Fracture energy for short brittle fiber/brittle matrix composites with three-dimensional fiber orientation

Adding brittle fibers to a brittle matrix can create a composite which is substantially tougher than the monolithic matrix by providing mechanisms for energy dissipation during crack propagation. A model based on probabilistic principles has been developed to calculate the increased energy absorption during fracture for a brittle matrix reinforced with very short, poorly bonded fibers. This model, previously developed for planar fiber orientations, is extended to consider the three-dimensional fiber orientations which may occur during composite fabrication. The fiber pull-out energy is assumed to dominate other fracture energy terms, and simple parametric studies are given to demonstrate the effect of fiber orientation, fiber length, fiber diameter, and fibermatrix interfacial shear stress. In particular, the fiber orientation effects may be grouped into an effective "orientation parameter''. The model predictions compare satisfactorily with the limited data available, and offer a conceptual framework for considering the effect of changing the physical variables on the fracture energy of the composite.