Significance of longitudinal and transversal size effects on the statistics of fibre strength

This paper examines the combined effects of regions of flaw distribution and variation in fibre dimensions on the strength of fibres. A scheme for the simultaneous interpretation of the effect of flaws distributed on the surface and in the volume, and the effects of longitudinal and transversal size effects is presented. A competing risk model, wherein the possible failure modes simultaneously generate random strengths with failure occurring when the lowest is realized, is used within a Monte-Carlo framework. The model assumes that flaws can be regarded as mode I cracks and that the strength of fibres follows a Weibull distribution function. The proposed scheme is used to investigate the effect of average flaw size, flaw density and fibre dimensions on fibre strength. Assuming that the weakest path is always followed, it is shown that surface flaws dominate at small fibre sizes and are replaced by volume flaw effects as size increases, resulting in a change of slope in a log(strength)—log(size) plot. It is emphasized that the region of flaw distribution as well as fibre diameter variations are of significant importance in the study of size effects. Implications of these results are discussed, and predictions are compared with some known results.