Homogenization of Porous Shape Memory Alloys Using Monte Carlo Technique

In this paper, the superelastic response of porous shape memory alloys (SMAs) containing spherical pore shape with pore volume fraction between 5% and 40% has been considered. Using digital images processing, the distribution of pores in 2D images of porous NiTi SMA has been extracted. In this method, the 3D distribution of pores has been appraised with the Monte Carlo method and 3D porous SMA models have been established. To investigate the superelastic behavior of shape memory alloys, the Lagoudas’s phenomenological model was used, in which a phase transformation function was used. To homogenize the porous SMAs, the Young’s modulus and the phase transformation function have been assumed to be a function of the pore volume fraction. Based on the proposed constitutive model a numerical procedure was proposed and executed by the commercial finite element code ABAQUS with developing a user material subroutine. The numerical results show that the Young’s modulus and the phase transformation function are the approximately linear function of the pore volume fraction; furthermore, these results demonstrate the accuracy of the proposed homogenization method to predict the superelastic behavior of porous SMAs.