement the data of Table 2.4 with data directly related to service situations.

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Table 2.4. Primary mechanical properties essential for an evaluation of a long-fibre composite. Tensile modulus Compressive modulus (uniaxial) Flexural modulus Shear modulus (in plane) Lateral contraction ratiosa Tensile strength Compressive strength (uniaxial) Flexural strength Apparent interlaminar shear strength Fracture toughnessb (various modes) a In principle these quantities need not be measured provided the various corresponding moduli are known. b There is as yet no firm consensus about which deformation modes are the most informative in relation to service.

Several of the properties listed in Table 2.4 might be cited as essential constituents in an evaluation of a homogeneous single-constituent material, and the same test machines might be used for both that class of material and long-fibre composites. Thus, for tensile and uniaxial compression testing, irrespective of the class of material, the primary requirements are that the testing machine should be ‘axial’ (i.e. the force should act along the longitudinal axis of symmetry), the specimen should be long and slender, the strain should be measured on a gauge section sufficiently remote from the grips to ensure that they exert no influence on the result (i.e. with due allowance for Saint Venant’s Principle) and, for strength measurements, fracture should occur within that section. The additional stipulations for tests on composites are secondary in nature although important nevertheless; they include specified minimum dimensions for test bars, to ensure that they are larger than the scale of the inhomogeneities and the size of any likely defect, testpiece grips commensurate with the overall properties and additional measurements related to the anisotropy, and so on. In practice, tensile machines are seldom axial, which can severely distort a tensile property datum if the testpiece has a high modulus and/or is not ductile. Extensometers tend to slip. Alternatively, strain gauges can interfere with the local strain. Testpieces tend to slip from the grips, or break there rather than within the gauge length. In addition, specimen size may be dictated by extraneous factors such as the availability of adequate samples, the cost of fabrication of test coupons, the load capacity of test machines and so on. Furthermore, even though the breaking force and

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ultimate extension of long-fibre composites may be measured accurately, the conversion of those quantities into failure stress and failure strain, respectively, are arbitrary and unreliable procedures because of the heterogeneity. All that may be claimed is that the notional failure stress and notional failure strain may be measured precisely. Flexure is a popular deformation mode for modulus measurements because it requires simpler apparatus and test specimens than tension. However, if the specimen is inhomogeneous, or if the properties vary otherwise through the thickness of the beam, the flexural response to transverse forces cannot properly be translated into a modulus because of the way in which the stiffness of the beam is dominated by the outer layers.This is generally termed ‘stacking sequence dependence’. In a tension test on a composite coupon with a laminated structure the properties of individual layers contribute in parallel and without bias (apart from tension–shear coupling) to the overall property. The force–deflection relationship defines a notional modulus which reflects the fibre alignments in the individual lamellae irrespective of the stacking sequence. In a flexure test, on the other hand, the contribution of each lamella depends on its disposition with respect to the neutral axis and hence the datum generated in the test is the stiffness of the particular beam rather than a modulus. The practical constraints on the dimensions of specimens in flexural tests correspond to those implicit in the Bernoulli–Euler elastic beam theory, with modifications necessitated by the high ratio of the Young’s modulus to the shear modulus. The relevant equation for a homogeneous, isotropic specimen subjected to three-point flexure is Equation [2.22]: d=

PL3 Ê Eh 2 ˆ 1 + 4bh3 E Ë GL2 ¯

[2.22]

where d is the deflection at the mid-point of the beam, P is the load at the mid-point, L is the span, b is the width, h is the thickness, with E and G being the flexural and shear moduli, respectively. Equation [2.22] is approximately valid for long-fibre composites if the substituted values of the moduli are appropriate for the particular anisotropy. Various modifications to the second term within the brackets (which are multiplying factors not very different from unity) have been proposed to allow for the heterogeneity; but even as it stands, the equation sets an approximate lower limit for the span/thickness ratio if shear is not to contribute significantly to the deflection of the beam. For example, the Young’s modulus of a unidirectional composite with a carbon-fibre volume fraction of 0.60 may be 120 GN m-2 and the shear modulus may be only 3 GN m-2, so that the span/thickness ratio should satisfy the condition:

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General principles and perspectives L2 > 100 40 h 2

27 [2.23]

if the shear correction is to be less than 1% of the measured value. This ratio is higher than the 16 : 1 normally regarded as sufficient for an isotropic material. A ratio of 60 : 1 is recommended by ASTM (American Society for Testing and Materials) for carbon-fibre reinforced resins. At the other extreme, the span/thickness ratio is variously specified as between 3 : 1 and 5 : 1 for the short-beam shear test, to favour interlaminar shear failure, but the high transverse forces that are required to flex a thick beam can cause excessive distortion or damage near loading points and thereby change the effective span. The damage can be limited and a tendency for fibres to buckle out of the compression face of the test piece can be reduced by the use of larger radii for the loading and support anvils. However, the greater the radii, the greater the uncertainty about the effective span, and ASTM D790-86, for instance, recommends that the radii should be no greater than four times the beam thickness. Apart from its uses as an alternative, or as a supplement, to tension, flexure is often the only practicable deformation mode for macrocomposite structures such as laminated honeycomb sandwich panels. Local crushing and indentation at loading points are a common difficulty with such specimens, and flat loading pads usefully replace cylindrical anvils. The specific details of tensile, flexural and other mechanical tests vary from company to company within a country, from country to country and with the nature of the sample. Most of the variations dictated by the nature of the sample are necessary for technical reasons, for instance, to accommodate specimens in which the axis of fibre orientation does not coincide with the stress axis, although others appear to have no more justification than casual prejudice. Similarly, the specifications for end-tabs, which have been used almost universally to reduce the probability of failure initiating at the grips during a tensile test, vary widely. End-tabs can also facilitate accurate alignment of the specimen in the test machine, provided that they are symmetrical and properly positioned on the specimen, but if they are deficient in these respects they can cause misalignment and introduce stress concentrations. In the absence of systematic evidence to the contrary, one must assume that the various specified test procedures might yield different values for modulus and strength on specimens of the same composition. Some light was shed on the issue in a paper by Sottos et al.,3 who compared the results obtained on one fibre–resin formulation in four different laminate layups by use of three standard test methods with permitted variants. In the case of tensile modulus and tensile strength there were 17 sets of data, with five specimens in each set. The coefficients of variation for the

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modulus measurements varied from 0.013 to 0.120 with a mean value of 0.068. For the strength they varied from 0.041 to 0.140 with a mean value of 0.075. Such coefficients of variation compare unfavourably with corresponding data for other classes of material (e.g. thermoplastics and thermosets) but they are similar to the coefficients reported elsewhere for other composite materials. For instance, values of 0.079, 0.080, 0.083 and 0.100 were tabulated by Johnson4 for tensile modulus measurements on a polyester resin with four different volume fractions of glass fibre and Owen et al.5 reported even higher levels of variability for sheet moulding compounds. It seems likely that relatively high coefficients of variation are an inherent characteristic of composite materials in general, probably caused by local variations in fibre volume fraction, fibre alignment and void content. Sottos et al.3 concluded that ‘with one or two exceptions, the different standards do, in fact, give data which are probably not significantly different’. They did, however, note that the recommended use of only five specimens for each data set was barely adequate for discrimination between the mean values when the coefficients of variation are at the level found in their test programme. Taking the mean values of the coefficients of variation as typical for this type of measurement and on the basis of a normalised distribution, one might expect 95% confidence limits in the region of 0.08 to 0.10 for sets of five specimens. The specifications for the other types of test listed in Table 2.4 are similarly varied, and the sparse published information on variability suggests similar coefficients of variation, though Sottos et al.3 reported lower mean coefficients of variation of 0.043 for ‘modulus’ and 0.056 for strength measured in flexure. In general, the possible disparities in measured property values arising from the different specimen dimensions have not been quantified, nor, until recently, has there been much advocacy of the merits of international standardisation. It seems that the active groups have a vested interest in perpetuating their use of whatever procedures had been adopted initially, probably because it enables them to make the best current use of their archive data, which are often extensive and which, in the absence of a science-justified database, are a pragmatic basis for materials selection and end-product design. If high variability is an inherent characteristic of fibre–composite materials and if, because of that, the various standard tests do not give obviously different results, except possibly via the generation of large sets of data, there is no reason for them all to be retained unless there are independent grounds for their retention. On the other hand, by a parallel argument it should not matter if they are retained because the disparities could be largely ignored. Substantial savings in evaluation costs could be achieved if this matter were to be resolved. However, little effort

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is expended on the acquisition of facts about the relative merits of the various standard procedures and the comparative variabilities, partly because of vested interests and partly because the statistically sound test programmes that would be necessary would be costly and rather tedious to conduct.

2.5.2 Engineering properties data The test programme implied by Table 2.4 has been expanded in scope by arbitrary procedures to satisfy various downstream requirements which vary from company to company. Table 2.5 lists the tests stipulated by a large commercial aeroplane manufacturer in the USA as being necessary in the ‘initial testing’ phase. The call for ‘open hole’ tests reflects reservations about the reliability of the theories of failure and about the relevance and relative paucity of the empirical evidence from conventional fracture toughness tests. The protagonists of such tests sometimes seem to be preoccupied with a search for authentic and/or definitive data which is perpetually frustrated by a preponderance of mixed-mode failures in their experiments. The same is true of short-beam shear testing. However, since most service failures are also mixed mode, it may be that the use of data generated through an empirical matching of laboratory configurations to service situations would be a better option than the use of arbitrary and unreliable data generated in a formally correct way. It could also be argued that a fracture which features all possible failure mechanisms indicates that the ultimate properties of fibre, matrix and interface were well balanced in the item and were being fully utilised in the composite structure. The inclusion of the sixth and seventh items in the list of Table 2.5 is a pragmatic response to the fact that in-service conditions can be arduous and may induce severe deteriorations in the structure and performance that are not revealed, or implied, by the data generated by traditional mechanTable 2.5. Primary engineering properties for preliminary selection of composite materials. Tensile strength at room temperature Uniaxial compression at room temperature Interlaminar shear at room temperature Open hole tension at room temperature Open hole compression at 93°C Hot /wet compression strength Edge-plate compression strength after impact at room temperature

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ical tests. It also compensates for the disparity which exists between the properties measured in a traditional evaluation programme and the attributes that are required of a serviceable end-product. Apart from the limitations mentioned above, the tests listed in Tables 2.4 and 2.5 generate only so-called ‘single-point’ data. These may be useful for quality control and materials selection purposes, but are of limited utility in design calculations for load-bearing service, for which creep, creep rupture, fatigue and other phenomena are relevant considerations. The previously mentioned partial failure of the composites testing community to recognise that viscoelastic behaviour is likely in some circumstances has been corrected, in that the automotive, aerospace and chemical plant industries demand creep, creep rupture and fatigue data, overlain by information on the degenerative effects of various environments. The list of topics of concern to end-users is formidable; the main headings of a list emanating from an automotive company in the USA are given in Table 2.6 as an example. Despite the inclusion of long-term data in the wants lists, the dearth of data in this area of durability persists. This leads directly to a common form of data misuse, namely short-term modulus and strength data being used in a design context of long-term load-bearing capability without an appropriate allowance being made for the ‘elapsed time’ effect. The errors are not serious when the fibres dominate the response, because the time dependence is then slight, but when the stress field is such that the matrix is influential, the neglect of time dependence may lead to inadequate load-bearing cross-sections and a short service lifetime.

Table 2.6. Primary data and design data as envisaged by the automotive industry.a Elastic and strength properties at various temperatures in the range -40°C to 150°C Effect of loading rate on tensile and compressive properties in the range 1.67 ¥ 10-3 s-1 to 1.67 ¥ 10 s-1 Long-term material propertiesb Environmental effects on long-term properties Energy absorption upon impact Manufacturing effectsc Characterisation of joints and fasteners a

This information is extracted from a document emanating from one company in the USA, but it is very similar to the data requirements stated by German, French and British automotive companies. b Creep, fatigue, residual strength after fatigue, effect of notches and holes on those properties. c Properties in ribs, bosses, at knit-lines, etc.

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Because impact is a common service hazard, impact testing features increasingly in evaluation programmes. Current test practices for composites loosely follow the standardised procedures recommended for unreinforced plastics, but the specimen dimensions and other details of the test configuration were chosen either arbitrarily or in attempts to simulate commonly encountered structural features. The test configurations are: • • •

bars in tension beams in flexure plates in flexure.

The impact is variously by swinging pendulum, falling dart, driven dart, spring-driven projectile and air-driven projectile, all of which deliver relatively low velocity impacts, and do not simulate aggressive service impacts. They do correspond, however, to the casual service hazard of a minor impact that may cause only slight direct damage but nevertheless leave the item prone to premature failure by a different mechanism during subsequent service. There have been a number of notable studies which have covered quasi-static through to ballistic impact.6 Many of the early impact studies, most notably by Adams7 of the University of Wyoming, USA, made use of the flexed beam methods, but the flexed plate configuration has now become the more popular. The former methods enable the measured quantity to be related to the overall anisotropy of the plate from which the beams have been cut, whereas the latter almost automatically identifies the easiest failure path and corresponds more closely than the flexed beam to the situation prevailing during a casual impact on a service item. However, the response to impact of a conventional laboratory test piece may, nevertheless, be very different from that of a service structure. Apart from a tenuous geometric similarity between the flexed plate test configuration and service impacts, a useful practical advantage is that the preparation of the test specimens is relatively undemanding, because results are generally not so sensitive to the quality of the edges as those from flexed beams. Various shapes and sizes of specimen, support and impactor have been employed and, similarly, so have various impactor velocities and incident energies. The use of a circular support constitutes a perpetuation of the general practice that has been established and standardised for unreinforced plastics. The use of a square aperture seems to have been encouraged by the manufacturers of test machines in the USA; it may be felt that a square aperture corresponds more closely than a circular one to the majority of panels in service. Another unresolved issue is international standardisation of the size of the aperture, the striker and so on, the details of which strongly affect the apparent impact resistance and the mode of failure.

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Each of the dimensional factors affects the stress field at and near the point of impact. The analysis for a flexed laminated plate is beset with uncertainties and the theoretical stress field will be distorted by the onset of even minor damage, so that comparisons between data emanating from different sources are likely to be unreliable until standardised test practices are established. Additionally, a distinction has to be drawn between the strain energy imparted to the entire structure (test specimen or service item), which can be measured, and the local strain energy density initiating and subsequently sustaining the failure processes, which cannot be measured. Impact tests at low incident energy provide insights into the mechanics of fracture. The data obtained set the impact resistance of composites in perspective relative to that of other classes of material; for example, in one of the standard flexed plate configurations an incident energy of 1–2 J suffices to damage a 16-ply laminate slightly and less than 10 J creates extensive damage, whereas in the same test configuration many unreinforced thermoplastics have impact resistances in the region 60–80 J. The slight damage incurred in a superficially innocuous impact may weaken a structure directly, by introducing stress concentrators and local weaknesses, or indirectly, through the creation of pathways for the subsequent ingress of water or solvents. The mechanical deterioration attributable to the damage may be assessed in various ways, for example strength in flexure of sandwich structures, or tensile and compressive strength, but the currently popular method is edge compression of a plate. In that test a rectangular plate is impacted transversely at low incident energy and then subjected to in-plane compression by force applied along one edge. The initial impact, which has not yet been standardised internationally, is such as to produce ‘barely visible damage’. However, that criterion is subjective, and the visible damage is known not to correlate well with the amount of damage as assessed by ultrasonic absorption, or with the residual strength of the damaged structure. Quite extensive internal delamination can occur with no apparent damage at the surface. Therefore, the several variants of the ‘damage tolerance test’ all stipulate relatively large plates to reduce the possibility of the internal damage extending to the edges, and this large size entails edge supports for the plate during the compression phase and a large load-capacity test machine. The collapse load cannot be translated into a specific physical property because practical factors limit the attainable precision in an edge-loading configuration. Also, prior damage can only be known accurately by dissection, and so on. Thus, the test is arbitrary and data emanating from various sources may not be directly comparable, so that the links between experimental data and service performance are tenuous and largely unquantified at present.

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The cost of comprehensive evaluations such as that implied by Table 2.6 is high and, in consequence, the downstream demand for data is rarely met in full, so that there is some uncertainty over which sector(s) of the industry should bear the main burden of the testing. There is a tendency for the data demands of a user industry to be excessive and, correspondingly, there is a tendency for information supplied by a materials producer to be the bare minimum and to be selectively biased to the advantage of the particular product. It is likely that the pragmatic compromise that always has to be achieved is determined more by the politics of the marketplace than by scientific rationalisation. Even so, the financial penalties for using inappropriate data can be severe. Overdesign is expensive and inefficient. Underdesign leads to malfunction, so that reliable design data are a prime requirement for most projects. Those properties tend to be dominated by the properties of the matrix and the fibre–matrix interface to varying degrees.

2.6

Concluding comments

A survey in 1987 of the then-current range of standardised, or semistandardised, mechanical tests8 concluded that the existing system of standardised test methods was deficient in three respects: •

• •

there were too many variants of some tests and a dearth of hard evidence about the effects of the variations on the reliability of the generated data some tests were not fit for their intended purpose some important phenomena and properties were neglected by the testing community.

Some tests for modulus and strength were deemed to be fit for their intended purpose; some (modulus and strength in uniaxial compression, modulus in shear, interlaminar shear strength, impact resistance, fatigue resistance) were deemed marginally or conditionally fit-for-purpose; others (damage tolerance, fracture toughness) were deemed not fit-for-purpose and some (creep, creep rupture) were seldom carried out. This unsatisfactory state of affairs was attributed in the report to the fragmented nature of the industry, poor interaction between academy and industry and a collective failure to establish an adequate infrastructure. Little has changed in the intervening years but even so, imperfect though the testing infrastructure might be, each test event contributes a datum to the hierarchy of information that supports each downstream operation. An apparent insufficiency of information/data is common to all classes of material, because evaluation programmes may be curtailed by constraints on costs, test procedures may be inappropriate for the intended

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purpose and circumstances may be such that direct testing cannot cover the requirement when, for instance, a specified load-bearing lifetime is much longer than the allocated product development time. Such testing insufficiencies are common in industry, particularly when the materials are novel, or the applications are innovative, but there is a set of procedures that partly compensate for them. In general, limited laboratory test data can be ‘adjusted’ or extended by one or more of the following procedures to match them to the data demands for particular end-products or components in specific service: • • • •

interpolation between data measured at standardised excitation levels and ambient conditions extrapolation of durability data to longer times than the duration of the tests, or to other frequencies acceleration of failure processes by exposure to aggressive environments allowance for likely changes of state in an end-product during its service lifetime.

Provided there is an established justifying rationale, even single-point data of the type listed in Table 2.4 can be used in a wider context than that implicit in the defined scope of the tests, especially if results can be interpreted in the light of previously established correlations with service performance. For long-fibre composites, although adjustment for the fibre volume fraction, for the spatial distribution of the fibres and for component size and shape is commonplace via the combination of simple tests and mathematical models, some of the ground rules for the adjustment procedures mentioned above have not yet been firmly established. Further consolidation of the prediction procedures is hampered by the high cost of the enabling tests and the validating stage, by the large number of possible combinations of matrix type, fibre type, fibre volume fraction and spatial arrangement, by a dearth of certain classes of critical data and by the ineffectual information pathways available. The ineffectual pathways were identified and remedial action was proposed in the survey referred to earlier.8 Testing is usually the first stage in the process of the prediction of service performance. However, inaccurate, incomplete or inappropriate test data will almost inevitably lead to questionable predictions and a consequential tendency for overdesign in prospective load-bearing structures.

References 1. R Martin, ‘Composite structures: a dual approach to design’, Materials World, 1995 3(7) 320–2.

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2. P J Hogg, ‘Designing for creep in composites’, Proceedings of the International Conference on Designing Cost-effective Composites, The Institution of Mechanical Engineers, London, UK, 15–16 September 1998, Professional Engineering Publishers, 1998, 93–106. 3. N R Sottos, J M Hodgkinson and F L Matthews, ‘A practical comparison of standard test methods using carbon fibre reinforced epoxy’, Proceedings of the Sixth International Conference on Composite Materials, Imperial College, London, UK, 20–24 July 1987, eds F L Matthews, N C R Buskell, J M Hodgkinson and J Morton, Elsevier Applied Science, London, 1987, Vol 1, 1.310–20. 4. A F Johnson, Engineering Design Properties of GRP, British Plastics Federation Publication No 215/1, 1978. 5. M J Owen, A M Tobias and H D Rees, ‘Design limits for polyester SMCs’, Plastics and Rubber Processing and Applications, 1984 4(4) 349–54. 6. W J Cantwell and J Morton, ‘Comparison of the low and high velocity impact response of CFRP’, Composites, 1989 20 545–51. 7. D F Adams and J L Perry, ‘Instrumented Charpy impact tests of several unidirectional composite materials’, Fibre Science and Technology, 1975 8 275–302. 8. P J Hogg and S Turner, The Mechanical Testing of Long-fibre Composites: Harmonisation and Standardization in the UK, Report for the Department of Trade and Industry, UK, January 1988 (Copies are available from Prof. P J Hogg, Materials Department, Queen Mary and Westfield College, London).

Bibliography 1. K A Brownlee, Industrial Experimentation, London, HMSO, 1957. 2. C A Dostal (ed), Engineered Materials Handbook, Vol 1: Composites, ASM International, Materials Park, Ohio, 1987. 3. J M Whitney, I M Daniel and R B Pipes, Experimental Mechanics of Fiber Reinforced Composite Materials, SESA Monograph No 4, Society for Experimental Stress Analysis, Brookfield Center, Connecticut, 1982. 4. L A Carlsson and R B Pipes, Experimental Characterization of Advanced Composite Materials, Prentice Hall, Englewood Cliffs, New Jersey, 1987.

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3 Specimen preparation F L M ATTHEWS

3.1

Introduction

There are a number of subsidiary, but vital, issues that are complementary to the main activity of mechanical testing. These issues, taken together, constitute the preparatory work required to produce test specimens of adequate quality. If insufficient attention is given to any of these activities, the results from a particular test could be invalidated. The following remarks relate to the use of specimens of high performance composites fabricated from continuous preimpregnated fibres, the subject of this text. The four stages considered are: laminate production; quality checking; specimen manufacture; application of strain gauges. The final three stages would, of course, apply to any material.

3.2

Laminate production

Thin sheets, known as laminates, usually 1 or 2 mm thick for coupon specimens, are manufactured from layers of fibres preimpregnated with partially cured (if epoxy-based) resin prepreg. The matrix is usually an epoxy, but BMI (bismaleimide) and thermoplastic prepregs are also used. It should be noted that the following discourse relates mainly to epoxy prepregs (owing mainly to their popularity). It should, however, be pointed out that the preparation of laminates with thermoplastic matrices is in many ways a similar but more straightforward process, because the plastic resin is not required to cure, but simply ‘melts’ at a suitably high temperature and resolidifies when cooled. A single prepreg layer is usually 0.125 or 0.25 mm thick and the fibres are either continuous and parallel (unidirectional), or in the form of a woven fabric. The prepreg is supplied as ‘tape’, normally 0.3 m wide (but suppliers having width preferences, woven materials being generally wider than unidirectional products), sandwiched between protective layers of paper or plastic and wound on a reel. If epoxy, the prepreg should be kept in a freezer 36

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Specimen preparation

37

until it is required; if thermoplastic, low temperature is not a requirement but it is advisable to store the material in a clean, light-free environment. Shelf-life (for epoxies) is normally around 18 months and will be clearly stated by the supplier; thermoplastics, on the other hand, generally degrade very slowly at ambient temperatures. If the prepreg has exceeded its lifetime it can probably still be used for a further six months, at least. However, its suitability should be checked by moulding a test panel, or by checking the cure state of the matrix resin using differential scanning calorimetry (DSC). Appropriate lengths are cut from the reel and placed on top of each other with the fibres in each layer oriented relative to one another in a predetermined sequence. Hand tools, such as a ‘Stanley’ knife drawn against a hard edge, are usually satisfactory for cutting. Fabric prepreg can be cut using shears or scissors. Where available, a rotary knife or water jet could be used. The protective layers are removed before each layer is placed on that previously laid down, and the layer carefully smoothed out to prevent air entrapment. It is essential that the layers are aligned with reference to a datum, since even a few degrees’ misalignment can cause a dramatic effect on mechanical properties. With properly prepared prepreg the edge of the protective backing sheets can be used as a reference. Care must be taken to ensure that twisted or knotted fibre bundles, or prepreg areas containing gaps between bundles, are not included in the laminate. Following completion of the layup, the stack of prepreg layers is prepared for curing in the case of epoxies, or consolidation for thermoplastics. The epoxy resin, which forms the matrix of the composite, is formulated for autoclave curing; the whole curing process lasts several hours and involves a combination of vacuum, raised temperature (to 120 or 175°C for epoxies, often higher for thermoplastics) and raised pressure. The prepreg layers are contained within a sealed ‘blanket’ as illustrated in Fig. 3.1. To prevent the laminate sticking to the base and caul (pressure) plates, the latter can be coated with release agent, or layers of release fabric or a polymeric film are inserted between the plates and the prepreg. A disadvantage of the second approach is that an impression of the fabric is left on the surface of the laminate, thus making it difficult to detect the fibre orientation in the surface layers with the naked eye. As an alternative to autoclave curing it is possible to use a heated press, in which case it is necessary to monitor separately the state of resin gelation, or a press-clave. The latter device, illustrated in Fig. 3.2, is placed in a heated press, in combination with a separate high pressure supply and a vacuum source.A heated press, with facilities for rapid cooling of its platens, would be used for processing advanced thermoplastic prepregs. Clearly the size of the laminate that can be produced will be determined by the size of press available.

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Mechanical testing of advanced fibre composites Vacuum bagging material

Air breather cloth

Laminated composite plate

Peel ply

Pressure plate

Vacuum connection Melinex Sealing tape

3.1 Arrangement for producing laminates by autoclaving.

Top plate Melinex Bleed cloth Peel ply Laminate Peel ply Perforated PTFE Peel ply Frame

Baseplate Vacuum connection

Pressure vessel

Baseplate

3.2 Layout of a press-clave.

Pressure connection Diaphragm Top plate Laminate, etc. Frame Vacuum connection

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3.3

39

Quality checking

The manufacturing process, if not properly controlled, can introduce defects into the laminate. Typical defects are voids (small cavities in the resin), delaminations (unbonded areas between layers) or, unusually, longitudinal cracks (lack of bonding between fibre and matrix). Voids can be caused if the prepreg is not allowed to warm to room temperature before laying-up, thus introducing moisture into the prepreg stack. Delaminations can be caused by entrapped air or the inclusion of pieces of backing sheet. Longitudinal splitting and delamination can occur in multidirectional laminates as a result of thermal stresses induced during cooldown from the curing temperature. All the above defects will degrade mechanical properties, particularly in compression, shear and flexure. It is, therefore, important that their presence is detected so that faulty laminates can be discarded. The standard method of detection is to use ultrasonic C-scan, which is good at detecting inclusions, porosity and delaminations, or, possibly, X-ray techniques, which can detect through-thickness cracks.

3.4

Specimen manufacture

Specimens, as defined by the relevant standard, or test to be carried out, are cut from the laminates using a diamond-tipped saw. The normal blade has 600 grit, but a cleaner cut, with less damage to the laminate, is obtained with 800 grit. In the latter case the blade can become clogged with debris and frequent cleaning may be required. Laminates produced by autoclaving will have a feathered edge which must be removed. It is clearly vital that edges produced after trimming, which effectively act as a datum for subsequent specimen cutting, are correctly aligned with the fibres in the layers. A commonly used method for establishing the 0° direction of a cured laminate prior to cutting is to split off a narrow strip of material along this direction (in multidirectional laminates this can be done if the 0° layer is made slightly wider), but it has been shown that this approach may not be sufficiently accurate, and a preferred method1 is to mark the outermost ply by scoring across in the 90° direction in a nonstressed region. High temperatures are generated during dry cutting, which can cause local degradation and damage at the machined edge. This can be largely prevented by the use of a coolant (water), but subsequent drying-out steps must be taken to remove any absorbed liquid from the specimen. Generally, specimen blanks are machined oversize, final dimensions being achieved by grinding. Drilling is readily achieved with tungsten carbide or diamond tipped bits,

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the laminate being supported by a (sacrificial) backing plate. It is advisable to use a drill bit tip angle of 55–60° for thin laminates and 90–100° for thick sections, rather than the usual 120°. Other operations are best achieved by grinding. Clearly, appropriate support is needed for thin laminates if through-thickness shaping is to be carried out. Kevlar fibre-reinforced materials need special attention. Owing to the nature of the fibre it is difficult to avoid a ‘furry’ edge. Specially adapted impregnated wheels can be obtained for cutting. Another alternative is to use a high pressure water jet. For many tests, for example tension and compression, it is often necessary to bond end-tabs to the specimen; this is done to diffuse the gripping loads and prevent failure at the specimen ends. According to the particular requirements, the tabs may be of aluminium alloy, GFRP (glass-fibre reinforced plastic) or CFRP (carbon-fibre reinforced plastic). When the tabs are of composite, the preferred method is to stick strips to the trimmed laminate before cutting into specimens. This approach is not only quicker, but it also ensures alignment of tabs and specimen. When the tabs are metal this approach cannot be adopted and the tabs must be bonded to individual specimens, using a jig to give accurate positioning. Surfaces where end-tabs are to be bonded should be abraded in order to remove surface contamination, whilst taking care not to damage the outermost fibres. This is done most easily, particularly if the laminate surface is rough, by grit blasting, the only objection to this method being that the surface may itself become contaminated, either by grease carried by the grit or embedment of the grit. Surfaces not needing to be abraded can be protected by masking with self-adhesive tape. The grade of grit used, typically 80–120 grade, does not appear to be critical if care is taken to avoid excessive abrasion and damage to the composite. The dust left behind on the material after grit blasting is most easily removed by flushing under running water. If the water lies on the surface in an unbroken film, a good standard of surface cleanliness is indicated. The amount of water absorbed by the laminate will be small, particularly if the material is dried immediately after washing. After drying, the surfaces are solvent wiped and bonded. Commercial ‘two-tube’ epoxy resin has been found to be suitable for bonding end-tabs to be used for tests at room temperature and should be applied sparingly to both bonding surfaces. The joint, when assembled, can be contained in a simple vacuum bag which will apply an adequate clamping force and remove entrapped air. The tab material can be located by using small pegs inserted in notches cut through the tab and test materials. An alternative to low temperature curing adhesive is to use bonding film which is cured under elevated temperature and pressure, although in some cases this can cause thermal stresses sufficient to split a 0° laminate. Whatever adhesive

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is used it should be tough, with a greater failure strain than that of the material under test. CRAG2 specifies that it should have a shear strength greater than 30 MPa. Special adhesives would be preferred for fatigue testing or high temperature work. An incidental advantage in using GFRP end-tabs is that the material is translucent and any gaps in the glue film can be seen by visual examination. Even if the joint is strong enough to withstand specimen failure loads, gaps in the glue line can result in uneven stresses in the underlying composite and cause premature failure.1 The crucial issue when bonding is to ensure that both the specimen and the tabs are properly prepared. Composites need to be degreased and abraded to remove all traces of release agent transferred during moulding. This procedure should be followed by wiping with a solvent. Similar procedures should be followed when making bonded joints. In addition to degreasing, aluminium alloy tabs need to be etched in chromic acid or phosphoric acid.

3.5

Strain gauging

All mechanical tests will involve the measurement of displacements or strains, as defined by the appropriate standard. When strain gauges are called for, it is important to follow the recommended procedures.The length of the gauge may be specified by the relevant standards, but should always be significantly shorter than the gauge length of the specimen. Composites can cause particular difficulties not encountered with metals.3 The issues that must be addressed are as follows: 1

2

3

4

5

High gauge resistances are desirable because high voltages (2–4 V) with low current can then be used; this improves hysteresis effects and zero load stability. If possible, use gauges with lead wires attached, or solder wires to the gauge before installation; this should avoid soldering damage to the composite. Ideally the pattern of the autoclave scrim cloth should be removed before gauge installation; this is particularly important if contact adhesives are used. Corrections may be necessary to gauge transverse sensitivity effects; errors of over 100% between actual and measured strains can be obtained. Gauges must be precisely aligned; errors of 15% can result from a 2° misalignment. There is no universally acceptable way of ensuring alignment. The scrim cloth pattern can be misleading. Sometimes C-scan after installation can be useful, or checking with failure surfaces after fracture.

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Mechanical testing of advanced fibre composites Dummy gauges are the preferred method for temperature compensation but, again, precise alignment is needed. It is necessary to mount the dummy gauges on an ‘identical’ piece of laminate, with the same orientation relative to the fibres as used for the active gauges.

3.6

Summary

In summary, it is essential that careful and consistent procedures are followed at every stage of specimen production. Failure to do so will throw doubt on the validity of any data generated.

References 1. P W Manders and I M Kowalski, ‘The effect of small angular fiber misalignments and tabbing techniques on the tensile strength of carbon fiber composites’, 32nd International SAMPE Symposium, Anaheim, CA, USA, eds R Carson, M Burg and K J Kjoller, Society for the Advancement of Material and Process Engineering, Covina, CA, USA, 1987. 2. P T Curtis (Ed), CRAG Test Methods for the Measurement of the Engineering Properties of Fibre Reinforced Plastics, Royal Aircraft Establishment, Farnborough, UK, Technical Report 88012, 1988. 3. M E Tuttle and H F Brinson, Resistance Foil Gauge Technology as Applied to Composite Materials, Report No. VPI-E-83-19, Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA, June 1983.

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4 Tension E W GODWIN

4.1

Introduction

Put simply, the purpose of a tensile test is to determine the ultimate tensile stress (UTS) and tensile modulus (E) of a material, and with additional instrumentation Poisson’s ratio may also be measured. However, a closely observed test of a material under controlled conditions should provide a great deal more information about the way it behaves under load. A composite may split or delaminate, for instance, and studying the material as it is subjected to increasing load may give an insight into the ways in which damage initiates and develops. Finally, the nature of failure is seen; it may be brittle, with no warning, or it may be preceded by obvious audible or visible signs. All such information is useful; knowledge of the UTS and the way in which failure occurs is vital if serious use is to be made of the material. Mechanical testing began being carried out on a scientific basis in the second half of the nineteenth century when metals were the commonest engineering material. The use of high performance composite materials, as distinct from ‘reinforced plastics’, as major load-carrying materials began almost a century later, and it follows that the test methods initially used to test composites were based very closely on ‘metallic’ techniques. Testing of metals is not a particularly difficult task, being aided by the strainhardening isotropic homogeneous nature of the material. At its simplest, a piece of stock material can be pulled in a testing machine and fail in its midlength: locally reducing the cross-section of the testpiece (‘waisting’) can ensure that failure occurs away from the grips. The inadequacy of established tensile testing techniques when used with composites became apparent in the 1960s, and emphasised how different the behaviour of composites could be from that of metals. The key differences are that composites, by definition, are inhomogeneous and may, as a result of their twophase nature, exhibit weakness under a particular loading mode, whilst having high strength under other modes. Thus a waisted specimen could fail 43

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because the low shear strength of the material results in the wider, or thicker, part of the specimen simply shearing away from the body of the specimen before reaching the tensile failure stress. The variety of specimens in use at that time is seen in the proceedings of the first ASTM (American Society for Testing and Materials) sponsored conference on testing and design of composite materials (ASTM STP 460).1 These are illustrated in Fig. 4.1. The names given to the designs are evocative (dog-bone, waisted, bow-tie) but the specimens themselves showed various failings which have been widely reported. Although in its time the elongated bow-tie was described2 as being the only design of GFRP (glassfibre reinforced plastic) specimen to fail consistently in the gauge length, that too has become obsolete. The ratio of UTS to ultimate shear strength was then roughly 4 : 1. By 1974 it had been calculated that, for a ratio of 16 : 1 (a value somewhat less than today) a radius of 1000 mm was needed to achieve an acceptable ratio of shear/tensile stresses in the specimen. The shouldered and waisted designs, which clearly owed their origins to metals testing, have ceased to be used and, of the geometries in use at that time, only the parallel-sided end-tabbed type remains in use today. The characteristics of the tab material may be radically different from that of the test material, being chosen to provide adequate gripping and protection of the underlying material. This, of course, exemplifies composites design, which is a matter of building up rather than machining down to size. Moreover, the properties of the material may be varied as required within the thickness of the material. It is important to understand that, where composite materials are concerned, there are two separate, and possibly distinct aims when carrying out a materials test. The first is to establish fundamental material properties for subsequent use with structural analysis and design techniques. These properties, sometimes referred to as ‘single ply data’, are obtained from well-aligned unidirectional fibres loaded in a variety of directions. If the fibres are aligned in the loading direction, this represents something of an ultimate test condition where the stresses developed will be higher than is possible with any other layup of the same fibres; conversely, if the fibres are at 90° to the loading direction, the testpiece is weak and requires careful handling. The second aim is to determine the properties, or investigate the behaviour, of an existing material. This is likely to involve testing material with fibres lying at a number of angles to the principal loading direction. In many cases this may require a clear understanding of laminate analysis techniques, and of the behaviour of non-axial fibres in a laminate, if sensible use is to be made of the results of the test. Again, there are two fundamental problems to be addressed in mechanical testing, irrespective of the material under test. The first of these is to minimise and, ideally, to eliminate undesirable interactions between

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Tension 76.2 R

45

57.2

(a) 19.1

12.7 114.3 between grips at start of test

215.9 End of test material

30° bevel ± 45° tab material

4.8 Ø

12.7

(b)

12.7 69.9

(c)

76.2 254.0 53.8

6.4 R

12.7

4.8 Ø

19.1

12.7 292.1 76.2 R

6.4 Ø

(d)

12.7 19.1

57.2 215.9

57.2

6.4 Ø (e)

12.7 19.1

57.2

228.6 45° bevel

(f)

12.7 50.8

254.0 31.8 R

6.4

(g)

19.1 57.2

50.8 203.2

4.1 Tensile test specimens being used in 1969.1 (a) ASTM D 638 plastics specimen; (b) straight-sided, tabbed (Dastin); (c) longneck, bow-tie (Dastin); (d) tabbed, shouldered, for 90° fibres (Hoggart); (e) tabbed, straight-sided, 0° fibres; (f) tabbed, straightsided (Elkin); (g) tabbed, dog-bone (Rothman and Molter). R = radius, ∆ = diameter.

the means of load application and the test material. This is particularly relevant in the case of composite materials where loads, frequently very large loads, have to be introduced into the body of a material through an inherently weak phase (the matrix) without overloading the outer layers of fibres. Depending on the construction of the material, these outer

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fibres may account for most of its strength and, because of their position, are susceptible to damage.The second is that of producing as nearly pure a state of stress, in this case tensile stress, as possible.Actually, it may be argued that such a stress state is never achieved in practice and that the nearest approximation occurs when a very long, very thin filament is tested. However, as there is a requirement to test bulk samples of material, then the object of specimen design must be to minimise the problems outlined above, whilst producing the best approximation to a pure stress within the testpiece. Testpiece specifications and testing procedures are detailed in a number of published standards, or guides, four of which are summarised in Table 4.1 and illustrated in Figs. 4.2 and 4.3. These are ASTM D3039,3 BS2782,4 CRAG5 and ISO 527.6 This is a very small selection from the standards which are available, but studying them serves to demonstrate how many details vary from one standard to another. They reflect a range of opinions about how a specimen should be designed and how a test should be carried out. It is assumed that tests will be carried out in accordance with one of these procedures wherever possible, but situations can arise where, for one reason or another, a standard design of specimen cannot be used. This ±45° composite tabs 15.0 (a)

56.0

1.0 7° (90° optional) 1.5 250.0 25.0

(b)

25.0

2.0

1.5

175.0 ±45° composite tabs

(c)

15.0 (0° matl.) 25.0 (90° matl.)

50.0 Edge of grips 250.0 Composite or light alloy tabs

(d)

50.0

100.0 to 150.0 1.0 (0° material) 2.0 (90° material)

1.0 (0° material) 2.0 (90° material)

0.5 to 2.0

10.0 (0° material) 20.0 (90° material) 0.5 to 2.0

200.0 to 250.0

4.2 Current tensile specimens for use with aligned (0° and 90°) fibrereinforced material: (a) ASTM D 30393 (0°); (b) ASTM D 30393 (90°); (c) ISO 5276 (0°); (d) CRAG5 methods 300 (0°) and 301 (90°).

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Tension

47

Unbonded abrasive cloth tabs 25.0 2.5

(a) 250.0

25.0 (Strength measurements) 12.5 (Modulus measurements) 45.0 (b)

1.0 to 10.0

3.0 (min)

200.0 (min) Composite or light alloy tabs 20.0 (min) 10 t (typ)

(c)

50.0 (min)

100.0 (min) or W(1+1/tan) 1.0 to 4.0

0.5 to 2.0

4.3 Current tensile specimens for use with non-0° fibre-reinforced material: (a) ASTM D 3039;3 (b) ISO 527;6 (c) CRAG5 method 302.

chapter aims to give some background to the reasons leading to one choice of detail or another, and it is intended that it should act as a guide to a testing technique that will enable valid tests to be carried out in such cases. If excessive reference appears to be made to the ASTM standard, this should not be seen as a sign of bias, rather that ASTM generally gives more information than most other standards for the rationale behind details of specimen design and testing procedure. Such additional information and guidance are often invaluable to the practitioner, and are a welcome feature of the ASTM standards series, which other standards organisations might emulate to their own credit. Whilst the majority of tensile tests are directed towards establishing tensile modulus, ultimate tensile stress and lateral contraction ratio (Poisson’s ratio) under tensile load, simple modifications to the specimen enable a number of other factors to be investigated. Notch sensitivity and bolt-bearing tests are two examples, and the Composites Research Advisory Group (CRAG)5 gives recommendations for testpiece dimensions. Tensile loading regimes are also used for two popular forms of shear test. One of these is the lap shear test which, in turn, can be modified to investigate the behaviour of adhesive and mechanically fastened joints.The other is the ±45° shear test.

1.0 to 10.0 ± 0.5 Machined if necessary 25 ± 0.5 for strength 12.5 ± 0.5 modulus only 200 (min) Gauge (free) length 110 min

1.0 (0° UD) ±4% 2.0 (90° UD) " 2.5 (Other)b "

15 (0° UD) ±1% 25 (90° UD and other)

250 ± 4% (0° UD and other) 175 (90° UD) Gauge length 10 to 50

56 (0° UD) 25 (90° UD)

1.5

0°/90° GFRP, commonly applied at +/-45° Emery cloth (Other)

Thickness (t)

Width (W )

Overall length (L)

Tab length (LT)

Tab thickness

Tab material recommended

Similar to that under test

Not less than 3 mm

45 (min)

Composites incorporating mat, cloth, woven rovings including prepregs.

Balanced symmetric composites reinforced with continuous or discontinuous high modulus fibre.

Applicability

BS 2782: part 3: method 320 E, EN 61

ASTM D3039

Standard

GRP for hot/moist conditions Light alloy ‘satisfactory’ for ambient conditions

0.5 to 2.0

50 (min)

100 to 150 + 2LT

10 to 20, uniform

1.0 ± 0.04 (Method 300) 2.0 ± 0.04 (Method 301)

Unidirectional fibrereinforced plastics 0° (Method 300) 90° (Method 301)

CRAG methods 300 & 301

Table 4.1. Comparison of selected details of standard tensile test methods.a

0.5 to 2.0

+/-45° GFRP

0.5 to 2.0

50

150 ± 1 + 2LTc Gauge length 50 Greater of (100 + 2LT) or [w(1 + 1/tan q) + 2LT]2 If q < 15° L = (w/tan q + 2LT) where q = fibre angle 50 (min)

15 ± 0.5 (0°) 25 ± 0.5 (90°)

1 ± 0.2 (0°) 2 ± 0.2 (90°)

Fibre reinforced polymers ‘Not normally suitable for multidirectional materials’.

ISO 527

9t min. 10t typical absolute min 20

1 to 4

Multidirectional tape or woven fibre-reinforced materials. Must be axially orthotropic.

CRAG method 302

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Failure within 1 to 10 min, or strain rate = 0.01 min-1, or displacement = 2 mm min-1

Self-aligning recommended

0.1–0.3% chord 25–50% ultimate strain if ultimate strain