A Micromechanical Constitutive Model for Porous Shape Memory Alloys

Abstract

A micromechanical constitutive model for responding the macroscopic behavior of porous shape memory alloys (SMA) has been proposed in this work. According to the micromechanical method, the stiffness tensor of the porous SMA is obtained. The critical stresses are calculated by elastic mechanics. Based on the general concept of secant moduli method, the effective secant moduli of the porous SMA is given in terms of the secant moduli of dense SMA and the volume fraction of pores. The model takes account of the tensile-compressive asymmetry of SMA materials and the effect of the hydrostatic stress. Only the material parameters of dense SMA are needed for numerical calculation, and can degenerate to dense material. Examples for the uniaxial response of porous SMA materials at constant temperature are then used to illustrate one possible application of the constitutive model. The numerical results have been compared with the experiment data for porous SMA, which show that the modeling results are in good agreement with the experiments.

Effect of Nanopores on Mechanical Properties of the Shape Memory Alloy

“…The is the martensitic volume fraction. Suppose that the Poisson’s ratio of SMA does not change during the deformation process, and is a linear function of applied stress, which is slightly different from popular models [ 25 ]. where is the effective stress and are the threshold stress at the beginning and end of the SMA transition, respectively.…”

Biomedical Porous Shape Memory Alloys for Hard-Tissue Replacement Materials

“…However, for porous SMAs, the numerical modeling of mechanical response is still very difficult due to phase transformation during loading and unloading, irregular pore shape and distribution, and complex micro-region internal stress situation around pores. Some researchers attempted to simulate the superelastic behavior of homogeneous or gradient porous NiTi [ 92 ] by specific numerical approaches, such as the micro-mechanical averaging technique [ 93 , 94 , 95 , 96 ], Eshelby’s effective medium model with Mori–Tanaka mean-field theory [ 96 , 97 , 98 ], or the Unit Cell Finite Element Method [ 90 , 92 , 99 , 100 , 101 , 102 , 103 ]. Most of the simulated relation between elastic modulus (or strength) and porosity agree well with their experimental data in small porosity range.…”

“…However, almost all of the modeling except few Refs. [ 96 ] do not take account for local phase transformation and even plastic deformation around pores. Thus, most of the simulations result obviously do not accord with the observed experimental results of SE mentioned above in Figure 13 and Figure 14 .…”