Fracture instabilities and scale effects in brittle solids and brittle matrix fibrous composites

The structural behavior of quasi-brittle materials and brittle-matrix composites ranges from stable to unstable depending on material properties, structure geometry, loading condition and external constrains. In this paper the fracture behavior of a composite characterized by a bilinear cohesive law is analyzed by means of a cohesive-crack model and a bridged-crack model. It is shown that the complex changes in the shape of the load-deflection curve for a three-point bending beam are controlled by two dimensionless parameters. The first, s(E)=G(F)/sigma(u)h, depends on the beam depth, h, and on the composite fracture toughness, G(F), and tensile strength, sigma(u). The second, G(h)/G(IC)(m), is the ratio of the energy necessary to develop the bridging mechanism of the secondary phases, G(b), to the intrinsic fracture energy of the matrix, G(IC)(m). If fundamentally depends on the shape of the cohesive law.