EFFECT OF INTERPHASE, THERMAL INDUCED DISLOCATIONS AND PRESENCE OF VOIDS ON THE FLOW STRESS OF METAL MATRIX NANOCOMPOSITES LIN KUNPENG A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2015 This page is intentionally left blank. DECLARATION I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Lin Kunpeng 01 June 2015 This page is intentionally left blank. ACKNOWLEDGEMENTS First and foremost, I would like to express my utmost gratitude to my supervisors, Dr. Pang Sze Dai and Prof. Quek Ser Tong, who have supported me throughout my graduate study with their motivation, enthusiasm and advice while gave me freedom to explore on my own. This work could not have been completed without their guidance and support. It has been my privilege to work closely with Dr. Pang Sze Dai and Prof. Quek Ser Tong, I have enjoyed the opportunity to watch and learn from their knowledge and experience. I would like to show my appreciation to Dr. Shailendra P. Joshi and Dr. Poh Leong Hien for their insightful comments and constructive criticisms. I am deeply grateful to Dr. Elliot Law for his encouragement and practical advice. I am also thankful to him for reading my draft paper, correcting grammars and commenting on my views. I would also like to acknowledge the National University of Singapore for supporting me with Research Scholarship for the entire duration of my study. I would like to express my warm thanks to my colleagues: Mr. Sixuan Huang, Dr. Yang Zhang, Mr. Yu Wang, Mr. Ming Luo and Ms. Zhongrui Chen, for their friendship, encouragement and support. i Last but not least, my heartfelt thanks go to my family, especially my parents Shujing Lin and Meiting Huang and my wife Xiao Lu, for their unconditional love and support throughout all these years. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS . i TABLE OF CONTENTS . iii SUMMARY vii LIST OF TABLES x LIST OF FIGURES . xi LIST OF SYMBOLS . xvi Chapter 1. Introduction . 1.1 Background and motivation . 1.2 Objective 1.3 Scope 10 1.4 Organization of Thesis . 11 Chapter 2. 2.1 Literature Review 15 Interphase in metal matrix composites (MMCs) 15 2.1.1 Experimental results 15 2.1.2 Effect of the interphase . 19 2.2 Interphase in metal matrix nanocomposites (MMNCs) . 24 2.3 Thermal residual stress in MMCs 27 2.3.1 Experimental results 27 2.3.2 Effect of thermal residual stresses 29 2.4 Thermal induced dislocations in MMCs 31 iii 2.4.1 Existence of thermal induced dislocations 31 2.4.2 Theoretical model of thermal induced dislocations 32 2.4.3 Effect of thermal induced dislocations . 34 2.5 Thermal induced dislocations in MMNCs . 35 2.6 Void in MMCs . 36 2.6.1 Experimental results 36 2.6.2 Effect of void 38 2.7 Void in MMNCs 40 2.8 Analytical model of MMNCs . 41 2.9 Numerical simulation of MMNCs . 43 Chapter 3. 3.1 Effects of Interphase on Mechanical Response of MMNCs . 45 Simulation of interphase using level set in extended finite element method (XFEM) 45 3.1.1 Types of discontinuities 45 3.1.2 Introduction to XFEM . 48 3.1.3 Level set method . 49 3.1.4 Enrichment and selection of enriched nodes 53 3.1.5 Discretization and numerical integration 55 3.1.6 Review discrete dislocation simulation of MMNCs and numerical procedure 60 3.1.7 Comparison with work by original author 69 3.2 Effects of interphase elastic properties . 71 3.2.1 Effect of interphase Poisson ratio . 71 3.2.2 Effect of interphase Young’s modulus . 73 3.3 Effect of interphase thickness 76 iv 3.4 Effect of particle volume fraction 77 3.5 Effect of resistance to dislocation motion in the interphase region . 81 3.6 Comparison with Mg-ZnO nanoxomposites experimental results . 84 3.7 Discussions . 88 Chapter 4. Effects of thermal residual stresses and thermal generated dislocation on the mechanical response of MMNCs 91 4.1 Formulation of thermal stress . 91 4.2 Multiple slip systems 93 4.2.1 Multiple slip systems orientations for an idealized fcc single-crystal 94 4.2.2 Formulation of inclined slip systems 95 4.2.3 Implementation of multiple slip systems 102 4.3 Numerical implementation . 103 4.3.1 Problem formulation . 103 4.3.2 Computation parameters . 106 4.3.3 Numerical validation using passivated metal interconnects . 107 4.4 Numerical simulation of thermal residual stress in MMNCs . 110 4.4.1 Problem formulation . 110 4.4.2 Temperature range and cooling rate . 111 4.4.3 Material parameters 114 4.5 Results of thermal residual stress in MMNCs 114 4.5.1 Thermal stress and thermal induced dislocation . 115 4.5.2 Effect of particle volume fraction . 119 4.6 Effect of thermal residual stresses and thermal induced dislocations 122 4.7 Comparison with Mg-ZnO nanoxomposites experimental results . 129 v Chapter 5. Effects of void on the mechanical response of MMNCs 133 5.1 Modeling of dislocations leaving non-convex domain 133 5.2 Numerical Implementation . 139 5.2.1 Problem formulation . 139 5.2.2 Computation parameters . 141 5.2.3 Numerical validation using a voided single crystal 142 5.3 Numerical simulation of voided MMNCs 144 5.4 Effect of void volume fraction . 146 5.5 Effect of void distribution 149 5.6 Effect of lattice orientation . 155 5.7 Effect of particle aspect ratio . 160 Chapter 6. Conclusions and future work 167 6.1 Conclusions 167 6.2 Recommendations for future work . 170 References . 173 List of Publications . 188 vi REFERENCES Aghababai, R. and Joshi S. P. (2013). Micromechanics of crystallographic size-effects in metal matrix composites induced by thermo-mechnical loading. International Journal of Plasticity 42: 65-82. Ahmad, S. N. A. S., Hashim, J. and Ghazali, M. I. (2007). Effect of porosity on tensile properties of cast particle reinforced MMC. 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Lin, K. and Pang, S. (2014). The influence of thermal residual stresses and thermal generated dislocation on the mechanical response of particulate-reinforced metal matrix nanocomposites. Composites Part B: Engineering (under re-review). 188 [...]... increase in the flow stresses The simulations of MMNCs shows that by including interphase regions in the simulation, one can obtain a more accurate estimate of the overall vii response The development of thermal residual stresses and thermal induced dislocations in MMNCs are predicted using discrete dislocation simulation The effect of thermal residual stresses and thermal generated dislocation on the overall... development of thermal residual stresses and thermal induced dislocations in MMNCs and study their effects on the overall responses of MMNCs; (3) model void in MMNCs and examine the effects of void content, void distribution, lattice orientation as well as particle aspect ratio on the overall responses of MMNCs 9 1.3Scope Numerical simulation will be carried out using discrete dislocation framework For the. .. (Johnson and Lee, 1983) The high density of thermal- generated dislocations results in the improvement of hardness (Shee et al., 1998) and yield strength (Goh et al., 2007) of the 6 composites In addition, the matrix around the reinforcements reveals much higher densities of thermal- generated dislocations than the bulk of the matrix (Dunand and Mortensen, 1991a) making the mechanical properties of that... (Ferkel and Mordike, 2001) The plastic zone and thermal- generated dislocations play important roles on the mechanical properties of the composite material When the material is to be subsequently deformed or work hardened, the plastic zone due to thermal residual stresses may essentially alter the rate at which dislocations bypass the particle, the yield stress, and the continued work hardening of the material... times lower than the matrix Image stresses due to dislocations reach the surface of the void are computed by embedding the discontinuities in the finite element solution Simulation results show that the stiffness, yield stress and flow stress of MMNCs decrease with increasing void content when the void is fixed at the center of the unit cell Under 2 % tensile strain, the difference of flow stress can be...SUMMARY Metal matrix nanocomposites (MMNCs) have attracted considerable research interest due to their high strength and stiffness, while retaining much of the ductility of the metallic matrix Due to the difficulties in material processing and fabrication, the experimental studies on the effect of morphology on the mechanical response of MMNCs have seldom been reported On the other hand, numerical... owing to the mismatch in thermal expansion between matrix and reinforcement The stresses develop upon cooling from a stress and dislocation free state Unless otherwise stated, matrix is analyzed that is an idealization of a facecentered cubic (fcc) single-crystal Unless otherwise stated, in the thermal stresses simulation, 10 the angles of slip orientations are taken to be near the FCC orientation and three... response is investigated by applying in-plane shear on a unit cell after the thermal cooling process The simulations show that thermal residual stresses in MMNCs are high enough to generate thermal induced dislocations Dislocation density is higher around particles compared to the rest of the matrix Under applied shear deformation, new generated dislocations are likely hindered by thermal induced dislocations. .. investigate the relation between the microstructure as well as the processes of MMNCs and their mechanical properties 1.2Objective The objectives of this study are: (1) introduce interphase into the MMNCs simulation and investigate the effects of elastic properties, thickness of the interphase and resistance to dislocation motion within the interphase regions on the overall responses of MMNCs; (2) simulate the. .. on the mechanical properties of MMNCs will be studied 1.4Organization of Thesis Chapter 2 presents a review on the previous literatures of interphases, thermal residual stresses and void in metallic matrix composites These literatures are categorized into four groups: the 11 first group mainly focuses on the existing and effects of interphases in MMCs and MMNCs; the second group deals with the thermal . EFFECT OF INTERPHASE, THERMAL INDUCED DISLOCATIONS AND PRESENCE OF VOIDS ON THE FLOW STRESS OF METAL MATRIX NANOCOMPOSITES LIN KUNPENG A THESIS SUBMITTED FOR THE DEGREE OF. 4.5.1 Thermal stress and thermal induced dislocation 115 4.5.2 Effect of particle volume fraction 119 4.6 Effect of thermal residual stresses and thermal induced dislocations 122 4.7 Comparison. 2.3.2 Effect of thermal residual stresses 29 2.4 Thermal induced dislocations in MMCs 31 iv 2.4.1 Existence of thermal induced dislocations 31 2.4.2 Theoretical model of thermal induced dislocations