On non stress-free junctions between martensitic plates

  • Francesco Della Porta

    Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany
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Abstract

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 junctions, which are non stress-free interfaces between different martensitic variants experimentally observed in TiNbAl. 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 junctions within the theory of elasto-plasticity, and show that for deformation gradients as in TiNbAl our characterisation agrees with experimental results. Furthermore, we are able to prove that, under suitable hypotheses that are verified in the study of TiNbAl, junctions are strict weak local minimisers of a simplified energy functional for martensitic transformations in the context of elasto-plasticity.

Cite this article

Francesco Della Porta, On non stress-free junctions between martensitic plates. Interfaces Free Bound. 22 (2020), no. 3, pp. 251–283

DOI 10.4171/IFB/441