Probability distributions for the strength of composite materials IV: Localized load-sharing with tapering

Abstract

This paper continues the study of the chain-of-bundles model for the statistical strength of composite materials by focusing carefully on the localized load redistribution in two-dimensional composites. A tapered load-sharing rule is considered which distributes the nominal load of a failed fiber among its four nearest neighbors, with the two adjacent fibers taking a greater proportion of the load. We consider three distinct probabilistic techniques of analysis and find that the basic probability structure for the distribution for composite strength turns out to be the same as for the idealized local load-sharing in earlier work; however, the median strength of the composite rises moderately due to the milder overloads on the fibers adjacent to breaks, while the presence of small overloads on more distant fibers has almost no effect on strength. Also, the variability in composite strength tends to decrease mildly, due to a slight increase in the critical fracture sequence size leading to catastrophic failure. Again, the Weibull distribution arises as a key model for the strength of unidirectional composites, and we give accurate approximations for its parameters.