Stress-induced phase transformations in shape-memory polycrystals
Kaushik Bhattacharya and Anja Schlömerkemper
Contact the author: Please use for correspondence this email.
Submission date: 02. Jan. 2009
published in: Archive for rational mechanics and analysis, 196 (2010) 3, p. 715-751
DOI number (of the published article): 10.1007/s00205-009-0263-4
Download full preprint: PDF (682 kB)
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.