Fracture Behaviour of Polymers

Fracture Behaviour of Polymers

Fracture Behaviour of Polymers

A. J. KINLOCH Department of Mechanical Engineering, Imperial College of Science and

Technology, University of London, Exhibition Road, London, UK

and

R. J. YOUNG Department of Materials, Queen Mary College, University of London,

Mile End Road, London, UK

Springer-Science+Business Media, B.V.

First edition 1983 by Elsevier Science Publishers Ltd Reprinted 1985 Reprinted 1988 Reprinted 1990 Reprinted 1995 by Chapman & Hall

© 1995 Springer Science+Business Media Dordrecht Originally published by Chapman & Hall in 1995 Softcover reprint of the hardcover I st edition ISBN 978-94-017-1596-6 ISBN 978-94-017-1594-2 (eBook) DOI 10.1007/978-94-017-1594-2

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library of Congress Cataloging-in-Publication Data available Kinloch, A. I.

Fracture behaviour of polymers. 1. Polymers and polymerisation I Title II. Young, R.I. 547.7'04541

Preface

Over recent years there has been a tremendous upsurge in interest in the fracture behaviour of polymers. One reason for this is the increasing use of polymers in structural engineering applications, since in such circumstances it is essential to have as complete an understanding as possible of the polymer's fracture behaviour. This book is designed to meet the requirements of those who need to be informed of the latest developments in the field of polymer fracture. It is written particularly for research workers but it should also prove invaluable for advanced students taking final-year undergraduate or postgraduate courses.

The main emphasis is upon the use of fracture mechanics in the study of polymer fracture but this approach is then developed to cover the micromechanisms of the fracture process. Particular prominence is given to the relationship between structure, mechanical properties and the mechanics and mechanisms of fracture. The first chapter is a brief introduction which has several aims. One is to introduce polymers to the reader who does not have a strong background in the subject and another is to provide background material that will be used at later stages. The book is then split into two main parts: the first deals with the mechanics and mechanisms whilst the second is concerned with materials. In Part I phenomena such as molecular fracture, fracture mechanics, shear yielding and crazing are covered from a general viewpoint. In Part II the properties of the different types of polymer are discussed separately. One problem with thif; approach is that some topics are dealt with in several different places and some repetition and cross-referencing is inevitable. For example, crazing is often studied as a general phenomenon but it is also important in controlling crack

v

VI PREFACE

propagation in glassy thermoplastics and as a major toughening mechanism in multiphase polymers. However, the usefulness of covering the topic in several different chapters is that the interrelationship between the different aspects can more readily be appreciated. Also the mathematical aspects of a topic such as crazing can be developed separately from the discussion of crazing during the fracture of particular types of polymer.

The authors would like to thank many of their friends and colleagues in the field of polymer fracture for many useful discussions and help in the preparation of this book. They are particularly grateful to E. H. Andrews, C. B. Bucknall, A. M. Donald, E. J. Kramer, G. J. Lake, P. E. Reed, S. J. Shaw, A. Thomas, D. Tod and J. G. Williams who have read various chapters, provided copies of manuscripts in advance of publication and supplied original micrographs. They are also grateful to Gillian Kinloch and Karen Wiggins for typing the manuscript. Finally they would like to extend their gratitude to their wives and families for their great patience and support throughout the period of preparation of the book.

A. J. KINLOCH

R. J. YOUNG

Acknowledgements

The authors wish to thank the following publishers for permission to reproduce illustrations from previous publications:

Chapman and Hall Ltd-Figs 1.7, 4.6, 4.8, 4.9, 4.14, 5.11, 5.12, 6.8, 7.7(c), 7.12, 7.16, 9.6, 11.2;

John Wiley and Sons Inc.-Figs 4.11, 4.13(a), 11.1. Springer Verlag-Fig. 6.10 (b-d). Taylor and Francis Ltd-Figs 5.2, 7.14(a, b). IPC Science and Technology Press Ltd-Figs 4.12, 4. 13 (b) ,

9.13(b, c). Society of Plastics Engineers Inc.-Fig. 10.12.

A number of other figures in the book are based upon already published material and, in these cases, an appropriate acknowledgement appears in the caption.

VII

Contents

Preface

Acknowledgements

Main Notation

Main Abbreviations

Chapter 1 Introduction 1.1 Basic Concepts

1.1.1 Definitions 1.1.2 Classification of polymers 1.1.3 Molar mass ..... .

1.2 Synthesis and Characterisation of Polymer Molecules 1.2.1 Synthesis . . . . . . . . 1.2.2 Identification of polymers . 1.2.3 Measurement of molar mass 1.2.4 Macromolecules in solution

1.3 Structure of Solid Polymers 1.3.1 Amorphous polymers 1.3.2 The glass transition 1.3.3 Crystalline polymers 1.3.4 Crystallisation and melting

1.4 Stress and Strain 1.4.1 Stress ........ . 1.4.2 Strain ........ . 1.4.3 Plane stress and plane strain 1.4.4 Relationship between stress and strain

1.5 Deformation of Polymers 1.5.1 Elastic deformation

ix

v

vii

xvii

xxv

1 2 2 3 7 8 8

10 10 11 12 12 14 15 15 18 18 20 20 22 23 23

x CONTENTS

1.5.2 Viscoelasticity . . . . . . 1.5.3 Hysteresis and plastic flow 1.5.4 Shear yielding .. . 1.5.5 Crazing .... .

1.6 Fracture of Polymers . . . 1.6.1 General approaches 1.6.2 General behaviour . 1.6.3 Stresses at crack tips 1.6.4 Griffith fracture 1.6.5 Toughening mechanisms

1.7 Concluding Remarks References ........ .

PART I-MECHANICS AND MECHANISMS

26 29 31 31 32 32 33 33 35 36 37 37

Chapter 2 Molecular Aspects . . . . . 43 2.1 Introduction . . . . . . . . . . . 43 2.2 Fracture on the Molecular Level . . 44

2.2.1 Theoretical strength of a solid 44 2.2.2 Molecular fracture in polymers 47

2.3 Kinetic Approach to Fracture 50 2.4 Techniques for Studying Molecular Deformation and Fracture 54

2.4.1 Techniques for studying bond straining 55 2.4.2 Study of bond breakage 57 2.4.3 Void formation and growth . . . . . 60

2.5 Micromechanisms of Polymer Fracture 61 2.5.1 Molecular fracture during deformation 62 2.5.2 Microvoid formation and craze growth 69

2.6 Concluding Remarks 70 References ....... 71

Chapter 3 Fracture Mechanics 74 3.1 Introduction . . . . . . 74 3.2 Energy Balance Approach . 75

3.2.1 Basic principles 75 3.2.2 Linear elastic fracture mechanics 77 3.2.3 Bulk non-linear elastic behaviour 79 3.2.4 Bulk inelastic behaviour 84

3.3 Stress-Intensity Factor Approach 86 3.3.1 Basic principles 86 3.3.2 Small scale yielding 88

3.4 Relationship between G and K 92 3.5 Thickness Effects . . . . . 93 3.6 Experimental Considerations 97

3.6.1 Flexible polymers 97 3.6.2 Rigid polymers 97

CONTENTS

3.6.3 Value of Gle and KIc 3.7 Concluding Remarks

References

Chapter 4 Shear Yielding ..... . 4.1 Introduction . . .. ..... . 4.2 General Aspects of Yield Behaviour

4.2.1 Definitions ....... . 4.2.2 Mechanical tests ..... . 4.2.3 Viscoelastic nature of yield behaviour 4.2.4 Criteria for shear yielding 4.2.5 Molecular theories . .

4.3 Inhomogeneous Deformation 4.3.1 Causes . . . . . . . 4.3.2 Types of inhomogeneous deformation 4.3.3 Shear bands in glassy polymers 4.3.4 Crystalline polymers . . . . .

4.4 Shear Yielding and Crack Initiation . . 4.5 Shear Yielding and Crack Propagation

4.5.1 Mechanisms 4.5.2 Criteria

4.6 Concluding Remarks References

Chapter 5 Crazing 5.1 Introduction . 5.2 Microstructure 5.3 Micromechanics

5.3.1 Mechanical properties of crazes and craze fibrils 5.3.2 Models of craze shape and stress distribution

5.4 Craze Initiation ...... . 5.4.1 Mechanisms and criteria 5.4.2 Kinetics

5.5 Craze Growth . . . . . . 5.5.1 Mechanisms 5;5.2 Kinetics and criteria

5.6 Craze Breakdown 5.6.1 Mechanisms 5.6.2 Kinetics 5.6.3 Criteria

5.7 Effect of Polymer Structure 5.7.1 Molar mass .... 5.7.2 The role of molecular entanglements 5.7.3 Orientation ... 5.7.4 Chemical structure

5.8 Concluding Remarks References ..... .

xi

101 104 104

107 107 108 108 110 111 114 117 119 120 120 122 127 128 132 132 139 142 143

147 147 149 152 152 155 158 158 165 165 165 167 169 169 171 173 174 174 175 176 177 177 178

xii CONTENTS

Chapter 6 Impact and Fatigue 6.1 Introduction . . . 6.2 Impact Tests . . . . . . .

6.2.1 Introduction 6.2.2 Experimental methods 6.2.3 Effect of specimen geometry 6.2.4 A fracture mechanics approach

6.3 Dynamic Fatigue . . . . . . . . 6.3.1 Introduction ..... . 6.3.2 Experimental considerations 6.3.3 Thermal fatigue failure . 6.3.4 Mechanical fatigue failure

6.4 Static Fatigue 6.4.1 Introduction 6.4.2 Mechanisms 6.4.3 Life-prediction

6.5 Concluding Remarks References .....

PART ll-MATERIALS

Chapter 7 Glassy Polymers I-Thermoplastics 7.1 Introduction . . . . . . . . . 7.2 Brittle Fracture ....... .

7.2.1 Effect of testing variables . 7.2.2 Effect of polymer structure

7.3 Crack Propagation 7.3.1 Crack velocity ..... . 7.3.2 Temperature ..... . 7.3.3 Relaxations and crack propagation 7.3.4 Adiabatic/isothermal transitions 7.3.5 Specimen thickness 7.3.6 Molar mass . 7.3.7 Orientation . 7.3.8 Environment

7.4 Micromechanisms 7.4.1 Craze initiation and growth 7.4.2 Environmental crazing . . 7.4.3 The structure of crazes . . 7.4.4 Shear yielding . . . . . . 7.4.5 Crazing versus shear yielding: entanglements 7.4.6 Crack propagation 7.4.7 Crack healing

7.5 Impact and Fatigue 7.5.1 Impact ...

182 182 182 182 185 188 192 197 197 197 200 202 211 211 212 214 220 220

229 229 230 231 237 241 242 245 247 247 249 251 252 254 255 256 256 260 261 263 267 269 270 270

7.5.2 Dynamic fatigue 7.5.3 Static fatigue


CONTENTS

Chapter 8 Glassy Polymers D-Thermosets 8.1 Introduction ....... . 8.2 Brittle Fracture .......... .

8.2.1 Stress/strain behaviour .... . 8.2.2 Fracture strength, fracture energy and flaws 8.2.3 Cross-link density

8.3 Crack Propagation ...... . 8.3.1 Fracture mechanics testing 8.3.2 Material variables 8.3.3 Testing variables 8.3.4 Crack velocity . . 8.3.5 Causes of unstable propagation

8.4 Failure Mechanisms 8.4.1 Crack propagation . . 8.4.2 Plastic deformation 8.4.3 Crazing ..... . 8.4.4 Polymer microstructure

8.5 Failure Criteria ..... . 8.5.1 Constant crack-opening displacement 8.5.2 Critical stress/distance criterion

8.6 Impact and Fatigue .. 8.6.1 Impact . . . . 8.6.2 Dynamic fatigue 8.6.3 Static fatigue


Chapter 9 Crystalline Polymers 9.1 Introduction . . . . . . .

9.1.1 General mechanical behaviour 9.2 Deformation ......... .

9.2.1 Elastic deformation of polymer crystals 9.2.2 Elastic deformation of semicrystalline polymers 9.2.3 Plastic deformation and drawing ..... .

9.3 Fracture of Polymer Crystals .......... . 9.3.1 Molecular fracture: macroscopic single crystals 9.3.2 Intermolecular cleavage ..... .

9.4 Fracture of Isotropic Semicrystalline Polymers . 9.4.1 Effect of morphology and structure 9.4.2 Crack propagation and fracture mechanics 9.4.3 Effect of testing conditions ...... .

xiii

273 277 279 280

286 286 287 287 289 290 291 291 293 296 298 300 301 301 304 306 307 309 309 311 315 315 316 317 320 320

324 324 324 326 326 330 331 332 333 337 338 338 342 346

xiv CONTENTS

9.4.4 Environmental fracture and crazing 9.5 Fracture of Oriented Semicrystalline Polymers

9.5.1 Tensile strength ..

354 357 358 360 361 363 365

9.5.2 Fatigue . . . . . . 9.5.3 Failure mechanisms

9.6 Concluding Remarks References . . . . .

Chapter 10 Rubbers . . . . . . . 370 10.1 Introduction ....... 370 10.2 Energy Dissipating Mechanisms 371 10.3 Initiation of Fracture 377

10.3.1 Introduction 377 10.3.2 Initiation under triaxial stresses 378 10.3.3 Intrinsic fracture energies 382

10.4 Crack Propagation 386 10.4.1 Stresses at crack tips . . 386 10.4.2 Amorphous rubbers 388 10.4.3 Strain-crystallising rubbers 393 10.4.4 Filled rubbers 394 10.4.5 Fatigue failure ..... 395

10.5 Tensile Fracture . .. ..... 398 10.5.1 Failure under combined stresses 398 10.5.2 Effect of rate and temperature 400 10.5.3 Effect of degree of cross-linking 403 10.5.4 Energy dissipating mechanisms and tensile fracture 405 10.5.5 Multiphase rubbers 406 10.5.6 Theories of tensile failure 411

10.6 Concluding Remarks 416 References . . . . . . . . . . 416

Chapter 11 Toughened Multiphase Plastics 421 11.1 Introduction ....... 421 11.2 Mechanisms of Toughening . 423

11.2.1 Particle deformation 423 11.2.2 Shear yielding . . . 425 11.2.3 Crazing ..... 428 11.2.4 Simultaneous shear yielding and crazing 432 11.2.5 Crack pinning . . . . . . . . . . . . 434

11.3 Stress/Strain Relationships . . . . . . . . . . 438 11.4 Structure !Property Relationships ....... 442

11.4.1 Concentration and size of second-phase particles 442 11.4.2 Particle/matrix adhesion 448 11.4.3 Matrix properties ..... 451

11.5 Test Variables .......... 452 11.5.1 Effect of temperature and rate 452 11.5.2 Dynamic fatigue . . . . . . 462

11.5.3 Static fatigue 11.6 Concluding Remarks

References . . . . .

Author Index

Subject Index

CONTENTS xv

465 467 467

473

489

Main Notation

a crack length or change in toughening semimajor axis of mechanism elliptical hole dv mean distance between

a crack velocity void centres ac critical crack velocity e strain af crack length at which ea strain amplitude

propagation becomes ec critical craze strain relatively fast ef fracture strain

aT time-temperature shift em mean strain factor ey yield strain

ao intrinsic, or inherent, eo applied strain crack, or flaw, length f a damage function

b specimen thickness f( ) a function bmin specimen thickness at g distribution function

ductile/brittle transi- ge spectroscopic splitting tion factor

bn specimen thickness in h specimen height plane of crack h Planck's constant

C critical distance ahead ha thickness of adhesive of crack layer

Cijkl tensor containing stiff- hm value of ha at max-ness constants imum adhesive frac-

cp specific heat capacity ture energy, df fibre diameter G1cmUoint) dp interparticle distance hp equilibrium separation dpc critical value of dp for of atomic planes

xvii

xviii MAIN NOTATION

hr hysteresis ratio zone radius at crack k thermal conductivity growth k Boltzmann's constant r" ye plane-stress plastic-zone kl ~kj constants radius at crack I specimen length growth Ie chain contour length S span

between entangle- Se spin vector ments Sf stress ratio

1m length of moment arm t time lr length of slow crack ter critical time for crack

growth region healing ~l fitting length constant tf time-to-failure m constant in Paris tj time for crack initiation

fatigue equation phase mp plastic constraint factor t\ loading period mw Weibull modulus to pre-exponential con-n constant in craze/crack stant

growth equations tp time for crack propaga-fib average number of tion phase

primary main chain v volume bonds between cross- v* activation volume links Vf volume fraction

P hydrostatic component Vfp volume fraction of of the stress tensor particles

p pressure driving fluid Vfv volume fraction of into a craze voids

Pc critical value of P W specimen width Pf failure probability Ws\ width of shear lip q constant in fatigue equ- x separation of atomic

ation planes r distance (polar coordi- y rate of extension

nate) rp particle radius A area ry plastic-zone radius Af constant in Paris r' y plane-strain plastic- fatigue equation

zone radius Av constant in craze/crack r" y plane-stress plastic-zone growth equation

radius AE pre-exponential con-rye plastic-zone radius at stant in Eyring equa-

crack growth tion , rye plane-strain plastic- AI constant relating infra-

MAIN NOTATION xix

red vibration fre- Go intrinsic fracture energy quency to applied (Subscripts I, II or III to the stress above indicate mode of

AL ligament area failure-see Fig. 3.6) AR constant relating LlG fracture energy range

Raman vibration fre- during fatigue cycling quency to applied LlG* activation energy for strain fracture

Bf constant in fatigue equ- LlG!B activation energy for ation chain scission

Bs constant CO shear modulus BG constant H magnetic field strength C compliance LlH* activation enthalpy ChCz constants in Williams- II first stress invariant

Landel-Ferryequa- 1(8) intensity of scattered tion X-rays

Ce constant in Williams I contour integral theory of craze Ie value of I for fracture growth 110ss loss compliance

Cr constant in fatigue equ- Jstorage storage compliance ation K stress-intensity factor

Dcr creep compliance Ke stress-intensity factor at Df constant in fatigue equ- fracture, or fracture

ation toughness E Young's modulus K' e plane-strain value of Kc Eo unit time Young's mod- K" e plane-stress value of Ke

ulus K* c stress-intensity factor LlE difference in energy for instability LlE* activation energy for Kea stress-intensity factor at

yielding crack arrest F work done Kef value of Ke at which Ge fracture energy relatively rapid crack G' e plane-strain fracture propagation occurs

energy Kci stress-intensity factor at G" e plane-stress fracture crack initiation

energy Kd dynamic fracture tough-Gem maximum value of Ge ness Gco energy needed to cause Kj value of K to initiate

crazing crazing Gic interfacial fracture Km critical value of K for

energy craze growth

XX MAIN NOTATION

Kmax maximum value of K Pa applied load at crack Kmin minimum value of K arrest Kn critical value of K for Pc applied load at onset of

rapid craze growth crack propagation aK stress-intensity factor Q geometry constant

range during fatigue R plastic-zone length in cycling Dugdale model ( = Kmax - Kmin) R molar gas constant

(Subscripts I, II or III to the Rc plastic-zone length at above indicate mode of crack growth failure-see Fig. 3.6) (R~s)! root mean square end-

i average distance be- to-end distance of a tween cross-links in polymer molecule the unstrained state (R;ms)e! root mean square end-

Lm dimension of a cavity to-end distance of a M molar mass chain of molar mass M" average molar mass be- Me

tween cross-links (R~ms)o! unperturbed dimensions ~t average molar mass be- of a polymer

tween physical en- molecule tanglements S shape factor

Mn number-average molar T temperature mass f crack tip temperature

Mv viscosity-average molar for instability mass Tb ductile-to-brittle transi-

Mw weight-average molar tion temperature mass Tc crystallisation tempera-

Mo 'zero strength' molar ture mass Tg glass transition temper-

N number of cycles ature N Avogadro's number Tm crystalline melting Na number of backbone temperature

bonds per unit area TO m equilibrium melting Nb number of chains per temperature

unit volume Tr reference temperature Nf number of cycles to TL line energy per unit

failure length of crack front Nm number of cavities per U stored elastic energy

unit volume Ub bond dissociation P applied load energy

MAIN NOTATION xxi

Uc stored elastic energy at criteria crack growth Z dimensional geometry

Ud energy dissipation rate factor UH loss in pendulum energy Zg factor related to cavity

during an impact test geometry UI energy consumed in

tossing the broken a c factor reducing craze impact specimen out surface stress in ac-of the machine tive environments

au* activation energy for af reduction in stress in thermal bond dissoci- fatigue damage zone ation aT primary molecular-

W strain-energy density relaxation (i.e. strain-energy per Jl Bohr magneton unit volume) {3g coefficient relating the

Wa thermodynamic work of pressure dependence adhesion for an inter- of Tg face {3r secondary molecular-

We applied strain-energy relaxation density for crack "I surface free-energy growth 'Ya surface free-energy of

Wd hysteresis, or loss, adhesive strain-energy density "las, 'YSL interfacial free-energies

Wdf value of Wd at fracture "Is surface free-energy of Wr applied strain-energy substrate

density for tensile 8 crack-opening displace-fracture ment

Wr retraction, or recovera- 8c craze thickness ble, strain-energy 8r phase angle density tan 8r loss factor

~e strain-energy density 8s solubility parameter around crack tip at 8t crack-opening displace-crack growth ment at crack tip

Wo applied, or input, 8te crack-opening displace-strain-energy density ment at crack tip at

X, Xl constants in Bowden crack growth and Oxborough craze 1] stress concentration criteria 1]v viscosity

Y, YI constants in Bowden 8 angle (polar coordinate and Oxborough .craze or X-ray scattering)

xxii MAIN NOTATION

(Jsb angle of shear bands ~ (l-~y (Jsz angle of inclined neck A extension ratio P crack tip radius Ac extension ratio at crack Pc crack tip radius at

growth crack growth Acf craze fibril extension Pd density

ratio (T stress Af extension ratio at frac- (Ta stress amplitude

ture (Tb stress bias Amax maximum value of ap- (Tc applied stress at crack

plied extension ratio growth Asz extension ratio in shear (Tcf craze fibril stress

deformation zone (Tcs craze surface stress Aw wavelength (Tf fracture stress, or Awc wavelength in meniscus strength

instability craze (Tfc critical tensile strength growth model at the ductile/brittle

Ao applied extension ratio transition IL, ILM' ILc, ILT coefficients in yield (Tfoo fracture strength of

criteria to model polymer with infinite the effect of pressure molar mass

ILmag magnetic moment of (Tic interfacial debonding free electron stress

v Poisson's ratio (Tij component of the stress Vd applied frequency in tensor

dynamic-fatigue tests (Tm mean stress level Ve Raman vibration fre- (Tmax maximum value of (To

quency Umin minimum value of (To

Vef effective number of (Tp plastic-zone surface network chains per stress unit volume (Tt stress at crack tip

Vem frequency of electron (Tte critical stress at crack magnetic radiation tip

Vr rate of bond breakage (Tth threshold stress VrO temperature- (Ttheo theoretical fracture

independent constant stress for bond breakage (Ty uniaxial tensile yield

Va Infra-red vibration fre- stress quency (To applied stress

MAIN NOTATION xxiii

0"1> 0"2, 0"3 principal stresses in pure shear, i.e. in absence T time variable of any hydrostatic component Tact octahedral shear stress to the stress tensor) Ty pure-shear yield stress 4> energy to fracture per unit Tc shear stress needed for volume of shear lip

yield in Coulomb 1/1 energy dissipated in yield criterion viscoelastic and plastic

TM shear stress needed for deformations at the flow in von Mises crack tip yield criterion 4 displacement

TT shear stress needed for e theta temperature yield in Tresca yield CI> loss function criterion n pressure activation

(Superscript 0 indicates value volume

ABS HOPE HIPS LOPE MOPE NR PBA PBT PC PES PET PMMA POM PP PPO-T PPO PTFE PVC SAN SBR

Main Abbreviations

acrylonitrile-butadiene-styrene copolymer high-density polyethylene high-impact polystyrene low-density polyethylene medium-density polyethylene natural rubber poly(p-benzamide) poly(p -phenylenebenzobisthiazole) polycarbonate poly(ether sulphone) poly( ethylene terephthalate) poly(methyl methacrylate) polyoxymethylene == polyacetal polypropylene poly(p-phenylene terephthalamide) poly(2,6-dimethyl l,4-phenylene oxide) polytetraftuoroethylene poly(vinyl chloride) styrene-acrylonitrile copolymer styrene-butadiene rubber

xxv

Fracture Behaviour of Polymers

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