On dissipation, interfacial energy and size effects in shape memory alloys

Abstract
This work presents a multiscale approach aimed at the modelling of evolution of martensitic microstructures with account for the interfacial energy effects. The total Helmholz free energy and the energy dissipated in the system are split into contributions from the bulk material, from phase interfaces and from other boundaries. Microstructure evolution is then determined by the incremental energy minimization. As an application, stress-induced transformation is considered which proceeds by formation and growth of internally twinned martensite plates within the austenite matrix. The interfacial energy is examined at three scales, namely at twin boundaries, austenite-martensite interfaces and at grain boundaries. Both atomic-scale and the elastic micro-strain interfacial energies are included and respective estimates are taken from the materials science literature or predicted using micromechanical finite element analysis. Examples are provided for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy. They illustrate the effect of grain size on the macroscopic stress-strain response including the hysteresis width.