Bending Analysis of Textured Polycrystalline Shape Memory Alloy Beams

In this paper a micro-mechanical model that incorporates single crystal constitutive relationships is used for studying the pseudoelastic response of polycrystalline shape memory alloy beams subjected to bending. In the micro-mechanical framework, the stress-free transformation strains of all the 24 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 a phase transformation. A three-dimensional finite element model is used and a polycrystalline beam is modeled based on Voronoi tessellations. The effect of crystallographic texture and the tension-compression asymmetry on the bending response of superelastic beams is studied. The results of texture measurements are used to assign appropriate crystal orientations to the grains in the model. By considering various combinations of crystal orientations, the effect of preferred crystallographic texture on the bending response is studied. The size effect is also studied by considering two polycrystal structures with different number of grains.