Modeling porous shape memory alloys using micromechanical averaging techniques

Abstract

A model for the macroscopic mechanical behavior of porous shape memory alloys (SMAs) is presented in this work. The derivation of the model is presented for the general case of a composite with phases undergoing rate-independent inelastic deformations. Micromechanical averaging techniques are used to establish the effective elastic and inelastic behavior based on information about the mechanical response of the individual phases and shape and volume fraction of the inhomogeneities. An explicit expression for the effective tangent stiffness and an evolution equation for the effective inelastic strain are derived. The results for porous SMAs are obtained using a constitutive model with internal variables for dense SMAs and assuming zero stiffness for the inhomogeneities. A detailed study on the choice of the pore shape is also performed for a random distribution of pores. Finally, the numerical results are compared with experimental data for porous NiTi SMA processed from elemental powders with 42% porosity.