Stochastic Models of Fracture of Unidirectional Fiber Composites

Abstract

Stochastic models of fracture of unidirectional fiber composites based upon the combination of dispersed damage accumulation and macrocracks nucleation and its further growth are considered. The case of continuous linear elastic fibers and an ideal elastic-plastic matrix are assumed. Both fiber breakage and composite delamination due to damage of the matrix and/or interface are included in the analysis. Macrocracks perpendicular to the fibers are interpreted as three-dimensional regions that account for the fiber strength scale effect.

Two types of final failure under tension along the fibers are considered: the loss of integrity, i.e., the simultaneous development of multiple cracks throughout the specimen, and the more common failure mode crack growth. The results on the unidirectional fiber composite are discussed in connection with the linear theory of fracture mechanics. Within the framework of the stochastic models, the Griffith-Irwin and Paris-Erdogan equations are recovered only when severely restricted assumptions are imposed on the distribution of fiber strength.