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The Growth of Cracks and Crazes in Polymers

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The Growth of Cracks and Crazes in Polymers THE GROWTH OF CRACKS AND CRAZES IN POLYMERS - A FRACTURE MECHANICS APPROACH GEORGE PHILIP MARSHALL MARCH W72 A thesis submitted for the degree of Doctor of Philosophy of the University of London and for the Diploma of Imperial College. Department of Mechanical Engineering Imperial College, . London S.W.7. ABSTRACT A study has been made of the use of fracture mechanics in describing crack and craze growth phenomena in plastics. The thesis which follows has been divided into three main parts. Part I has two component chapters. The first (Ch. 2)/ outlines the basis of the fracture mechanics concepts used in the analysis of results and the second chapter (Ch. 3) contains a literature survey of the state of knowledge on crazing and environmental stress cracking in plastics. Part II describes experimental work which has been undertaken to study crack growth phenomena in both air and liquid environments. Chapter 4 gives results obtained from slow crack propagation tests in PMMA in air and shows that there is a unique relationship between the fracture toughness measure Kc and the crack speed. Analysing results on a /crack speed basis is shown to ration- alise results from many different types of test and also accounts for the rate dependent material characteristics. This approach is extended in Chapter 5 to include the effects of crack propagation in polystyrene in air. For the first time, realistic values of fracture toughness have been obtained for the propaga- tion of a single crack/craze system. The Kc vs crack speed relationship is again found to provide a good basis against which results may be compared and dis- cussed. A criterion of unnotched tensile failure is also given. In Chapter 6, • , the Kc vs crack speed approach has been used to correlate data for the environ- mental stress cracking of polyethylene in alcohol environments. The approach is entirely successful and excellent reproducibility of data has been obtained. Part ill of the thesis describes a large volume of experimental work which describes craze propagation in PMMA in an alcohol environment. In Chapter 7 2 the craze growth behaviour in pre-notched specimens under constant load is analysed and a model is presented which provides a good description of the kinetics of craze growth in terms of flow of the environment through the micro- structure of the craze. The model is couched in terms of the stress intensity factor based on the original crack dimensions since it is found that macroscopi- cally this parameter controls the rate of craze growth. The model has been successfully extended in Chapter 8 to account for the effects of cyclic loading on environmental craze growth in PMMA. Excellent correlation of data has been achieved for low cyclic frequencies. The effects of higher test fre- quency have been examined in a tentative manner and a qualitative description of the results is given. 3 ACKNOWLEDGEMENTS The author is indebted to many members of the Mechanical Engineering Department at Imperial College for their assistance and advice during the course of this work. In particular he would like to thank Dr. J.G. Williams for his unstinted help and the enthusiasm with which he has supervised the project and Dr. L.E. Culver for his advice and encouragement throughout. For their assistance on the technical aspects of the experimental work the author wishes to thank Mr. L. Coutts and Mr. P. Ewing of the Polymer Engineering Group. Thanks are also given to the Plastics Institute for providing personal sponsorship for the project. 4 NOTATION a Inherent flaw size. a0 Initial crack length. Crack length at instability. al 'Crack + craze + plastic zone length. a2 . Crack + craze length. x (X) Craze length. a Crack speed. Craze speed. B Specimen thickness. Specimen width. Surface energy. Yp 'Surface work'. G Strain energy release rate. G Fracture Toughness. c K Stress Intensity Factor (S.I.F.). K Critical S.I.F. for crack growth. K Value of S.I.F. at crack instability. Ic K S.I.F. calculated using initial crack length. 0 K m S.I.F. at craze initiation. K n Critical S.I.F. for transition 'end flow' to 'side flow'. K Critical S.I.F. for maximum 'end flow'. z Equivalent value of static K in fatigue test. 0 o V K Minimum value of (K ) in fatigue test. o o A K in fatigue test. o Maximum value of (Ko ) 1 Process zone size (void spacing). o 5 Reduced size of material in process zone. 6(y) Crack opening displacement. d Craze tip displacement. e r Plastic zone size. 6 Void size. 11) Void area. a Applied stress. a Yield stress. y a Craze stress. c Craze ligament yield stress (wet craze). Failure stress. Stress amplitude-fatigue. N Cycles. E Young's Modulus. E(t) Time-dependent modulus. Density. A Solubility parameter. ro My Viscosity-average molecular weight. Viscosity. Glass transition temperature. Atmospheric pressure. t( Time. ) (A,C.,m,n, Constants. 6 ABBREVIATIONS MFI Melt Flow Index. ESC Environmental stress cracking. COD Crack opening displacement. PMMA Poly (methyl methacrylate). HIPS High impact polystyrene. PS Polystyrene. PPO Poly (2,6-dimethyl 1-1, 4-phenylene oxide). PE Polyethylene. PVC Poly (vinyl chloride) PC Polycarbonate SEN Single edge notch(ed) specimen SIF Stress Intensity Factor 7 CONTENTS CHAPTER - 1 : INTRODUCTION 12 1.1 - FRACTURE OF PLASTICS 12 1.2 - SCOPE OF THE PROJECT 15 1.3 - PLAN OF THESIS 17 CHAPTER - 2 REVIEW OF FRACTURE MECHANICS CONCEPTS 19 2.1 THE GRIFFITH APPROACH 19 2.2 - SURFACE ENERGY AND SURFACE WORK 20 2.3 - STRAIN ENERGY RELEASE RATE (T 21 2.4 - CRACK EXTENSION FORCE 22 2.5 - STRESS INTENSITY FACTOR APPROACH 23 24 t 2.5.1 Fracture modes 2.5.2 Derivation of stress intensity factor (K) 25 2.6 - PLASTIC ZONES 27 2.6.1 The Duddale model 27 2.6.2 Crack opening displacement 28 CHAPTER - 3 CRACKING AND CRAZING IN PLASTICS - LITERATURE SURVEY 30 3.1 - INTRODUCTION 30 3.2 - CRAZING IN GLASSY PLASTICS 31 3.2.1 Nature of the craze 32 3.2.2 Craze structure 34 3.2.3 Craze initiation 35 3.2.4 Craze growth 37 3.3 DEFORMATIONAL RESPONSE OF CRAZES 38 3.4 EFFECT OF STRAIN RATE 40 3.5 EFFECT OF TEMPERATURE 42 3.6 CRAZES AND FRACTURE OF GLASSY PLASTICS 44 3.6.1 Molecular orientation at crack tips 44 3.6.2 Crazing at crack tips 45 3.6.3 Energy contributions to surface work 46 3.7 - CRAZE BREAKDOWN AND FRACTURE 47 3.7.1 Slow speed fracture 47 3.7.2 High speed fracture 48 3.8 - CRAZE TOUGHENING 50 - 8 3.9 - - ENVIRONMENTAL STRESS CRAZING 51 3.9.1 Role of the environment 51 3.10 - ENVIRONMENTAL STRESS CRACKING OF POLYETHYLENE 54 3.10.1 Nature of the problem 54 3.10 2 Structure of polyethylene 55 3.10.3 Crack initiation 56 3.10.4 External variables 57 (a) Molecular weight 57 (b) Density 57 (c) Orientation 58 (d) Temperature .58 3.10.5 Finale 59 CHAPTER 4 FRACTURE OF PMMA IN AIR - 293°K 4.1 INTRODUCTION 61 4.2 EXPERIMENTAL PROGRAMME 66 4.2.1 Specimen geometries 66 4.2.2 Apparatus 66 4.2.3 Calculations 68 4.2.4 Notching 71 4.3 EXPERIMENTAL RESULTS 75 4.3.1 Constant load tests 75 4.3.2 Instron tests (tapered and torsion 78 specimens) 4.4 CRAZE APPEARANCE 80 4.5 COMPARISON OF RESULTS 81 4.6 EFFECT OF STRAIN RATE ON K 83 -Tc 4.7 DISCUSSION OF K vs CRACK SPEED CURVE 85 c 4.7.1 Viscoelastic effects 86 4.7.2 Thermal effects and instability 87 4.7.3 Complete Kc vs a curve 88 4.8 COMPARISON OF RESULTS IN LITERATURE 91 4.8.1 Experimental factors 91 4.9 CLOSURE 93 CHAPTER - 5 FRACTURE OF POLYSTYRENE IN AIR AT 293°K 5.1 - INTRODUCTION 95 5.2 - EXPERIMENTAL 98 5.2.1 Tapered cleavage tests (I) 98 9 5.3 - NOTCHING METHODS 99 5.3.1 Slow razor notching 100 5.3.2 Impact notching 102 5.3.3 Fatigue notching 105 5.4 - EXPERIMENTAL-FATIGUE NOTCHED SPECIMENS 107 5.4.1 Tapered cleavage tests (II) 107 5.4.2 SEN tests 109 5.4.3 Fractography 111 5.5 DISCUSSION OF RESULTS 113 5.5.1 Validity of results 113 5.5.2 Comparison of results 115 5.5.3 Craze stress 116 5.5.4 Fracture mechanism for polystyrene 118 5.6 CLOSURE 122 CHAPTER - 6 : ENVIRONMENTAL STRESS CRACKING OF POLYETHYLENE 6.1 - INTRODUCTION 123 6.1.1 Test methods for E.S.C. 12.3 6.1.2 Paradoxes in testing 12.5 6.2 - SCOPE OF PROJECT 126 6.3 - TEST PROGRAMME 127 6.3.1 Experimental detai Is 127 6.3.2 Constant load tests 127 6.3.3 Strain rate tests 134 6.4 - DISCUSSION OF RESULTS 136 6.4.1 Kc vs crack speed curve 136 6.4.2 Relevance of fracture mechanics 136 CHAPTER - 7 CRAZE GROWTH IN PMMA IN METHANOL - 293°K 7.1 - INTRODUCTION 140 7.2 - TEST PROGRAMME 142 7.2.1 Preliminary tests 142 7.2.2 Craze growth tests 143 7.3 CRITICAL K VALUES 147 o 7.3.1 Craze initiation 147 7.3.2 Craze propagation 149 10 7.4 CRAZE APPEARANCE 150 7.4.1 General 150 7.4.2 Craze front geometries 152 7.4.3 Craze shape 7.5 - ANALYSIS OF CRAZING MECHANISM 155 7.5.1 Model for craze formation and growth 155 (a) Craze formation 156 (b) Void formation 157 (c) Craze growth 158 7.5.2 Void area 159 7.5.3 Void area in terms of COD 161 7.5.4 Flow of environment into a craze 163 7.5.5 End flow of environment 165 7.5.6 Side flow of environment 166 7.6 - SIDE AND END FLOW EFFECTS 168 7.6.1 No side flow tests 168 7.6.2 No side flow Km < K0 < Kn 168 I 7.6.3 No side flow K0 > Kn 169 7.7 - DISCUSSION OF RESULTS 170 7.7.1 Application of model 171 (a) _fnd flow results 171 (b) Side flow results 176 7.8 ESTIMATION OF CRAZING PARAMETERS 178 7.8.1 Void spacing 178 7.8.2 Void size 179 7.8 3 Craze yield stress 179 7.9 FRACTURE PROCESSES - PMMA IN METHANOL 182 7.9.1 'Mirror' surface 182 7.9.2 'Corrugated' surface 186 7.9.3 Other markings 1.89 7.10 CLOSURE CHAPTER 8 PMMA IN METHANOL - EFFECT OF CYCLIC LOAD 193 8.1 FATIGUE TESTING 193 8.1.1 Fatigue of plastics 194 8.1.2 Fracture mechanics and fatigue 196 8.1.3 Environmental fatigue 197 8.2 EXPERIMENTAL PROGRAMME 199 •- 11 8.3 CRAZE GROWTH UNDER VARYING LOADS 200 8.3.1 Varying K0 tests 200 8.3.2 Load/unload tests 201 8.4 ANALYSIS OF CRAZE GROWTH - CYCLIC LOADING 204 8.4.1 Craze growth - K0 = 0 204 8.4.2 Craze growth - K0 > Kn 206 8.5 RAMP LOADING TESTS 209 8.5.1 Very slow cycling rates x 10-4 Hz) 209 8.5.2 Cyclic loading at 10-1 Hz 210 8.5.3 Craze appearance 211 8.5.4 No side flow tests 212 8.6 CRAZE BREAKDOWN 212 8.7 MODELLING THE RESULTS 216 8.8 FREQUENCY EFFECTS 220 8.8.1 Tests at 10-1 ÷ 5 x 10-1 Hz 220 8.8.2 High frequency tests (30 Hz) 221 8.8.3 Discussion of results 222 8.9 CLOSURE CONCLUSIONS REFERENCES 12 CHAPTER 1.
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