Stress distributions in single shape memory alloy fiber composites

Shape memory alloy (SMA) in the form of wires or short fibers can be embedded into host materials to form SMA composites that can satisfy a wide variety of engineering requirements. The recovery action of SMA inclusions induced by elevated temperature can change the modal properties and hence the mechanical responses of entire composite structures. Due to the weak interface strength between the SMA wire and the matrix, interface debonding often occurs when the SMA composites act through an external force or through actuation temperature or combination of the two. Thus the function of SMAs inside the matrix cannot be fully utilized. To improve the properties and hence the functionality of SMA composites it is therefore very important to understand the stress transfers between SMA fibers and matrix and the distributions of internal stresses in the SMA composite. In this paper, a theoretical model incorporating Brinson’s constitutive law of SMA for the prediction of internal stresses is successfully developed for SMA composites, based on the principle of minimum complementary energy. A typical two-cylinder model consisting of a single SMA fiber surrounded by epoxy matrix is employed to analyze the stress distributions in the SMA fiber, the matrix, and at the interface, with important contributions of the thermo-mechanical effect and the shape memory effect. Assumed stress functions that satisfy equilibrium equations in the fiber and matrix respectively are utilized, as well as the principle of minimum complementary energy, to analyze the internal stress distributions during fiber pull-out and the thermal loading process. The entire range of axisymmetric states of stresses in the SMA fiber and matrix are developed. The results indicate substantial variation in stress distribution profiles for different activation and loading scenarios.