Stress-Induced Phase Transformations in Shape-Memory Polycrystals
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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.
KeywordsAustenite Martensite Critical Stress Transformation Strain Recoverable Strain
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 Anja Schlömerkemper held a postdoctoral position at the University of Oxford and was continued while Anja Schlömerkemper was affiliated to the Institute for Analysis, Dynamics and Modeling at the University of Stuttgart. The work was completed during Kaushik Bhattacharya’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).
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