On non stress-free junctions between martensitic plates

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 $V_{II}$ 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.