The toughness of brittle matrix composites reinforced with discontinuous fibers

The effective fracture toughness of brittle matrix materials can be increased through the addition of short, poorly bonded fibers which bridge the growing crack. Using a fundamental crack opening-restraining traction law for the resistance to crack propagation provided by an arbitrarily oriented fiber which bridges a crack, together with the fiber orientation and location density functions, a micromechanical model is developed. This model determines the effective crack opening-traction law of the bridging fibers. The steady-state toughness increment is obtained by integrating the contributions of the individual fiber pull out energies. This model includes the observed effect that fibers at large angles to the crack face normal may break rather than pull out. The shear stress at the fiber-matrix interface is allowed to vary during pull out, simulating fiber or matrix damage. Results are presented for a variety of representative fiber orientation states and interfacial shear cases.