Speaker
Description
In shape memory alloys, the competition between interfacial and elastic strain energy contributions leads to twin branching, i.e., to refinement of the twin laminates close to the macroscopic interface between twinned martensite and austenite. We have developed a 1D model of twin branching in which the average twin spacing is a continuous function of the distance from the austenite-twinned martensite interface. The free energy of the branched microstructure comprises the interfacial and elastic strain energy contributions, the latter calibrated using the respective upper-bound estimate derived by Seiner et al. (2020). The total free energy is then minimized, and the corresponding Euler-Lagrange equation is solved numerically using the finite element method. The results show a good agreement with the model of Seiner et al. (2020) in the entire range of physically relevant parameters. Importantly, our continuum framework admits incorporation of energy dissipation into an incremental problem of evolution of the branched microstructure. The effect of rate-independent dissipation is thus studied for an evolving microstructure. The results show that significant effects on the microstructure and energy of the system are expected only for relatively small domain sizes.
