Effect of fiber inclination on crack bridging stress in brittle fiber reinforced brittle matrix composites

The mechanical behavior of brittle matrix composites is strongly affected by the bridging of cracks by fibers. In random fiber composites, fibers can lie at an angle to the crack plane. Under such conditions, the bridging stress for a certain crack opening is governed by various micromechanisms including fiber debonding, fiber bending and rupture as well as matrix spalling. While fiber debonding has been widely investigated, the coupled fiber bending/matrix spalling mechanism has received little attention. In this paper, the fiber bending/matrix spalling mechanism is analyzed by treating the fiber as a beam bent on an elastic foundation with variable stiffness and the possibility of spalling. The foundation stiffness and spalling criterion are derived from a finite element analysis. The bridging stress due to bending alone as well as the total bridging stress are then obtained for the case with brittle fibers. Through this analysis, the effect of various microstructural parameters (such as fiber and matrix moduli, matrix spalling strain and fiber/matrix interfacial friction) on the behavior of random fiber composites can be studied. Prediction of maximum bridging stress for inclined fibers based on the present model is shown to be in good agreement with experimental results.