A probabilistic approach to the toughening mechanism in short-fiber-reinforced ceramic-matrix composites

The toughening mechanism in brittle ceramic-matrix composites reinforced with short fibers is analytically studied by considering probabilistic aspects of fiber strength. Energy for broken and/or unbroken fibers to be pulled out is given on the assumption that the resistant force at the fiber interface is uniform along the sliding area. The effect of fiber inclination is incorporated by the introduction of a resistant force proportional to the normal component of the bridging force on the fiber and a stress magnification factor. This considers significant local deformation of the fiber near the crack surface. Fiber breakage is assumed to occur at the randomly distributed flaws whose expected number in a unit length follows a power law of the stress. This assumption is consistent with the fact that the strength of a fibre of a certain length is expressed by a Weibull distribution function. The energy dissipated as a result of fiber pull-out for a unit area of major crack propagation is estimated for continuous unidirectional composites, aligned short-fiber composites and two- and three-dimensional random short-fiber composites.