Combined Effect of Flaw Distribution and Diameter Variation on the Statistics of Glass Fiber Strength

This paper examines the combined effects of flaw-severity distribution and fiber diameter distribution on the fracture statistics of glass fibers. The approach adopted is to assume specific forms (Gaussian and Weibull) for the diameter distribution, a Weibull distribution for the true strength, and then to calculate the measured strength distributions. Exact analytical results are obtained in the cases of flawless fibers, uniform size flaws, and when true strength and fiber diameter are Weibull distributed. Approximate analytical expressions have been derived for the general case. A procedure is described to obtain the parameters of the true strength distribution from the knowledge of measured strength distribution and the coefficient of variation of fiber diameters. Implications of these results for the fracture statistics of high-strength glass fibers are discussed.