On large scale sliding in fiber-reinforced composites

A critical examination is made of the use of the line-spring model to represent fiber bridging of matrix cracks in the analysis of failure phenomena in fiber-reinforced brittle matrix composites. Attention is focused on composite systems designed to undergo fiber debonding and sliding when matrix cracking occurs. For most composites of this class, it is found that the distance along the fiber within which sliding occurs is often too large to justify use of the line-spring representation. A model which allows for large scale sliding (the LSS model) is proposed and applied to three problems : a matrix crack emerging from a semi-infinite unbridged through-crack in a uni-directional fiber-reinforced composite, the same problem for the finite length unbridged through-crack, and matrix cracking of a cross-ply composite. Primary emphasis is placed on the stress concentration in the bridging fibers. Predictions from the LSS model are compared with those from the line-spring model. In general, the line-spring model is found to overestimate the stress concentration in critically located fibers. A discussion of the significance of the lower estimates of the stress concentration factors is given for several composite systems.