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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
1/2009

Stress-induced phase transformations in shape-memory polycrystals

Kaushik Bhattacharya and Anja Schlömerkemper

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.

Received:
Jan 2, 2009
Published:
Jan 7, 2009

Related publications

inJournal
2010 Journal Open Access
Kaushik Bhattacharya and Anja Schlömerkemper

Stress-induced phase transformations in shape-memory polycrystals

In: Archive for rational mechanics and analysis, 196 (2010) 3, pp. 715-751