Twin branching in shape memory alloys: a 1D model with energy dissipation effects

TL;DR

This paper presents a 1D continuous model for twin branching in shape memory alloys, incorporating energy dissipation effects, and demonstrates good agreement with discrete models while exploring microstructure evolution.

Contribution

It introduces a continuous 1D model that includes energy dissipation effects, extending previous discrete models of twin branching in shape memory alloys.

Findings

Model agrees with discrete models across relevant parameters

Energy dissipation significantly affects microstructure evolution in small domains

Rate-independent dissipation impacts energy and microstructure for small sizes

Abstract

We develop a 1D model of twin branching in shape memory alloys. The free energy of the branched microstructure comprises the interfacial and elastic strain energy contributions, both expressed in terms of the average twin spacing treated as a continuous function of the position. The total free energy is then minimized, and the corresponding Euler-Lagrange equation is solved numerically using the finite element method. The model can be considered as a continuous counterpart of the recent discrete model of Seiner et al. (2020), and our results show a very good agreement with that model in the entire range of physically relevant parameters. Furthermore, our continuous setting facilitates incorporation of energy dissipation into the model. The effect of rate-independent dissipation on the evolution of the branched microstructure is thus studied. The results show that significant effects on the microstructure and energy of the system are expected only for relatively small domain sizes.