A micromechanical constitutive model of high-temperature shape memory alloys

Abstract

In this work, a new micromechanical constitutive model is constructed for high-temperature shape memory alloys. Different from the classical constitutive models, the microstructural patterns, heterogeneities of stress and strain fields at the microscopic scale are addressed. In the proposed model, three different inelastic deformation mechanisms, i.e., reversible martensitic transformation, irreversible transformation-induced plasticity, viscoplasticity, as well as their complex interactions, are considered. In addition to the well-known austenite and martensite phases, a new austenite-martensite interface phase is introduced to address the high local stress induced by the martensitic transformation. The modified Mori-Tanaka's homogenization scheme and Hill's interfacial operator are employed to determine the non-uniform stress fields of the three phases. To satisfy the thermodynamic compatibility of the proposed model, the driving forces and evolution equations of the three inelastic deformation mechanisms are derived based on the constructed Helmholtz free energy and the fundamental laws of irreversible thermodynamics. Inheritances of the plastic deformation induced by moving austenite-martensite (A-M) interface during repeated martensitic transformation and its reverse are incorporated. Temperature evolution caused by internal heat production and heat exchange with the ambient medium is also addressed. To validate the capability of the new constructed model, the predicted results of creep behavior and stress-assisted two-way shape memory effect of NiTiPd high-temperature shape memory alloys are compared with the experimental ones. The proposed model provides a theoretical tool for simultaneously analyzing the deformation behaviors at the macroscopic scale and underlying mechanisms at the microscopic scale.