Simulations of nonlinear deformations in Ni–Ti shape memory alloys under tension/compression using an energy minimization model

•We propose a 3-D, load-history related computational model.•Asymmetries in single crystals depend on orientation.•Asymmetries in polycrystals depend on textures.•Polycrystals show higher critical stresses and smaller remnant strains. Ni–Ti shape memory alloys (SMA) have been widely used in industrial, medical and aerospace fields due to its superior mechanical properties including the shape memory effect, superelasticity and anti-corrosion. The macroscopic deformation of Ni–Ti SMA under thermal–mechanical loading typically shows intensively nonlinearity due to the martensitic phase transformation and/or the martensite variants reorientation. In this paper, we proposed a three-dimensional computational model based on energy minimization to simulate the asymmetric deformation behaviors of Ni–Ti single crystal and polycrystals under tension and compression. The volume fractions of austenite and each type of martensite variant in a specific grain (or single crystal) are obtained by minimizing the total energy using the sequential quadratic programming optimization algorithm. For polycrystals, the mechanical constraints from the neighboring grains are considered in an Eshelby inclusion manner. The proposed model is employed to simulate the superelasticity, the asymmetric deformations and the pure martensite variants reorientation of both Ni–Ti oriented single crystal and textured polycrystals under tension and compression. The simulated asymmetric deformation behaviors under tension and compression at different temperature regions accord well with the experimental results. The volume fractions of martensite variants under stress loading were also explored, reproducing the stress induced martensitic transformation. Simulation results also show that the volume fraction variations of martensite variants under tension and compression are consistent with the observed asymmetric deformation behavior.