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Crofton-PSJ-1980-Phd-Thesis.Pdf 1 THE ROLE OF INCLUSIONS IN THE INITIATION AND PROPAGATION OF FATIGUE CRACKS IN LOW ALLOY STEELS by P.S.J. Crofton, MSc, DIC A thesis presented for the degree of Doctor of Philosophy of the University of London July 1980 Department of Mechanical Engineering Imperial College of Science & Technology London SW7 2BX ABSTRACT The role of inclusions in the initiation and propagation stages of fatigue crack growth in low alloy steels has been studied. Special attention is given to fatigue caused by repeated internal pressurisation in axisymmetric components. Large diameter ratio thick cylinders containing double opposed cross- holes have been tested for five l•ow alloy steels. Analysis of the results shows that the fatigue limit under a repeated internal pressure regime is independent of steel composition. The fatigue limit is shown to increase with tensile strength, but to be more dependent on the geometry of the intersection between the main bore and cross-hole. A technique has been developed to measure crack growth rate in plain cylinders subjected to repeated internal pressure fatigue cycling. Results are given to show that a fracture mechanics formalism gives a sensible representation of crack growth in cylinders. Fatigue crack initiation and propagation has been investigated in two steels of nominally similar composition but with differing inclusion contents. It is shown that anistropy in mechanical properties is reflected in the fatigue behaviour of these two steels. Fractographic analysis shows that inclusions are a major cause of fatigue crack initiation in both steels. • The same fracture mechanism is observed to occur in repeated direct stress fatigue tests in air as occurs when these steels are subjected to repeated pressurisation in the form of thick cylinders. 'A consistent theory is developed to show that a mode I fatigue crack propagation limit is determining at the fatigue limit of these steels. Differences in fatigue crack propagation rate measured in air are explained in terms of the inclusion population in the respective steels. The significance of the experimental findings are discussed in the light of a proposed design code for pressure vessels working in the kilobar region. Finally, recommendations for further work are made to determine the range of materials and situations to which the proposed direct stress fatigue criterion can be applied. 3 ACKNOWLEDGEMENTS The author wishes to thank Dr J. Rogan, under whose supervision this work was carried out. His generous provision of financial support throughout the course of this work is greatly appreciated. Special thanks are also due to the many staff members of this Institution for valuable advice and practical help. In particular, the assistance of Dr D.P. Isherwood, Dr C.L. Tan, Mr P. Grant, Mr G. Eles, Mr G.C. Klintworth and Mrs E.A. Hall is gratefully acknowledged. Finally, the author is especially grateful to his wife for her patience and forebearance during the course of this work. -4 CONTENTS Page Title Page 1 Abstract 2 Acknowledgements 3 Contents 4 Nomenclature 10 CHAPTER 1: INTRODUCTION 12 1.1 Introduction 12 1.2 Objectives of Present Work 15 1.3 Outline of Present Work 16 CHAPTER 2: REVIEW OF THE LITERATURE 19 2.1 Early History of Fatigue 19 2.2 The Mechanisms of Fatigue 19 2.2.1 Effect of stress conditions 24 2.2.1.1 Mean stress 24 2.3 Continuum Mechanics Approach to Fracture 26 2.3.1 Linear elastic fracture mechanics (LEFM) 26 2.4 The Application of LEFM to Fatigue Crack Propagation 29 2.4.1 Crack growth rate models 29 2.5 Fluctuating Pressure Fatigue 35 2.5.1 Fatigue of thick-walled cylinders subjected to repeated internal pressure 35 2.5.1 (a) Fatigue of thick cylinders subjected to repeated internal pressure about a mean pressure 43 -5 Page 2.5.2 Fatigue strength of other thick-walled configurations 47 2.5.3 Stress intensity factors for thick-walled cylinders 48 2.5.4 Stress intensity factors for semi-elliptic cracks in thick-walled cylinders 54 2.6 The Influence of Microstructure on Fracture and Fatigue 57 2.6.1 Fatigue 57 CHAPTER 3: EXPERIMENTAL PROCEDURES 71 3.1 Aims of Project 71 3.2 Experimental Programme 71 3.2.1 Notched fatigue strength of thick cylinders 71 3.2.2 Plain cylinder fatigue strength 72 3.2.3 Fatigue tests in air 73 3.2.4 Plane strain fracture toughness tests 73 3.2.5 Further internal pressure fatigue tests 74 3.3 Materials 74 3.3.1 Steels 74 3.3.2 Nomenclature for steels tested 75 3.3.3 Orientation 76 3.4 ' Specimen Preparation 77 3.5 Experimental Techniques 80 3.5.1 Mechanical properties of materials 80 3.5.2 Quantitative metallography 81 3.6 Repeated Internal Pressure Fatigue Tests 86 -6 Page 3.6.1 Description of Bristol machine 86 3.6.2 Double cross bore specimens 89 3.6.3 Plain cylinder tests (diameter ratio 2) 90 3.6.4 Specimen testing programme (diameter ratio = 2) CH steel 97 3.6.5 Specimen testing programme (diameter ratio = 3) B and G steels 99 3.7 Fatigue Tests in Air 100 CHAPTER 4: RESULTS OF EXPERIMENTAL PROGRAMME 107 4.1 Materials - Chemical Analysis 107 4.2 Mechanical and Physical Properties 107 4.3 Quantitative Metallography 107 4.4 Qualitative Metallography 108 4.5 Repeated Internal Pressure Fatigue Tests: Double Cross-Bore Specimens (D = 3) 111 4.6 Repeated Internal Pressure Fatigue Tests: Plain Cylinders (D = 2); Steel CH 111 4.6.1 Analysis of crack growth in plain cylinders (D = 2); steel CH 113 4.7 Repeated Internal Pressure Fatigue Tests: Plain Cylinders (D = 3); Steels B and G 114 4.8 Fatigue Tests in Air 115 4.8.1 Results of crack growth rate tests in air for steels B and G 115 4.8.2 Repeated tension fatigue tests in air for steels B and G 116 -7 Page 4.8.3 Torsion fatigue tests in air for steel B and G 116 CHAPTER 5: DISCUSSION OF RESULTS AND FURTHER RESULTS 117 5.1 Introduction 117 5.2 Cross-Bored Cylinders 117 5.2.1 Materials 119 5.2.2 Choice of specimen configuration and pressure cycle 120 5.2.3 Comparison of results 120 5.2.4 Comparison of steels 125 5.3 Plain Cylinders (D = 2) 132 5.3.1 Crack growth tests 132 5.3.2 Considerations in analysis of results 135 5.3.3 Comparison of results 139 5.3.4 Fractographic investigation of steel CH fatigue cracks 141 5.4 Fatigue Tests on Steels B and G 143 5.4.1 Introduction 143 5.4.2 Steels B and G: background information 143 5.4.3 Comparison of steels B and G 144 5.4.4 Comparison of thick cylinder fatigue results (D = 3): steels B and G 145 5.4.5 Fatigue crack shapes in thick cylinders of steels B and G 148 5.4.6 Fractographic investigation of fatigue cracks in cylinders 148 -8 Page 5.4.7 Repeated tension fatigue tests 150 5.4.8 Repeated and reversed torsion tests 151 5.4.9 Fractography on repeated tension and reversed torsion specimens 153 5.4.10 Qualitative correlation of results 155 5.4.11 Quantitative correlation of results 166 5.4.12 Comparison of fatigue failure criteria for internally pressurised cylinders 173 5.5 Implications of a Direct Stress Controlled Fatigue Criterion 175 5.6 Fatigue Crack Growth in Steels B and G 178 5.6.1 Introduction 178 5.6.2 Crack growth in air: steel B 179 5.6.3 Crack growth in air: steel G 180 5.6.4 Comparison of crack growth rates in air for steels B and G 181 5.6.5 Fractography of fatigue crack growth in steels B and G 184 5.6.6 Prediction of fatigue endurance in thick cylinders 187 5.7 Estimation of Errors 190 5.7.1 Accuracy of fatigue limits 190 5.7.2 Accuracy in inclusion sizing 191 5.7.3 Accuracy in crack growth rate measurement 192 CHAPTER 6: PRESSURE VESSEL DESIGN 194 6.1 Possible Application of Results 194 Page 6.2 Design for Static Pressure Containment 194 6.3 Design for Fluctuating Pressure Containment 201 6.3.1 Low cycle fatigue 201 6.3.2 High cycle fatigue 202 CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS 206 7.1 Conclusions 206 •7.2 Recommendations for Future Work 208 7.2.1 Cross-bored cylinders 208 7.2.2 Fatigue crack growth in pressurised components 209 7.2.3 Plain cylinders 210 References 212 List of Tables 224 Tables 225 List of Figures 239 Figures 245 List of Drawings 311 Drawings 312 List of Photographs 320 Photographs 323 - 10 - NOMENCLATURE a, b, c : crack length or half length for central cracks ao, bo, co : semi-axes of ellipsoidal or cylindrical inclusions C : material constant in Paris' law D : diameter ratio of cylinders K : stress intensity factor KIc : plane strain fracture toughness (opening mode) max : maximum value of stress intensity min : minimum value of stress intensity DK : range of stress intensity (K —min) oxth : range of stress intensity below which a fatigue crack will not propagate (threshold value) L : longitudinal axis of forging (length) m, n : exponent in Paris' law N : number of load cycles : internal pressure Q : short transverse axis of forging (thickness) R : stress ratio (mom/min) T : long transverse axis of forging (width) W : wall thickness or specimen net thickness in direction of crack growth x, y, z : coordinates or directions in an orthogonal system Greek Symbols se hoop or tangential strain in a cylindrical component a : normal stress ae : effective hoop or tangential stress in a cylindrical component hoop or tangential stress in a cylindrical component (Lame value) - 12 - CHAPTER 1 INTRODUCTION 1.1 INTRODUCTION The increasing world demand for raw materials and energy conservation has recently begun to pose new problems for designers and engineers.
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