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Elastic-Plastic Fatigue Crack Growth Analysis Under Variable Amplitude Loading Spectra

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Elastic-Plastic Fatigue Crack Growth Analysis Under Variable Amplitude Loading Spectra Elastic-Plastic Fatigue Crack Growth Analysis under Variable Amplitude Loading Spectra by Semen Mikheevskiy A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Mechanical Engineering Waterloo, Ontario, Canada, 2009 © Semen Mikheevskiy 2009 AUTHOR'S DECLARATION I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract Most components or structures experience in service a variety of cyclic stresses. In the case of cyclic constant amplitude loading the fatigue crack growth depends only on the crack, the component geometry and the applied loading. In the case of variable amplitude loading it also depends on the preceding cyclic loading history. Various types of load sequence (overloads, under-loads, or combination of them) may induce different load-interaction effects which can cause either acceleration or reduction of the fatigue crack growth rate. The previously developed UniGrow fatigue crack growth model for constant amplitude loading histories which was based on the analysis of the local stress-strain material behaviour at the crack tip has been improved, modified and extended to such a level of sophistication that it can be used for fatigue crack growth analyses of cracked bodies subjected to arbitrary variable amplitude loading spectra. It was shown that the UniGrow model enables to correctly predict the effect of the applied compressive stress and tensile overloads by accounting for the existence of the internal (residual) stresses induced by the reversed cyclic plasticity around the crack tip. This idea together with additional structural memory effect model has been formalized mathematically and coded into computer program convenient for predicting fatigue crack growth under arbitrary variable amplitude loading spectra. The experimental verification of the proposed model was performed using 7075-T6, 2024- T3, 2324-T7, 7010-T7, 7050-T7 aluminium alloys, Ti-17 titanium alloy, and 350WT steel. The good agreement between theoretical and experimental data proved the ability of the UniGrow model to predict fatigue crack growth and fatigue crack propagation life under a wide variety of real variable amplitude loading spectra. iii Acknowledgements I would like to thank my supervisor Professor Grzegorz Glinka for the scientific support, helpful discussions, and useful comments. The Office of Naval Research, USA and Dr. A.K.Vasudevan are gratefully acknowledged for the financial support and technical guidance. I would also like to thank all graduate and undergraduate students who, in any sense, participated and helped me in my research work. In particular, I am grateful to Elena Atroshchenko for her contribution into weight functions development, Aditya Chattopadhyay for his time spent by reading and commenting my thesis, Maria El Zeghayar for gentle criticism of the proposed model, and Mohammad Amin Eshraghi for his moral support. Additionally I would like to acknowledge Jakub Schmidtke, Krzysztof Hebel and Jakub Gawryjolek for the contribution into the UniGrow software development. iv Dedication This thesis is dedicated to Svetlana Magovskaya who has always supported me in my work. v Table of Contents List of Figures.............................................................................................................................................ix List of Tables ............................................................................................................................................xiv Nomenclature ............................................................................................................................................xv Chapter 1 Introduction and Research Objectives....................................................................................1 Chapter 2 Literature Review .....................................................................................................................4 2.1 The Linear Elastic Fracture Mechanics...............................................................................................4 2.2 Constant Amplitude Fatigue Crack Growth Models...........................................................................6 2.2.1 Fatigue Crack Growth equations proposed by Paris....................................................................7 2.2.2 Two-parameter models ................................................................................................................8 2.2.3 The crack closure model ............................................................................................................11 2.3 Variable Amplitude Fatigue Crack Growth Models .........................................................................13 2.3.1 The Crack tip blunting ...............................................................................................................13 2.3.2 Residual stresses ........................................................................................................................14 2.3.3 The Crack tip plasticity..............................................................................................................15 2.3.4 The Plasticity induced crack closure..........................................................................................17 Chapter 3 The Two-Parameter Total Driving Force Model.................................................................24 3.1 Introduction and basic assumptions ..................................................................................................24 3.2 Residual compressive stresses at the crack tip, the residual stress intensity factor, and the total stress intensity parameters..................................................................................................................25 3.2.1 Linear Elastic analysis of stresses and strains ahead of the crack tip ........................................26 3.2.2 Linear Elastic analysis of stresses and strains ahead of the crack tip under compressive minimum load .....................................................................................................................................27 3.2.3 Elastic-plastic stresses and strains ahead of the crack tip ..........................................................29 vi 3.3 Residual compressive stresses near the crack tip..............................................................................31 3.3.1 Calculation of the residual stress intensity factor, Kr ...............................................................32 3.3.2 The Total maximum stress intensity factor and total stress intensity range...............................33 3.4 The Bilinear two parameters driving force .......................................................................................34 3.4.1 The average stress over the elementary material block..............................................................34 3.4.2 The Fatigue crack growth expression based on the SWT fatigue damage accumulation parameter.............................................................................................................................................35 Chapter 4 Determination of the Elementary Material Block Size, ρ* .................................................42 4.1 The Method based on the fatigue limit and the threshold stress intensity range; (Method #1) ........42 4.2 The Method based on the experimental fatigue crack growth data obtained at various stress ratios; (Method #2)..............................................................................................................................44 4.3 The Method based on the Manson-Coffin fatigue strain-life curve and limited fatigue crack growth data; (Method #3) .....................................................................................................................46 4.4 Summary of methods for the determination of the ρ* parameter .....................................................49 4.5 The effect of the elementary material block size on the residual stress intensity factor...................50 Chapter 5 Two-parameter Total Driving Force Model for Variable Amplitude Loading Spectra – the UniGrow Fatigue Crack Growth Model...........................................................................................56 5.1 The Maximum stress memory effect ................................................................................................57 5.2 The resultant minimum stress field and the residual stress intensity factor......................................58 5.3 The UniGrow analysis of simple loading spectra .............................................................................61 5.3.1 Constant amplitude loading .......................................................................................................61 5.3.2 Constant amplitude loading history interrupted by a single overload or underload ..................62 5.3.3 Loading spectra with single over- and uder-loads .....................................................................64 Chapter 6 Fatigue Crack Growth Analysis under Spectrum Loading – Predictions/Experiments ..72 vii 6.1 Fatigue crack growth in the Ti-17 titanium alloy under constant amplitude loading spectra with under-loads...............................................................................................................................75
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