The objective of this research program is to establish the relationship between the observable and measurable properties of the fiber-matrix interfacial surface on the micro-scale and the macro-properties (strength and toughness) of a fiber reinforced composite specimen. The first step in the development of the proposed three (micro, meso and macro) scale model consists of a scale invariant (fractal) representation of the interfacial surface based on experimental measurements. Next, all interlock, adhesive and capillary forces are determined on the asperities in actual contact. These predictions are corroborated by experiments. Once the statistics of the surface (corresponding to particular materials and specific processing) and contact forces on the contact spots are determined it becomes necessary to study the strength and stability of that system. The onset of debonding and/or frictional slip is determined applying the percolation theory and self-organizing criticality. All phases of this program will be mutually consistent. Geometry and physics of the underlying physical phenomena will be rigorously treated.
