Stiffness of Smart Composites with Shape Memory Alloy Fibers in the Presence of Matrix Cracks

The paper presents a methodology for evaluating the effective stiffness of unidirectional composite materials with shape memory alloy (SMA) fibers in the presence of matrix cracks. The solution is obtained for the case where SMA fibers in the intact composite are in the austenitic phase. However, elevated stresses in the sections of SMA fibers adjacent to the crack planes cause the martensitic transformation affecting the stiffness of the material. The solution has to account for thermal residual stresses in SMA and `ordinary' fibers and in the matrix. The order of magnitude of these stresses is calculated in the paper for two representative composite systems. As follows from the numerical examples, thermal residual stresses in the SMA fibers increase proportionally to their volume fraction but remain relatively small. However, thermal stresses in the matrix may reach rather high values reducing the strength of the matrix by a significant factor.