Modeling the interface effect of shape memory alloy composite materials

Purpose - The purpose of this paper is to investigate the stress distribution in shape memory alloy (SMA) composite due to phase transformations in the fiber in view of the applied boundary conditions on the matrix. Design/methodology/approach - A consistent homogenization of a SMA wire-reinforced polymer composite volume element undergoing quasi-static deformation was performed and SMA wire-matrix interface behaviour was presented. For the SMA wire, a one-dimensional phenomenological constitutive model was used. Eshelby's inclusion theory was employed for homogenization. A strain averaging approach was reviewed in which the average strain was substituted back to obtain the expressions for the effective stiffness, the inelastic strain, and the average stresses in the constituent phases. In order to study the stress distribution in SMA composite and constituent phases (fiber and matrix) as a consequence of the SMA wire-matrix interface effect, interfacial stress model was derived. Interfacial axial and shear stress distribution is characterized for forward and reverse phase transformations. Finally, the thermomechanical behaviours were computed by applying strain energy approach incorporating the interface effects. Findings - The results presented show that due to the difference between the shear modulus of matrix and SMA wire, and because of the strain non-uniformity at the SMA wire-matrix interface, shear stress is developed within the matrix under the axial loading of the representative volume element (RVE). The shear stress increases more rapidly as the SMA wire radius is increased but not with increase in the length. However, the axial stress does not increase much with increase in the SMA wire radius and length. Further, the average stress equation of the RVE at the SMA wire-matrix interface is effectively addressed. The modeling approach is successfully validated extensively for different geometric and volumetric parameters for different loading conditions. It is evident that the interface effect of SMA wire composites is SMA stiffness dominated due to the fact that the geometric parameters do not influence much the stresses as compared to the change in SMA wire stiffness. Originality/value - The approach is based on modeling the fiber matrix interface effect using homogenization scheme. Further, the strain energy approach is applied to compute the stress-strain response. This indicates the importance of modeling the SMA wire-matrix interface effect, and in particular, the energy exchange between the constituent phases. The results have been compared for different geometric parameters as well as volume fractions of the constituent phases under different loading conditions.