Modeling of the thermomechanical behavior of porous shape memory alloys
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Two methods are used in this work to estimate the porous shape memory alloy (SMA) thermomechanical behavior. The porous SMA is assumed to be made of two components, the dense SMA matrix and the pores. An existing rate-independent type constitutive model is employed to describe the matrix behavior. Two contrasting strategies are used to estimate the overall thermomechanical behavior: (1) the unit cell finite element method (UCFEM) to account for periodic distribution of pores in the SMA matrix, and (2) an averaging micromechanics method based on the incremental formulation of the Mori-Tanaka method to account for random distribution of pores in the matrix. Cylindrical and spherical shapes are considered as approximations of open and closed pores, respectively, in both methods. Results are presented for both types of pores and comparisons are made between the two methods under various loading conditions. Both methods compare well in predicting the isothermal elastic material properties and pseudoelastic response under axial and out-of-plane shear loading. However, the transformation results differ under transverse and in-plane shear loading. This difference is found to be due to the use of an average value of stress for the SMA matrix in the micromechanics averaging method, which diminishes the effect of local stress concentration thereby delaying the onset of phase transformation caused by an applied load. On the other hand, the actual values of stress at all material points in the SMA matrix are used in the UCFEM causing phase transformation in regions near the pores at smaller applied load values than what is calculated by the micromechanics averaging method. 2001 Published by Elsevier Science Ltd.
