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Fatigue Characterization and Cyclic Plasticity Modeling of Magnesium Spot-Welds

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Fatigue Characterization and Cyclic Plasticity Modeling of Magnesium Spot-Welds by Seyed Behzad Behravesh 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, 2013 © Seyed Behzad Behravesh 2013 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. Seyed Behzad Behravesh ii Abstract The automotive industry is adopting lightweight materials to improve emissions and fuel economy. Magnesium (Mg) alloys are the lightest of engineering metals, but work is required to assess their structural strength, especially for spot-welded applications. In the present research, fatigue behavior of magnesium spot-welds was characterized and compared with steel and aluminum spot-welds. A fatigue model was proposed to predict the failure location and crack initiation life in magnesium structures. The material under investigation, AZ31B-H24 Mg alloy, and its spot-welds were characterized from microstructural and mechanical points of view. Microstructure and hardness of the base metal (BM) and different regions in the spot-welds were studied. Monotonic testing of the BM demonstrated asymmetric hardening behavior under tension and compression. Under cyclic loading, the BM had an asymmetric hysteresis loop. Static behavior of spot-welds was studied with different specimen configurations. The effect of nugget size on the static peak load was similar to that of aluminum and less than steel. Cyclic behavior of magnesium spot-welds was measured using different specimen configurations, and the effect of geometrical factors on fatigue life was evaluated. Fatigue strength (in terms of load range) of magnesium spot-welds was similar to aluminum and less than steel. Crack initiation location and life as well as crack propagation path for different life ranges were compared. A constitutive model was developed, implemented, and verified to model the asymmetric hardening behavior of wrought magnesium alloys under cyclic loading. The proposed phenomenological model is continuum-based and utilizes the Cazacu-Barlat asymmetric yield function along with an associated flow rule and a combined hardening rule. An algorithm for numerical implementation of the proposed model was developed. The numerical formulation was programmed into a user material subroutine to run with the commercial finite element software Abaqus/Standard. The proposed model was verified by solving two problems with available solutions. A number of available fatigue models, as well as a new model proposed in this research were assessed by predicting fatigue life of magnesium spot-welds. One reference model from each of the following groups, fracture mechanics, structural stress, and local strain approaches, were implemented. The new model used a strain energy damage parameter. All models were evaluated by iii comparing the predicted and experimental fatigue lives for different Mg spot-welded specimens. The effect of considering the asymmetric hardening behavior of wrought magnesium alloys on the accuracy of the fatigue life prediction was not significant for the available experimental data. This was attributed to the limited experimental data on spot-welded specimens. The proposed material model and fatigue damage parameter were verified by simulating a real- life structure manufactured and fatigue tested by the US Automotive Materials Partnership. The structure was simulated under different experimental loading conditions. The results obtained from the proposed asymmetric model were compared with available symmetric simulation results and experimental data. The asymmetric material model along with the proposed damage parameter resulted in more accurate prediction of fatigue failure location and life. iv Acknowledgements First of all, I wish to praise and thank God for all His blessings. I would not have made any progress without His providence. I would like to express my sincere gratitude to my supervisor, Professor Hamid Jahed, and my co-supervisors, Professor Steve Lambert and Professor Gregory Glinka, for their valuable supports and guidance. I owe my deepest gratitude to my beloved parents and brothers for their unconditional love and inspiration throughout my education. I wish to remember my recently deceased father and two lovely brothers, Benyamin and Bahman; may God shower His blessings upon their souls. I would like to extend my appreciation to my parents-in-law for their sincere love and continuous supports. Special thanks to my dear wife, Roja, for her understanding, encouragement, and patience which made this research possible. The financial support from AUTO21 and Automotive Partnership Canada is acknowledged. I am also grateful to General Motors for providing materials required for this research. I am thankful to Tom Gawel, Andy Barber, Steve Hitchman, Martha Morales, and Richard Forgett for their technical supports. The collaboration of the resistance spot welding laboratory of the University of Waterloo, in particular Ray Liu and Tirdad Niknejad, for providing spot-weld specimens is appreciated. I greatly appreciate my colleagues, Dr. Mohammad Noban, Arash Tajik, Dr. Amin Eshraghi, Dr. Morvarid Karimi, Dr. Jafar Al Bin Mousa, Elfaitori Ibrahim, Ali Roostaei, Bahareh Marzbanrad, and Mohammad Diab for their precious thoughts and discussions. I am especially thankful to Mi Chengji for his invaluable assistance. v Dedicated to the Leader of the Age, the ultimate savior of humankind, who is promised to fill the earth with peace and justice, as it has been filled with injustice and tyranny. (May God hasten his reappearance) vi Table of Contents List of Figures ....................................................................................................................................... x List of Tables ...................................................................................................................................... xvi Nomenclature .................................................................................................................................... xvii Chapter 1 Introduction ...................................................................................................................... 1 1.1 Motivation .......................................................................................................................... 2 1.2 Objectives .......................................................................................................................... 4 1.3 Thesis Overview ................................................................................................................ 5 Chapter 2 Background and Literature Review ............................................................................... 7 2.1 Background ........................................................................................................................ 8 2.1.1 Magnesium ............................................................................................................. 8 2.1.2 Resistance Spot Welding ...................................................................................... 11 2.2 Literature Review ............................................................................................................. 13 2.2.1 AZ31B Mg Alloy and Spot-Weld Characterization ............................................. 13 2.2.2 Constitutive Modeling .......................................................................................... 20 2.2.3 Fatigue Modeling of Spot-Welded Structures ...................................................... 25 Chapter 3 Experimental Work ........................................................................................................ 30 3.1 Material and Specimens ................................................................................................... 31 3.1.1 Material ................................................................................................................. 31 3.1.2 Base Metal Specimens .......................................................................................... 31 3.1.3 Spot-Welded Specimens ....................................................................................... 34 3.2 Microstructural Characterization ..................................................................................... 38 3.2.1 Microstructure ...................................................................................................... 38 3.2.2 Hardness ............................................................................................................... 41 3.3 Mechanical Characterization............................................................................................ 43 3.3.1 Monotonic Behavior ............................................................................................. 43 vii 3.3.2 Cyclic Behavior .................................................................................................... 53 3.4 Cyclic Loading Effects .................................................................................................... 71 3.4.1 Microstructure ...................................................................................................... 71 3.4.2 Hardness ..............................................................................................................
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