STATISTICAL ISSUES IN THE FRACTURE OF BRITTLE-MATRIX FIBROUS COMPOSITES

This paper reviews recent work and presents new results on statistical aspects of the failure of composites consisting of brittle fibers ali gned in a brittle matrix. The failure process involves quasi-periodic matrix cracking in planes perpendicular to the fiber, frictional slidi ng of the fibers in fiber break zones, and fiber bridging of cracks in a load-sharing framework that may vary from global to fairly local. F irst, we review the overall statistical features of the failure proces s, and identify certain issues in terms of critical geometric, statist ical and mechanical parameters. This leads to two interesting cases, o ne where the spacing of matrix cracks is small relative to the length scale of load transfer in the fibers, and one where it is larger. Next we consider 'characteristic' bundles in the composite which capture e ssential features of the statistics of the failure process, and develo p their distributions for strength in terms of certain characteristic stress and length scales. We then model the composite as a chain arran gement of such bundles both longitudinally and laterally, as the scale of load transfer among fibers in a bundle may be smaller than the ful l composite cross-section. This scale, though not precisely quantified , depends on such things as the stiffness of the matrix relative to th e fibers, the volume fraction of the matrix and the spacing of periodi c cracks. We then consider the strength distribution for the composite on the basis of the failure of the weakest characteristic bundle. We also consider issues related to fiber pull-out and the work of fractur e as well as the possibility of severe strain localization especially within the bundle triggering overall failure. Substantial reductions i n strength are predicted for smaller bundle sizes, but composite relia bility is typically very high and the size effect very mild. Finally, we mention limited comparisons with Monte Carlo simulations and experi mental results.