Stress Concentration of Shape Memory Alloy Fiber Reinforced Composites in Elastic Axisymmetric Deformations

In an effort to investigate the mechanical properties of shape memory alloy (SMA) fiber reinforced composites, the stress distribution due to the phase change in the fiber is examined. We study a simple model involving a single infinite fiber embedded in an infinite elastic matrix. A portion of the fiber is allowed to undergo uniform phase transformations along the axial direction while the matrix remains linearly elastic. Under perfect bonding condition, the deformation of the fiber forces the matrix to deform in the elastic regime in order to accommodate the transformation strain. To simplify the analysis, the elasticity of the fiber is ignored. The problem is formulated as axisymmetric deformations for the matrix with a piecewise linear boundary condition at the interface with the fiber as a result of the phase transformation in the fiber. The exact elasticity solution (in integral form) to this problem is found using Love’s stress function and Fourier transform. The normalized forms of the solution are presented. The asymptotic behaviors of the stress distributions near the phase boundary are analyzed in details. The characteristics of the singularities near the phase boundary are obtained for this model. Numerical evaluations are also performed to obtain the distributions of the displacements, the strains, and the stresses in the matrix. In particular, the shear load transfer profiles along the interface are obtained for various aspect ratios of the transformed region.