Micromechanics of shape memory alloy fiber–reinforced composites subjected to multi-axial non-proportional loadings

Abstract

In this article, micromechanical behavior of metal matrix reinforced with shape memory alloy fibers under combined thermo-mechanical loadings is investigated. A representative volume element consisting of circular/rectangular cross-sectional shape memory alloy fibers surrounded with aluminum matrix is considered to model micromechanical behavior of shape memory alloy composites. In order to simulate main features of shape memory alloy fibers, especially under multi-axial non-proportional loadings, Panico–Brinson constitutive model is employed. This model is able to predict martensite transformation, shape memory effect, pseudo-elasticity, and in particular reorientation of martensite variants which is responsible for non-proportional loadings. Furthermore, the response of aluminum matrix is assumed as a thermo-elastic-plastic material with linear kinematic work hardening. A finite element formulation containing incremental and iterative processes is developed to analyze the representative volume element in the state of generalized plane strain. Convergence, cost, and comparative studies are conducted to examine efficiency and accuracy of the developed solution. Then, a set of parametric study is directed to provide an insight into the influence of fiber volume fraction, fiber cross-sectional shape, pre-strain, and temperature on the micromechanical behavior of shape memory alloy composites subjected to multi-axial loadings. A significant coupling is observed between normal–normal/normal–shear/shear–shear strains during non-proportional multi-axial loadings which confirms the importance of simulation of martensite reorientation.