On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material

A thermomechanical description of the martenstitic phase transformation and the associated shape memory effect in polycrystalline shape memory alloys (SMAs) is presented. The rate-independent constitutive relations are derived in the stress-temperature space using a Lagrangian formulation. The Kuhn–Tucker optimality conditions, constraints on evolution equations for transformations strain and shape of transformation function in thermodynamic force space are obtained naturally through the principle of maximum transformation dissipation. Various transformation functions are investigated and a generalized type transformation function is proposed. Numerical results of the model based on different transformation functions are compared with experimental results to determine their accuracy to predict SMA characteristics like tension–compression asymmetry, negative volumetric transformation strain and pressure dependence.