Coupled rate-dependent superelastic behavior of shape memory alloy bars induced by combined axial-torsional loading: a semi-analytic modeling

Abstract

In this article, the coupled thermomechanical response of superelastic shape memory alloy bars and tubes in combined tension and torsion is studied both analytically and experimentally. Using the Gibbs free energy as the thermodynamic potential and choosing appropriate internal state variables, a three-dimensional phenomenological macroscopic constitutive model for shape memory alloys is derived. Taking into account the effect of latent heat during the forward and reverse martensitic phase transformation, the appropriate form of the energy balance relation is obtained. The three-dimensional coupled relations for the energy balance in the presence of the internal heat flux and the constitutive equations are reduced to a two-dimensional form for the tension-torsion case. An explicit finite difference approach is utilized to discretize the governing boundary conditions of bars. An empirical expression for the free heat convection from the surface of a shape memory alloy bar was proposed and experimentally validated. Several sets of experiments were then carried out to evaluate the mechanical and thermal responses of the model for a shape memory alloy tube subjected to uniaxial, pure torsion and non-proportional tension and torsion loading–unloading conditions. The approach could be used in the design of shape memory alloy devices undergoing combined loads with high strain rates or in the fatigue design of shape memory alloy devices subjected to cyclic loading.