A comparison of probabilistic techniques for the strength of fibrous materials under local load-sharing among fibers☆

Abstract In this paper we compare three distinct asymptotic analyses for the probability distribution for strength of a certain class of fibrous materials. This class, which contains composite materials and twisted yarns and cables, is characterized by strong, mechanical interaction among neighboring fibers as is generated by a binding matrix or by transverse frictional forces. The model is the chain-of-bundles model, and we focus mainly on a planar geometry and a simple type of local load-sharing among fibers in a cross-section wherein the load of a failed fiber is shifted in equal portions to its two nearest flanking survivors. Through the study of typical examples we find that the results of the three methods all underscore the importance of the Weibull distribution for modeling composite strength, and are in excellent numerical agreement despite their differing analytical form. This is fortunate because only the two least accurate of the analyses show promise of being extended to more general three-dimensional geometries and local load-sharing rules of interest in applications. The paper lays the groundwork for considering such extension in future papers.