FATIGUE AND FRACTURE MECHANICS ANALYSIS OF THREADED CONNECTIONS Feargal Peter Brennan Submitted for the Degree of Doctor of Philosophy Department of Mechanical Engineering University College London September 1992 -1- fc\ LONDII4. Uk V. Abstract This thesis aims to develop a comprehensive usable engineering design approach to the fatigue analysis of threaded connections. Although primarily concerned with the fatigue - fracture mechanics behaviour of screw threads, a broad review of stress analysis investigations in such connections is reported. Connection types, their functions and standardisation authorities are presented with the purpose of familiarising the reader with the subject and the options available to the design of threaded fasteners. Fatigue crack initiation is discussed with reference to the specific setting of a critical thread root. A crack initiation model is adapted for employment in thread root design. A novel weight function approach is developed for use in the determination of stress intensity factors for threaded connections. A generic solution is proposed valid for the fatigue crack growth from any thread root under any symmetrical stress system. Its development and discussion is examined in detail, remaining close to its proposed application. Two engineering situations where the chief structural components are comprised of threaded members are taken as case studies. The background to each situation is elaborated in detail and full-scale fatigue tests were conducted on the critical components. In all, fourteen full-scale tests under constant and variable amplitude loading are reported. -2- The results of these are analysed and used to validate the fatigue crack initiation and propagation models. Useful observations which are helpful to understanding the fracture mechanisms operating during the fatigue of threaded connections are reported. Material and environmental considerations are examined and a survey of relevant materials and their behaviour in environments associated with threaded fasteners is presented. The merits or otherwise of some common engineering practices are discussed with regard to fatigue. A method has been developed for predicting fatigue life in large threaded connections under random loading. Experimental results have been gathered on two types of components used on certain oil rigs, tether joints and drill strings. The agreement found between prediction and experiment is appreciably better than by previous methods of analysis and also points to aspects open to further improvement. -3- Acknowledgments The rotating bend drill collar tests reported in this thesis were undertaken by Dr R. F. Karé (TSC). I am grateful to Professor W. D. Dover for tactful and comprehensive supervision. I would like to thank the SERC for funding the most part of this work, and to Agip, BP and Norsk Hydro who permitted the use of their Drill String fatigue data in this thesis. I am also grateful to Dr J. H. Ong (Nanyang Technological University, Singapore) for access to his work prior to publication and to Dr L. P. Pook (UCL), Dr J. A. Witz (UCL) and Dr E. R. Jefferys (Conoco) for their suggestions and advice. -4- Table of Contents Abstract 2 Acknowledgements 4 List of Tables 9 List of Figures 10 Nomenclature 17 Chapter One - Introduction 1.1 Types of Threaded Connections 23 1.1.1 Structural Nuts and Bolts 23 1.1.2 Pressure Threaded Joints 25 1.2 Stress Analysis of Threaded Connections 26 1.2.1 Theoretical Models 27 1.2.2 Photoelastic Models 30 1.2.3 Strain Gauged Models 33 1.2.4 Finite Element Models 35 1.2.5 Electrical Analogue Model 38 1.2.6 Review 39 1.3 Fatigue Analysis 41 1.3.1 S-N Approach 42 1.3.2 Deterministic Approach 44 1.3.3 Probabilistic Approach 44 1.3.4 Cycle Counting Variable Amplitude Time Histories 47 1.4 Fracture Mechanics Evaluation of Crack Growth 49 1.4.1 Analytical SW Solutions 51 1.4.2 SW Solutions from Finite Element Analysis 55 1.4.3 Experimental SW Solutions 56 1.4.4 Weight Function SW Solutions 57 1.4.5 Crack Opening Displacement 60 1.4.6 i-Integral 63 1.5 Summary 64 1.6 References 66 -5- Chapter Two - Fatigue Crack Initiation in Threaded Connections 2.1 Introduction 82 2.2 The Mechanics of Strain Cycling 83 2.3 Fatigue Life from Materials Data 87 2.3.1 Fatigue Ductility Properties 90 2.3.2 Fatigue Strength Properties 92 2.3.3 Determination of the Local Strain 93 2.4 Mean and Residual Stresses 96 2.5 Variable Amplitude Cycling 102 2.6 Discussion 104 2.7 Summary and Conclusions 109 2.8 References 111 Chapter Three. Fatigue Crack Propagation in Threaded Connections 3.1 Introduction 130 3.2 Petroski-Achenbach COD 131 3.3 Multiple Reference States 135 3.3.1 A Bueckner Representation 135 3.3.2 Arithmetic Series Representation of COD Derivative 137 3.4 Comparison of Models 140 3.5 Weight Function for Threaded Connections 142 3.5.1 2-D Solution 142 3.5.2 3-D Solution 146 3.6 Stress Distribution 147 3.6.1 Stress Concentration Factors 149 3.6.2 Stress Distribution Due to Notches 151 3.7 Crack Shape Evolution 154 3.8 Discussion 156 3.9 Summary 160 3.10 References 162 -6- Chapter Four - Experimental Work 4.1 Introduction 205 4.2 Fatigue Tests of Tethers for Tension Leg Platforms 205 4.2.1 Determination of Load Response Spectrum 206 4.2.2 Experimental Procedure 211 4.2.3 Experimental Results 214 4.3 Fatigue Tests of Drill String Connections 216 4.3.1 Test and Specimen Details 219 4.3.2 Experimental Stress Analysis of Test Specimens 221 4.3.3 Axial Test Results 223 4.3.4 Rotating Bend Test Results 228 4.4 Discussion 230 4.5 Summary 232 4.6 References 233 Chapter Five - Failure Appraisal of Threaded Connections 5.1 Introduction 286 5.2 Stress Analysis of the Joint Geometries 286 5.3 Crack Initiation Lives 289 5.4 Fatigue Crack Growth 291 5.5 Crack Aspect Ratio 295 5.6 Summary and Conclusions 296 5.7 References 298 -7- Chapter Six - Degradation of Threaded Connections: Factors Associated with their Locale 6.1 Introduction 323 6.2 Threaded Fasteners: Steels, Coatings and Lubricants 323 6.3 Corrosion Mechanisms 325 6.4 Fatigue Behaviour of Connector Steels 328 6.5 Summary 333 6.6 References 334 Chapter Seven - Review / Future Recommendations 7.1 Introduction 363 7.2 Threaded Connections 363 7.3 Stress Analysis of Threaded Connections 364 7.4 Fatigue Crack Initiation in Threaded Connections 365 7.5 Fatigue Crack Propagation in Threaded Connections 366 7.6 Future Improved Analyses 367 Appendix I Determination of Fatigue Crack Growth Rates 369 for API C75 Steel Appendix II Derivation of the Preload Formulae 376 Appendix III Constitutive Equations for 3-D Solution 378 Appendix IV Full-Scale Fatigue Test Details 385 -8- List of Tables Table 2.1 Cyclic Material Properties of Selected Steels Table 2.2 Sensitivity of Fatigue Life Prediction to Cyclic Material Properties Table 2.3 Estimation of cy and cY'r Table 4.1 Characteristics of the Tether Load Spectrum and its Corresponding Time Series Table 4.2 Chemical Composition and Mechanical Properties of API Grade 5A 05 Steel Table 4.3 Tether Fatigue Test Details Table 4.4 Typical Chemical Composition of AISI 4145H and AG 17 Steels Table 4.5 Typical Mechanical Properties of AISI 4145H and AG17 Steels Table 4.6 Geometrical Dimensions of Drill Tool Joints (Fig 4.21) Table 4.7 Axial Load Fatigue Test Details Table 4.8 Rotating Bend Fatigue Test Details Table 5.1 Fatigue Crack Initiation Lives for C75 Steel Specimens Table 5.2 Fatigue Crack Initiation Lives for AISI 4145H Steel Specimens Table 5.3 Fatigue Crack Initiation Lives for Staballoy AG17 Steel Specimens Table 6.1 Chemical Composition of Steel Bolts and Screws Table 6.2 Mechanical Properties of Steel Bolts and Screws Table 6.3 Ladle Chemical Composition of Hot-rolled and Cold-finished Bars used for Threaded Connections Table 6.4 International Equivalent Steel Standards Table 6.5 Chemical Composition and Mechanical Properties of Selected Thread Steels Table 6.6 Fatigue Endurance (MPa) of Plated 4340 Steel -9- List of Figures Fig 1.1 ISO Metric Thread Form Fig 1.2 ISO Metric Waisted Shank Fig 1.3 Whitworth Thread Form Fig 1.4 Distribution of Load Along Thread [1.7] Fig 1.5 Patterson's Load Distribution [1.24] Fig 1.6 Rainflow Cycle Counting Fig 1.7 Polar Notation for an Embedded Crack Fig 1.8 Dugdale "Strip Yield" Model for Crack Plasticity Fig 2.1 Cyclic Stress-Strain Behaviour Fig 2.2 Stress-Life Diagram Fig 2.3 Gerber Diagram Fig 2.4 Fatigue Square Fig 2.5 Goodman Diagram Fig 2.6 Fatigue Life Prediction and Four Point Correlation Approximation Fig 2.7 Fatigue Life Prediction and Manson-Hirschberg Universal Slopes Approximation Fig 2.8 Fatigue Life Prediction and Muralidharan-Manson Universal Slopes Approximation Fig 2.9 Sensitivity of Predicted Life to a'1 Fig 2.10 Sensitivity of Predicted Life to C'1 Fig 2.11 Sensitivity of Predicted Life to b Fig 2.12 Sensitivity of Predicted Life to c Fig 3.1 Bending of an Edge Crack in a Finite Width Sheet Fig 3.2 Bending of a Circular Arc Edge Crack in a Circular Bar -10- Fig 3.3 Uniform Uniaxial Tension Fig 3.4 Pure Bending Fig 3.5 Surface Shear Fig 3.6 SIFs under Three Loading Conditions Fig 3.7 Weight Function SIP Solutions for an Edge Crack under Shear Loading Fig 3.8 Assumed Profile SW Versus Multiple Reference States Approach Fig 3.9 Edge Crack in a Thread Root Fig 3.10 Applied Loads Contributing to Thread Root Stress Fig 3.11 External Surface Crack in a Tube Fig 3.12 Internal Surface Crack in a Tube Fig 3.13 Stress Concentration Factors for a Shoulder in a Strip [3.37] Fig 3.14 Stress Distribution Through a Section due to a Notch: KT = 3.0 Fig 3.15 Stress