Bhattacharya, Kaushik and Schlömerkemper, Anja (2008) Stress-induced phase transformations in shape-memory polycrystals. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechSOLIDS:2008.005
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Shape-memory alloys undergo a solid-to-solid phase transformation involving a change of crystal structure. We examine model problems in the scalar setting motivated by the situation when this transformation is induced by the application of stress in a polycrystalline material made of numerous grains of the same crystalline solid with varying orientations. We show that the onset of transformation in a granular polycrystal with homogeneous elasticity is in fact predicted accurately by the so-called Sachs bound based on the ansatz of uniform stress. We also present a simple example where the onset of phase transformation is given by the Sachs bound, and the extent of phase transformation is given by the constant strain Taylor bound. Finally we discuss the stress-strain relations of the general problem using Milton-Serkov bounds.
|Item Type:||Report or Paper (Technical Report)|
|Additional Information:||We are delighted to acknowledge various enlightening and enjoyable discussions with Pierre Suquet and Christian Lexcellent during the course of this work. This work started when AS held a postdoctoral position at the University of Oxford and was continued while AS was affiliated to the Institute for Analysis, Dynamics and Modelling at the University of Stuttgart. The work was completed during KB's sabbatical leave of absence at the Cavendish Laboratory and Clare Hall of Cambridge. We gratefully acknowledge the financial support of the EU TMR Network (FMRX-CT 98-0229, AS), the US Department of Energy (PSAAP, KB), UK EPSRC (KB).|
|Group:||Solid Mechanics Research Group|
|Usage Policy:||You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.|
|Deposited By:||Imported from CaltechSOLIDS|
|Deposited On:||23 Dec 2008|
|Last Modified:||22 Jan 2016 23:12|
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