The effect of diameter variation along a fiber on the determination of fiber strengths and the parameters of the distribution

The effect of variable fiber diameter among the fibers in a bundle, and along the length of individual fibers, on the determination of individual fiber strength values and on the estimates of the parameters of the distribution of fiber strengths was investigated using Monte Carlo simulations. In this analysis it is assumed that the average fiber diameters in a bundle are distributed according to a known distribution (e.g. normal), that the diameter of a fiber varies randomly along its length, and that fiber strengths are distributed according to a two-parameter Weibull distribution. It is shown that the magnitude of the error that is incurred in the determination of a fiber strength, when the fiber diameter is measured at a location that doesn't coincide with the fracture plane, increases with the magnitude of the variability of diameter along the fiber length. Similarly, the error in the determination of the Weibull modulus, for example, increases with the variability of average fiber diameters in a bundle when fiber strengths are calculated using the average of the cross-sectional area of the fibers in the bundle. The implications of these findings on the development of a standardized test method for the tensile evaluation of single fibers are discussed.