Elastic deformations in shape memory alloy fiber-reinforced composites.

摘要

The elastic deformations of SMA fibers reinforced composite associated with phase transformations in parts of the SMA fibers are investigated. A simple case involving a single infinite fiber embedded in an infinite elastic matrix is studied. In the study, parts of the fiber are allowed to undergo uniform phase transformation along the axial direction, and there exist sharp boundaries between transformed and untransformed phases. The interaction between the fiber and the matrix is directly described by certain bonding conditions, while the sharp phase boundary in the fiber is directly modeled by piecewise linear constitutive law. The elastostatic problem is simplified as axisymmetrical ones. Two kinds of bonding models (“perfect bonding”and “spring bonding”) and two kinds of stiffness models (“rigid fiber” and “elastic fiber”) are considered. The exact solutions to the distributions of stress, strain, and displacement for each of these models are obtained in integral forms. A single finite segment transformation pattern is discussed in detail to display the local properties at crucial location—the intersection of fiber-matrix interface and phase boundary in the fiber. The asymptotic expansion technique is employed to further analysis the behavior of stresses. In the “perfect bonding” condition, the normal stresses have finite jumps across the phase boundary, whereas the shear stress approaches infinity. The singularities are isolated. The jumps of the normal stresses and the intensity of singularity of the shear stress are determined by the material properties of the matrix and fiber and transformation strain, and are independent of the geometry of the phase transformed region. In the “spring bonding” condition, all stresses are finite and continuous in fiber and matrix. The shear stress concentrates at the intersection of the fiber-matrix interface and the phase boundary of the fiber. The softer fiber, matrix, and bonding condition will reduce the shear stress concentration. The shear stress concentration increases as the aspect ratio of phase transformed region increases.