

Preprint 1/2009
Stress-induced phase transformations in shape-memory polycrystals
Kaushik Bhattacharya and Anja Schlömerkemper
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Submission date: 02. Jan. 2009
Pages: 34
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
Bibtex
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Abstract:
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.