Probability distributions for the strength of composite materials. III: The effect of fiber arrangement

Abstract

This paper continues the study of the chain-of-bundles model for the statistical strength of composite materials. The focus is onthree-dimensional composites where the fibers in a cross-section form atwo-dimensional array. In particular, two-layer tapes and hexagonal arrays are considered, and bounding distributions are obtained based on the occurrence of at least two adjacent fiber fractures in the material. As in earlier work, various approximate and limiting Weibull distributions arise for the strength of the composite. In comparing the new results with those obtained earlier for tapes and tubes (one-dimensional arrays), the bounds suggest that the median strength is moderately increased for the two-dimensional arrays, while the variability in strength is unchanged. In situations where the occurrence of two adjacent fiber fractures leads almost certainly to composite fracture, such conclusions are warranted. In cases where the bounds are clearly conservative, the same results are expected, although a slight decrease in the variability in composite strength may occur. Nevertheless, the bounds discussed in this paper yield considerable insight.