Probabilistic aspects of the strength of fiber-dominated short-fiber composites II: Biased fiber distribution

A statistical model for the strength of short non-aligned fiber composites is derived from first principles for fiber-dominated fracture. Exact implementation of this model must rely on Monte Carlo methods; however, simple approximations for the mean and standard deviation of the strength may be obtained. The model shows that the mean strength increases and the coefficient of variation (COV) decreases with increasing fiber length, exclusive of any critical length considerations. Decreasing fiber volume fraction is predicted to lower mean strength and to increase its COV. The utility of the model is demonstrated for comparing the relative strength-reinforcing efficiencies of various aligned-fiber, random fiber and biased fiber distributions. This comparison is robust with respect to assumed parameters in the model. Either continuous random or [0°, ±60°] quasi-random composites are shown to have 37% of the strength of aligned-fiber composites; a simple cosine orientation distribution has 53% of the aligned-fiber strength.