Uni- and bimodal Weibull distribution for analyzing the tensile strength of Diss fibers

The present work considered several statistical distribution functions with the aim to critically analyze the strength data of natural Diss fibers. Besides the Weibull two-parameter distributions, three-parameter and bimodal Weibull were used. Kolmogorov–Smirnov, Anderson–Darling and chi-square goodness-of-fit test were used to judge how accurate the theoretical Weibull probability density function (PDF) fits with tensile strength data.

Tensile test results indicated that the fibers have good tensile strength and Young’s modulus. However, their fracture strength exhibits high scatters due to the presence of defects within the fiber and/or on the fiber surface. Microscopic observation revealed that the rupture of the fibers is governed by two types of defects, the rough surface of the fiber formed by several spines and the internal defects such as the defects of connection between fibrils.

The statistical analysis of variability in strength showed that the results of the shape and scale parameters calculated using bimodal Weibull distribution give larger values compared to those using the single Weibull distribution. Also, the strength data points fit well to the bimodal Weibull PDF curve. All three goodness-of-fit tests indicated also that the bimodal Weibull model gives a more accurate prediction of data strength compared to the unimodal Weibull model.