A micromechanical analysis of the coupled thermomechanical superelastic response of textured and untextured polycrystalline NiTi shape memory alloys

In this paper a micromechanical model that incorporates single crystal constitutive relationships is used for studying the pseudoelastic response of polycrystalline shape memory alloys (SMAs). In the micromechanical framework, the stress-free transformation strains of the possible martensite twinned structures, correspondence variant pairs (CVPs), obtained from the crystallographic data of NiTi are used, and the overall transformation strain is obtained by defining a set of martensitic volume fractions corresponding to active CVPs during phase transformation. The local form of the first law of thermodynamics is used and the energy balance relation for the polycrystalline SMAs is obtained. Generalized coupled thermomechanical governing equations considering the phase transformation latent heat are derived for polycrystalline SMAs. A three-dimensional finite element framework is used and different polycrystalline samples are modeled based on Voronoi tessellations. By considering appropriate distributions of crystallographic orientations in the grains obtained from experimental texture measurements of NiTi samples, the effects of texture and the tension–compression asymmetry in polycrystalline SMAs are studied. The interaction between the stress state (tensile or compressive), the number of grains and the texture on the mechanical response of polycrystalline SMAs is studied. It is found that the number of grains (or size) affects both the stress–strain response and the phase transformation propagation in the material. In addition to tensile and compressive loadings, textured and untextured NiTi micropillars with different sizes are also studied in bending. The coupled thermomechanical framework is used for analyzing the effect of loading rate and the phase transformation latent heat on the response of both textured and untextured samples. It is shown that the temperature changes due to the heat generation during phase transformation can affect the propagation of martensite in samples subjected to high strain rates.