# On non stress-free junctions between martensitic plates

## TL;DR

This paper investigates non stress-free junctions between martensitic plates, specifically $V_{II}$ junctions in Ti74Nb23Al3, providing a mathematical characterization and proving their stability as local energy minimizers.

## Contribution

It introduces a mathematical framework for $V_{II}$ junctions in martensitic microstructures and demonstrates their stability within elasto-plasticity theory, extending understanding beyond stress-free interfaces.

## Key findings

- $V_{II}$ junctions are strict weak local minimisers of the energy functional.
- The mathematical characterization aligns with experimental observations.
- The study extends compatibility theory to non stress-free interfaces.

## 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 Ti74Nb23Al3. 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 Ti74Nb23Al3 our characterisation agrees with experimental results. Furthermore, we are able to prove that, under suitable hypotheses that are verified in the study of Ti74Nb23Al3, $V_{II}$ junctions are strict weak local minimisers of a simplified energy functional for martensitic transformations in the context of elasto-plasticity.