Overview no. 100 Scalings in fracture probabilities for a brittle matrix fiber composite

Abstract

This paper considers the statistical aspects of strengthening of a monolithic ceramic by the addition of continuous ceramic fibers in parallel. The failure process involves quasi-periodic matrix cracking, frictional sliding of the fibers in break zones, and fiber bridging of cracks in a global load-sharing framework. First we consider a “characteristic” bundle in the composite and develop its distribution for strength in terms of certain characteristic stress and length scales. We then consider the strength distribution for a chain arrangement of such bundles where failure of the weakest bundle triggers failure of the composite. The scale of load transfer among fibers in a bundle may be smaller than the full composite cross-section depending on such things as the stiffness of the matrix relative to the fibers and the spacing of periodic cracks. Substantial reductions in strength are predicted for smaller bundle sizes, but composite reliability is typically very high and the size effect very mild.