Analytical Modeling for Stress-Strain Curve of a Porous NiTi

Two models for predicting the stress-strain curve of porous NiTi under compressive loading are presented in this paper. Porous NiTi shape memory alloy is considered as a composite composed of solid NiTi as matrix and pores as inclusions. Eshelby’s equivalent inclusion method and Mori-Tanaka’s mean-field theory are employed in both models. Two types of pore connectivity are investigated. One is closed cells (model 1); the other is where the pores are interconnected to each other forming an open-cell microstructure (model 2). We also consider two different shapes of pores, spherical and ellipsoidal. The stress-strain curves of porous shape memory alloy with spherical pores and ellipsoidal pores are compared. It is found that the ellipsoidal shape assumption is more reasonable than the assumption of spherical pores. Comparison of the stress-strain curves of the two models shows that use of open-cell microstructure (model-2) makes the predictions more agreeable to the experimental results of porous NiTi whose microstructure exhibits open-cell microstructure.