The effective behavior of a fiber bridged crack

Abstract

We propose a multiple scale based method to find the effective behavior of a two-dimensional linear elastic periodically layered medium containing a series of aligned cracks cutting a large number of layers of one material (the matrix), the layers of the second one (the fibers) remaining intact. The obtained effective behavior is that of an homogeneous body with, in place of the actual microcracks, a line segment across which the displacements and the stresses suffer jump discontinuities. The coefficients entering in these jump conditions can be related to the mechanical and geometrical parameters of the composite by solving two elastic problems posed on an infinite cracked strip. Moreover, these jump conditions are generally different from those provided by the “line-spring model” which is usually adopted in mechanical engineering in such a situation.