Statistical Treatment of Transverse Crack Propagation in Aligned Composites

This paper theoretically examines the failure process of unidirectiona lly reinforced fiber composites with a transverse notch under a tensile load. The fiber stress distribution around the crack tip and the fiber stress redistribution during the initial failure steps have been obtained based upon the explicit solutions of two- dimensional crack problems by the shear-lag method. Failure sequence analysis is conducted to study the effect of variability in fiber strength on the failure process of the composite. Numerical results show that the failure steps ahead of the first intact fiber are not negligible when the Weibull shape parameter of fiber strength distribution is less than four. HE tensile failure of a unidirectionally reinforced fiber composite is a complex process that involves an accumulation of microstructur al damage. In such a material, fibers are relatively weakly coupled by the matrix so that failure of one fiber does not generally precipitate immediate failure of the composite as a whole. Due to this redundancy of the composite's structure, its failure has been considered as a statistical process in which strength is expressed as some measure of the probability of failure such as the mean or median stress. Zweben and Rosen1'2 first analyzed the tensile failure of a fiber reinforced composite in terms of crack instability. However, due to the complexity of the problem, they were unable to arrive at a general failure criterion and proposed a conservative approximation of the failure load. Recently, Harlow and Phoenix outlined the complexity of the problem3 and have obtained exact expressions4 for the probability of failure of small bundles of fibers under the simplified assumption of stress distribution around fiber fractures. Approximate solutions have also been obtained for larger bundles.5'11 In this paper we examine the failure process of uni- directionally reinforced fiber composites with a transverse slit notch, precisely considering the stress field around the crack tips. Based upon the explicit solution12 of two-dimension al crack problems by the shear-lag method,13'14 we obtain the fiber stress around the crack and fiber stress redistribution after several fibers ahead of the crack tip have failed. The knowledge of the fiber stress distribution is incorporated into the failure sequence analysis. In the present analysis, we assume the elastic behavior of the matrix material. However, discussion based upon the inelastic analysis15 will be reported in a future publication. The primary purpose of the study is to provide some insight into the mechanism of failure of notched composites.