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Predicting the Response of Aluminum Casting Alloys to Heat Treatment by Chang Kai (Lance) Wu A thesis submitted to the faculty of the WORCESTER POLYTECHINC INSTITUTE in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Materials Science and Engineering April, 2012 Professor Makhlouf M. Makhlouf, Advisor Professor Richard D. Sisson Jr., Director of the Material Science and Engineering Program

i ABSTRACT The objective of this research was to develop and verify a mathematical model and the necessary material database that allow predicting the physical and material property changes that occur in aluminum casting alloys in response to precipitation- hardening heat treatment. The model accounts for all three steps of the typical precipitation hardening heat treatment; i.e., the solutionizing, quenching, and aging steps; and it allows predicting the local hardness and tensile strength, and the local residual stresses, distortion and dimensional changes that develop in the cast component during each step of the heat treatment process. The model uses commercially available finite element software and an extensive database that was developed specifically for the aluminum alloy under consideration – namely A356.2 casting alloy. The database includes the mechanical, physical, and thermal properties of the alloy all as functions of temperature. The model predictions were compared to measurements made on commercial cast components that were heat treated according to standard heat treatment protocols and the model predictions were found to be in good agreement with the measurements.

ii ACKNOWLEDGEMENTS This research could not have been completed without the support of many individuals. Their contributions in various ways to my work and the making of this thesis deserve special mention. It is a pleasure to convey my gratitude to them all in my humble acknowledgement. I am deeply grateful to Professor Makhlouf M. Makhlouf for giving me the opportunity to work with him during my journey at Worcester Polytechnic Institute. It has been an honor to be his student. I would like to deliver my special gratitude to him for sharing his invaluable insight, advice and knowledge with me for nearly six years. His words of encouragement and motivation came a long way in bringing this work to completion. I would like to thank Professor Diran Apelian for his advice, guidance and friendship throughout these years. He has been a great mentor not only in my academic performance, but also in my personal life. Thanks are also extended to the members of my dissertation committee, Professor Richard D. Sisson Jr. and Mr. Christof Heisser for their time and assistance in this work. It is my pleasure also to pay tribute to all the WPI faculty and staff. I would like to express my great gratitude to my wife and parents, without their never- ending love, understanding and support, this thesis would be impossible. Collective and individual acknowledgements are also due to my colleagues, classmates and friends whose enthusiasm and support in one way or another was helpful and memorable. The group at Advanced Casting Research Center has contributed immensely to my personal and professional experience at WPI. The team has been a wonderful source of friendships, good advice and collaboration. I want to thank the Metals Processing Institute and the Department of Materials Science and Engineering at WPI who gave me the opportunity to be a part of them. Finally, I thank everyone who supported and believed in me, and I express my apology to anyone who I did not mention personally. Chang Kai (Lance) Wu Worcester Polytechnic Institute

iii TABLE OF CONTENTS ABSTRACT .................................................................................................................... i ACKNOWLEDGEMENTS ........................................................................................... ii TABLE OF CONTENTS ............................................................................................. iii LIST OF FIGURES ....................................................................................................... v LIST OF TABLES ........................................................................................................ ix 1. INTRODUCTION ..................................................................................................... 1 2. METHODOLOGY .................................................................................................... 2 Plan of Research .................................................................................................... 2 Background ............................................................................................................ 3 3. DATABASE GENERATION ................................................................................... 10 Materials .............................................................................................................. 10 Determination of the Physical Properties of A356 Alloy ..................................... 12 Determination of the Mechanical Properties of the Supersaturated Solid Solution A356 Alloy ........................................................................................................... 12 Determination of Thermal Conductivity of A356 Alloy ...................................... 15 Determination of the Quenching Heat Transfer Coefficients .............................. 17 Determination of the Creep Properties ................................................................ 21 Determination of the Quench Factor Analysis Constants .................................... 24 (1) Determining the maximum and minimum attainable strength ............... 25 (2) Measuring the hardness and strength with matched thermal data for different quench paths .................................................................................. 26 (3) Calibrating the K constants based on the measurements ....................... 30

iv Determination of the Shercliff-Ashby Aging Parameters .................................... 32 4. MODEL CONSTRUCTION .................................................................................... 36 Thermal-Stress Module ........................................................................................ 36 Creep Module ....................................................................................................... 43 Volumetric Dilation Module ................................................................................ 44 Strength and Hardness Module ............................................................................ 46 5. VALIDATION OF THE INTEGRATED MODEL .................................................. 48 Heat Treatment ..................................................................................................... 51 Predicting the thermal profiles in the commercially cast part ............................. 55 Predicting the Heat-treated Tensile Strength and Hardness ................................. 56 Predicting dimensional changes ........................................................................... 67 Predicting Residual Stresses ................................................................................ 71 6. SUMMARY AND CONCLUSIONS ....................................................................... 75 7. REFERENCES ........................................................................................................ 77 APPENDIXES ............................................................................................................. 79 Appendix A Predicting the Response of Aluminum Casting Alloys to Heat Treatment ...................................................................................................................................... 80 Appendix B A Mathematical Model and Computer Simulations for Predicting the Response of Aluminum Casting Alloys to Heat Treatment ......................................... 86 Appendix C Modeling the Response of Aluminum Alloy Castings to Precipitation Hardening Heat Treatment ........................................................................................... 93

v LIST OF FIGURES Fig. 1 . Block diagram describing the Integrated Heat Treatment Model. .......... 3 Fig. 2. Typical Ct function and its use in calculating the quench factor. ............ 5 Fig. 3. The process diagram for the Shercliff-Ashby aging model. .................... 7 Fig. 4. SEM micrograph of the A356 alloy solutionized, quenched in 80 o C (176 o F) water, and then aged at 155 o C (311 o F) for 4 hours. ..................... 11 Fig. 5. Location of Energy Dispersive Spectrometer (EDS) scanning. ............ 11 Fig. 6. Energy Dispersive Spectrometer (EDS) scan at the Location labeled “Spectrum 3” in Fig. 5. ............................................................................. 12 Fig. 7. Stress-strain curves for supersaturated A356 alloy at elevated temperatures. ............................................................................................. 14 Fig. 8. Stress-strain curve for supersaturated A356 alloy samples at room temperature. Strain rate = 0.005/s. ............................................................ 15 Fig. 9. Schematic representation of the apparatus used to measure thermal conductivity. .............................................................................................. 16 Fig. 10. Measured, software generated and public available thermal conductivities of A356.2 alloy. ................................................................. 16 Fig. 11. Schematic representation of the quenching system . ............................ 18 Fig. 12. The newly-designed cylindrical quenching probe. .............................. 19 Fig. 13. The newly-designed disk quenching probe. In this disk probe the ratio of the bottom surface area to the total surface area of the disk is 79.7%.. 19 Fig. 14. Metal-Fluid HTCs measured by the newly designed probe and disk quenched in hot water (80 o C). .................................................................. 20 Fig. 15. Metal-Air and Air HTCs measured by the newly-designed probe. ..... 20 Fig. 16. Measured creep-rupture data adapted from reference [22]. ................ 21 Fig. 17. Measured creep-rupture data adapted from reference [22]. ................ 22 Fig. 18. Measured creep-rupture data adapted from reference [22]. ................ 22 Fig. 19 . Measured hardness as a function of aging time for A356 alloy that was

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