Abstract
The axisymmetric elastic deformations in shape memory alloy (SMA) fiber reinforced composites are studied. We analyze the stress concentration near the interface between the fiber and the matrix as a result of a pre-described phase transformation in the active fiber. A typical model involving a single infinite fiber embedded in an infinite elastic matrix is studied. A portion of the fiber is allowed to undergo phase transformation along the axial direction so that its length is changed by the corresponding transformation strain (typically a few percentages), while the matrix is assumed to be linearly elastic and isotropic. Under certain bonding conditions, the deformation of fiber forces the matrix to deform in the elastic regime in order to accommodate the transformation strains.
The problem is formulated as axisymmetric deformations coupled with a finite transformation region in the fiber. In order to avoid infinite stresses found under perfect bonding conditions, we adopt a “spring” model which accounts for the elasticity of a transition layer at the interface. This model allows for relative displacements between the fiber and the matrix. A linear relation between this relative displacement and the shear stress is used. The exact elasticity solution (in integral form) to this problem is found using Love’s stress function and Fourier transform. Numerical integration is performed to produce the stress distributions. In particular, the shear load transfer profiles along the interface are calculated for various spring stiffness. It is found that the singularity is eliminated and the stress concentration factor depends on the stiffness of the transition layer.
