Stress concentration factors in two-dimensional composites: effects of material and geometrical parameters

In the study of fracture processes in composite materials, the interactions between broken and intact fibers are of critical importance. Indeed, the redistribution of stress from a failed fiber to its unfailed adjacent neighbors, and the stress concentration induced in these, determine the extent to which a break in one fiber will cause more breaks in neighboring fibers. The overall failure pattern is a direct function of the stress concentration factors (SCFs). In this paper, we propose a new model for the SCFs in two-dimensional unidirectional composites containing broken fibers. A closed-form expression is derived for the SCF profiles as a function of material and geometrical parameters. The model differs significantly from earlier schemes, as the local effect of a fiber break on nearest neighbors is much milder than previously calculated, both as a function of the inter-fiber distance and of the number of adjacent broken fibers. Comparison with experimental results for silicon-carbide/epoxy composites demonstrates the validity of the proposed scheme. Since the overall fracture pattern in fiber composites is a direct function of the SCFs, the model may help shed light on fracture nucleation and growth in composites.