Constitutive Modeling of Porous Shape Memory Alloys Using Gurson–Tvergaard–Needleman Model Under Isothermal Conditions

Abstract

Based on the Gurson–Tvergaard–Needleman (GTN) model, a constitutive relationship considering both the effects of strain hardening and hydrostatic stress for porous shape memory alloys (SMAs) is proposed. To capture the relationship between microscopic and mesoscopic behaviors, a representative volume element (RVE) containing an array of spherical voids is presented. In this paper, an approximate solution including strain hardening exponent [Formula: see text] is deduced by considering the porous SMA as a two phase composite with the SMA matrix and the second phase representing voids. The model parameters, [Formula: see text] and [Formula: see text], accounting for interactions between voids are investigated to take into account their influences on strain hardening, critical phase transformation stress and yield surface. In addition, the evolution equations of phase transformation are derived and then applied to the simulation of porous Ni–Ti SMAs with a porosity of 13%. Using the calibrated GTN model parameters, the critical phase transformation stress closer to experimental data is obtained. The predictions of stress–strain curve by the proposed constitutive model are found to be in excellent agreement with published experimental data and finite element results. The results prove that the model is capable of reproducing the features of porous SMAs such as superelasticity, tensile-compressive asymmetry and internal loops under uniaxial even combined loading conditions. A conclusion is drawn that the present constitutive relationship is powerful and useful for the analysis of porous SMAs.