Toughening of ceramics by short aligned fibers

Abstract

Abstract The tensile strength of a ceramic composite reinforced by short, aligned fibers is studied. The composite contains an initial, through-the-fibers Mode-I crack of arbitrary size. It is assumed that the parallel fibers have equal lengths and are randomly arrayed. The fiber length is chosen to be “optimal” in the sense that it has the largest value consistent with the occurrence of pull-out before fiber fracture, no matter where a propagating matrix crack intersects a fiber. The crack-bridging fibers are modeled by an array of non-linear bridging springs, and the consequent nominal fracture toughness associated with a long crack is calculated. The tensile strength of the composite containing an initial crack of finite size is determined by monitoring the load history as a matrix crack emanating from the tips of the original through-the-fibers crack extends. It is found that the long-crack fracture toughness produced via optimal short-fiber reinforcement is much larger than that provided by continuous fibers of equal deterministic strength. However, for sufficiently small initial cracks, the continuous fibers provide more strength, approaching double that of the short-fiber composite as the initial crack size decreases. For realistic values of physical parameters, the cross-over initial crack length for equal strengths of composites reinforced by short or long fibers is in the millimeter range, comparable to the optimal fiber length.