The Matrix-Fiber Crack in an Elastic Solid

Abstract

In the presence of strong interface adhesion, the fracture of an embedded fiber can also result in the cracking of the surrounding matrix. While the orientation of such matrix cracks can be varied, the flat penny-shaped crack represents a critical crack orientation which is of particular interest to the study of the micromechanics of fracture processes in fiber-reinforced solids. This paper considers the axisymmetric problem of the uniform straining of a composite elastic solid which contains a penny-shaped crack occupying both the fiber and matrix regions. The isolated cracked fiber-matrix crack interaction is formulated as a mixed boundary value problem related to a two-domain half-space region. The resulting integral equations are solved in a numerical fashion to evaluate the stress intensity factor at the boundary of the penny-shaped crack. The numerical results presented, in the paper illustrate the influence of the elasticity mismatch between the fiber and the matrix on the stress intensity factor at the crack-tip located in the matrix. The numerical results are presented for typical fiber-reinforced composites consisting of epoxy and ceramic matrices reinforced with silicon, glass, and kevlar fibers.