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, sE=GF/uh, depends on the beam depth, h, and on the composite fracture toughness, GF, and tensile strength, u. The second, Gb/ , is the ratio of the energy necessary to develop the bridging mechanism of the secondary phases, Gb, to the intrinsic fracture energy of the matrix, . It fundamentally depends on the shape of the cohesive law.