A microcracked solid reinforced by rigid-line fibers

Abstract

The effective elastic properties of a solid containing two extreme types of line inclusions—cracks and rigid-line fibers—are investigated in this paper. This is done using a two-dimensional, self-consistent method combined with crack and rigid-line energy-release concepts. It is established that the fiber density has to be approximately five times the crack density in order to offset the effect of microcracks on the tensile modulus of a solid containing randomly distributed microcracks and fibers. For parallel and perpendicular cracks and fibers, it is found that fibers have almost no effect on the tensile modulus normal to the fiber direction and neither do microcracks in the crack direction. However, microcracks reduce the composite modulus normal to the crack direction, and fibers enhance the modulus in the fiber direction. A two-dimensional differential method is also used for a material containing randomly distributed rigid-line fibers or cracks. The difference between the composite elastic moduli obtained by the differential and self-consistent methods is very small for the rigid-line-fiber reinforcements, but is pronounced for the microcracks.