Grain-size effect in micromechanical modelling of hysteresis in shape memory alloys

Size effects in pseudoelastic polycrystalline shape memory alloys are studied by considering a representative spherical laminated domain (subgrain) and its interfacial energy at three scales: at the subgrain boundaries, at the austenite-martensite interfaces, and at the twin boundaries. Two sources of interfacial energy are accounted for, namely the atomic-scale energy of twin and phase boundaries and the elastic strain energy at microstructured interfaces, the latter being predicted theoretically The evolution of microstructure of the representative domain is determined using the incremental energy minimization rule applied to the sum of the increments in the Helmholtz free energy and rate-independent dissipation The size-dependent part of dissipation is estimated by assuming that negative increments in interfacial energy, associated with annihilation of interfaces, cannot be reverted back into the bulk free energy and are thus dissipated. Simple analytic formula for the interfacial energy dissipated in a complete forward-reverse transformation cycle is derived and combined with a micromechanical model of a polycrystalline NiTi shape memory alloy. A numerical example illustrating size-dependent hysteresis in the stress-induced martensitic transformation is presented. (C) 2010 WILEY-NCH Verlag GmbH & Co KGaA, Weinheim