A two-scale thermo-mechanically coupled model for anomalous martensite transformation and elastocaloric switching effect of shape memory alloy

Conventional shape memory alloys (SMAs) exhibit an approximately linear relationship between the critical stresses of martensite transformation (MT) and ambient temperature (Clausius-Clapeyron relationship). Meanwhile, depending on the sign of entropy difference between the parent and martensite phases, these alloys behavior either a conventional or an inverse elastocaloric effect which originates from the latent heat release/absorption during stress-induced MT. Recently, MT with a non-monotonic Clausius-Clapeyron relationship (denotes as anomalous MT) and an elastocaloric switching effect (changes from the inverse elastocaloric effect at relatively low temperature to the conventional elastocaloric effect at relatively high temperature) were reported in CoCr-based Heusler-type SMAs. In this paper, to understand and quantitatively describe these new phenomena, a two-scale thermo-mechanically coupled constitutive model is constructed. In the mesoscopic scale, the fine twinned structure and the potential correspondent variant pairs of martensite phase are analyzed based on the crystallographic symmetry and the geometrically nonlinear theory of MT. The classical Debye's model is employed to describe the lattice and electronic heat capacities of the parent and martensite phases; while, a Monte Carlo simulation for the three-dimensional (3D) Ising's model is performed and a scaling law for the magnetic heat capacity of parent phase is proposed. Then, a new constitutive model is established based on the fundamental laws of irreversible thermodynamics to describe the non-isothermal stress-induced MT between parent and martensite phases. To consider the thermo-mechanical interactions between the parent phase and correspondent martensite variant pairs, each variant pair is regarded as an inhomogeneous inclusion with a mobile interface and embedded in the parent phase. With the help of interfacial operator, the thermodynamic driving force of MT is derived from the constructed Helmholtz free energy and dissipative inequality. Internal heat generation originated from the thermo-elasticity, inelastic deformation dissipation and latent heat is derived from the conservation law of energy. In the macroscopic scale, the thermo-mechanical response of SMA specimen is obtained by solving the equations of force balance, deformation compatibility, and thermodynamic equilibrium through the full-field calculation and mean-field approximation. Finally, the proposed model is verified by comparing the predictions with the experiments. It can be found that the anomalous MT and elastocaloric switching effect of CoCrAlSi SMA can be well captured by the proposed model.