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Interfaces and Free Boundaries

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Volume 22, Issue 3, 2020, pp. 251–283
DOI: 10.4171/IFB/441

Published online: 2020-09-01

On non stress-free junctions between martensitic plates

Francesco Della Porta[1]

(1) Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany

The analytical understanding of microstructures arising in martensitic phase transitions relies usually on the study of stress-free interfaces between different variants of martensite. However, in the literature there are experimental observations of non stress-free junctions between martensitic plates, where the compatibility theory fails to be predictive. In this work, we focus on $V_{II}$ junctions, which are non stress-free interfaces between different martensitic variants experimentally observed in Ti$_{74}$Nb$_{23}$Al$_3$. We first motivate the formation of some non stress-free junctions by studying the two well problem under suitable boundary conditions. We then give a mathematical characterisation of $V_{II}$ junctions within the theory of elasto-plasticity, and show that for deformation gradients as in Ti$_{74}$Nb$_{23}$Al$_3$ our characterisation agrees with experimental results. Furthermore, we are able to prove that, under suitable hypotheses that are verified in the study of Ti$_{74}$Nb$_{23}$Al$_3$, $V_{II}$ junctions are strict weak local minimisers of a simplified energy functional for martensitic transformations in the context of elasto-plasticity.

Keywords: Martensitic transformations, compatibility, two-well problem, local minimiser

Della Porta Francesco: On non stress-free junctions between martensitic plates. Interfaces Free Bound. 22 (2020), 251-283. doi: 10.4171/IFB/441