Modelling the stress-induced multi-step martensite transformation of single crystal NiMnGa ferromagnetic shape memory alloys

Abstract

Existing experimental results have shown that multi-step martensite transformation can be induced by the applied stress in single crystal NiMnGa ferromagnetic shape memory alloys (FSMAs) and the transformation property depends on the ambient temperature strongly. In this work, a crystal-plasticity based constitutive model is established to quantify such a phenomenon. Based on the crystallographic symmetry, the lattice structures and eigenstrains of austenite (A) and three different martensite phases, i.e., the modulated martensite phases with a periodicity of 5 lattice cells (5M) and a periodicity of 7 lattice cells (7M), and a non-modulated (NM) martensite phase are analyzed. A three-dimensional (3D) single crystal constitutive model is constructed in the framework of finite strain by considering five different martensite transformation processes, i.e., the transformations between A and 5M, A and 7M, A and NM, 5M and 7M, and 7M and NM phases. Thermodynamically consistent kinetic equations for the five different martensite transformation processes are proposed based on the constructed Helmholtz free energy and Clausius's dissipative inequality. The capability of the proposed model to describe the tensile stress-induced multi-step martensite transformation of single crystal NiMnGa FSMA in [100] crystallographic orientation is verified by comparing the predictions with corresponding experimental results. Further, the proposed model is used to predict the deformations of the single crystal under the tension and compression in various crystallographic orientations.