Fracture mechanics of brittle matrix ductile fiber composites

A model to predict the increase in critical flaw size or stable crack growth potential which can occur by the inclusion of ductile fibers in a brittle matrix is considered. The model is based upon the super-position of two known stress intensity solutions; one for the crack opening mode resulting from a remotely applied stress and the second, an opposing stress intensity that results from a crack closing force exerted by unbroken fibers spanning the crack surfaces. The extent of stable growth possible is computed at the ultimate stress of the brittle phase as functions of fiber strength and of volume fraction for various amounts of fiber rupture. A hot pressed beryllium matrix is used as an example. The crack surface displacement over which a given fiber is capable of deforming without rupture is found to be sensitive to the fiber-matrix interface strength. The factors leading to maximum crack surface displacement without rupture are a high strain hardening capability of the fiber and an interface designed to fail at fiber stresses between yield and ultimate strengths.