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Constitutive Behavior of Aluminum Alloy Sheet at High Strain Rates

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Constitutive Behavior of Aluminum Alloy Sheet at High Strain Rates CONSTITUTIVE BEHAVIOR OF ALUMINUM ALLOY SHEET AT HIGH STRAIN RATES by Rafal Olaf Smerd A thesis presented to the University of Waterloo in fulfillment of the thesis requirement of the degree of Master of Applied Science in Mechanical Engineering Waterloo, Ontario, Canada, 2005 © Rafal Olaf Smerd 2005 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 electronically available to the public. ii ABSTRACT The drive to produce lightweight vehicles with improved fuel economy has resulted in an increased interest in utilization of aluminum alloys for automotive body structures due to their higher strength-to-weight ratio. To support the utilization of aluminum alloys in automobile structures, their dynamic behavior must be considered under crash conditions, although traditionally, the strain rate sensitivity of aluminum alloys has been considered to be low. In this work, three aluminum sheet alloys, AA5754, AA5182 and AA6111, which are prime candidates for replacing mild steel in automobile structures, are tested in tension at quasi-static and high strain rates. In order to characterize the constitutive response of AA5754, AA5182 and AA6111 at high strain rates, tensile experiments were carried out at strain rates between 600 s-1 and 1500 s-1, and at temperatures between ambient and 300°C, using a tensile split Hopkinson bar (TSHB) apparatus. As part of this research, the apparatus was modified in order to provide an improved means of gripping the sheet specimens. Quasi-static experiments also were conducted using an Instron machine. The tensile experiments showed that the rate sensitivity of the flow stress is low for these alloys, with the strain hardening response of AA5754 showing a mild sensitivity to strain rate in the range of strain rates considered. However, increases in strain rate appeared to significantly enhance the ductility of these alloys. Analysis of the stress-strain data demonstrated that the strain at which Considere’s criterion is satisfied increased at rates of high strain. This behavior implies that the onset of necking is delayed under high rate conditions, permitting the material to elongate more prior to localization. Levels of damage in AA5754 and AA5182 were also found to increase with strain rate, presumably due to the elevated strains to failure. The experimental data was fit to the Johnson-Cook and Zerilli-Armstrong constitutive models for all three alloys. The resulting fits were evaluated by numerically simulating the tensile experiments conducted using a finite element approach. Of the two models, the Zerilli- iii Armstrong constitutive model was more accurate in predicting the flow stress of these materials at the strain rates and temperatures considered. The finite element simulations using both constitutive models were unable to accurately predict the necking strain of these alloys. iv ACKNOWLEDGEMENTS I would like to thank my supervisor, Professor Michael Worswick for giving me the opportunity to pursue a Master’s degree as part of his research group and for his knowledge, guidance and support during my graduate studies. I am grateful to Novelis Global Technology Centre for making this work possible, and would like to acknowledge David Lloyd and Mark Finn for their support. I would like to thank Chris Salisbury for his guidance and help in understanding various aspects of the split Hopkinson bar and in developing the test method employed in this work. Thanks to Tom Gawel for installing a countless number of strain gauges. Don’t worry Tom, I won’t be breaking anymore. A special thanks to Dr. Sooky Winkler for her invaluable metallographic work and damage analysis. There have been many people who have supported me along way. To Dino, thanks for the years of friendship and laughs, and for putting me in contact with Professor Worswick. Thanks to Jose for sharing sources on high rate testing, material properties and FK9. Blake I thank for all his help with LS-DYNA and for his “witty” comments. The office was always a friendly environment with Oleg, Alex B., Rassin, Chris, Sooky, Javad, Zengtao, and Hari around, thanks guys. To all my friends, the soccer boys, and the “Kitchener Crew” (you know who you are), I can’t thank you enough for all the years. And finally, my family. I don’t think this would have been possible without your support and understanding. Mom, Dad, my brother Dave, aunt Roma, you have been there for me through thick and thin, and have allowed me to grow into who I am. Words cannot describe my gratitude. Thank you. v TABLE OF CONTENTS 1 Introduction.......................................................................................................................... 1 1.1 Split Hopkinson Bar Apparatus ................................................................................... 2 1.1.1 Split Hopkinson Bar Principles............................................................................ 3 1.1.2 Tensile Split Hopkinson Bar................................................................................ 4 1.1.3 Hopkinson Bar Equations .................................................................................... 8 1.1.4 Wave Propagation Effects.................................................................................. 11 1.2 High Strain Rate Material Behavior .......................................................................... 14 1.2.1 Thermally Activated Dislocation Motion .......................................................... 15 1.2.2 Inertia Effects..................................................................................................... 16 1.2.3 High Rate Properties of Aluminum Alloys........................................................ 20 1.3 Material Models......................................................................................................... 28 1.3.1 Johnson-Cook Material Model .......................................................................... 29 1.3.2 Zerilli-Armstrong Material Model..................................................................... 31 1.3.3 Mechanical Threshold Stress Model.................................................................. 33 1.4 Present Research ........................................................................................................ 34 2 Experimental Methods....................................................................................................... 36 2.1 Material...................................................................................................................... 36 2.2 Equipment.................................................................................................................. 38 2.2.1 Tensile Split Hopkinson Bar Apparatus ............................................................ 38 2.2.2 Elevated Temperature Experiments................................................................... 44 2.2.3 Instrumentation .................................................................................................. 48 2.3 Metallography............................................................................................................ 51 2.4 Experimental Procedures ........................................................................................... 52 3 Numerical Models.............................................................................................................. 57 3.1 Mesh........................................................................................................................... 57 3.2 Boundary Conditions and Loads................................................................................ 58 3.3 Material Models......................................................................................................... 60 3.4 Axial Inertial Stress Calculations............................................................................... 61 4 Specimen Design ............................................................................................................... 64 4.1 Numerical Simulations of 3 mm Gauge Length Samples.......................................... 66 vi 4.2 Post-Uniform Elongation Effects on Gauge Length.................................................. 68 5 Experimental Results ......................................................................................................... 74 5.1 Constitutive Behavior ................................................................................................ 74 5.1.1 Effect of Strain Rate........................................................................................... 74 5.1.2 Effect of Temperature........................................................................................ 79 5.2 Strain Rate and Temperature Effects on Elongation.................................................. 86 5.2.1 Effect of Strain Rate on Elongation................................................................... 87 5.2.2 Effect of Temperature on Elongation ................................................................ 90 5.3 Tensile Instability Predicted By Considere’s Criterion ............................................. 93 5.3.1 Strain Rate Effects on Instability Criterion........................................................ 94 5.3.2 Temperature Effect on Instability Criterion....................................................... 97 5.4 Fracture
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