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Equilibrium morphology of misfit particles in elastically stressed solids under chemo-mechanical equilibrium conditions
Affiliation:1. Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA;2. Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208, USA;3. University of Luxembourg, Research Unit in Engineering, Computational Mechanics Group, Luxembourg;4. Cardiff School of Engineering, Institute of Mechanics and Advanced Materials Theoretical, Applied and Computational Mechanics, Cardiff University, The Parade, Cardiff CF24 3AA, Wales, UK;1. Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan City 030024, PR China;2. Department of Chemical and Materials Engineering, Hefei University, Hefei City, 230601, PR China;3. National Center of Coal Chemical Products Quality Supervision and Inspection, Huainan City, 232007, PR China;1. State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, PR China;2. CAPT, HEDPS and IFSA Collaborative Innovation Center of MoE, Peking University, Beijing 100871, PR China;3. State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, PR China;4. Department of Mechanics and Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200444, PR China;5. State Key Laboratory for Mechanical Behavior of Materials, Xi''an 710049, PR China;6. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai, 200072, PR China;1. Eindhoven University of Technology, Department of Mechanical Engineering, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands;2. Philips Research, High Tech Campus 34, 5656 AE Eindhoven, The Netherlands;1. Laboratoire de Mécanique de Lille, UMR CNRS 8107, Université de Lille 1, Cité scientifique, F59655 Villeneuve d''Ascq, France;2. Institut Jean Le Rond d''Alembert, UMR CNRS 7190, Université Pierre et Marie Curie, 4 place Jussieu, F75005 Paris, France;1. Université de Lyon, INSA-Lyon, LaMCoS UMR CNRS 5259, F69621 Villeurbanne, France;2. SNECMA, Centre de Villaroche, 77550 Moissy Cramayel, France;1. Karlsruhe Institute of Technology (KIT), Institute of Engineering Mechanics (Continuum Mechanics), Kaiserstraße 12, 76131 Karlsruhe, Germany;2. Mines ParisTech, Centre des Matériaux, CNRS UMR 7633 BP 87, 91003 Evry Cedex, France
Abstract:This paper studies the effects of chemical, elastic and interfacial energies on the equilibrium morphology of misfit particles due to phase separation in binary alloys under chemo-mechanical equilibrium conditions. A continuum framework that governs the chemo-mechanical equilibrium of the system is first developed using a variational approach by treating the phase interface as a sharp interface endowed with interfacial excess energy. An extended finite element method (XFEM) in conjunction with the level set method is then developed to simulate the behaviors of the coupled chemo-mechanical system. The coupled chemo-mechanics model together with the numerical techniques developed here provides an efficient simulation tool to predict the equilibrium morphologies of precipitates in phase separate alloys.
Keywords:Chemo-mechanical coupling  Equilibrium morphology  Phase transformation  Extended finite element method (XFEM)  Level set method
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