Distribution function of fiber length in thermoplastic composites

Due to the strong correlation with material properties, fiber length distribution in polymer composites has been extensively investigated. The distribution exhibits steep increase until a peak followed by a long tail decay, which has been analyzed in terms of Weibull distribution. However, interpretation of the stochastic process behind Weibull distribution is not trivial, particularly for the shape parameter. In this study, a simple distribution function is proposed based on the two Poisson processes at the breakage of loaded fibers; one of them is a series of memoryless events for the fiber breakage with a characteristic length λa, and the other one is another series of memoryless events blocking the adjacent breaks with an interval length of λb. The proposed function was examined against literature data for nylon-6 composites containing glass fibers and carbon fibers. For the glass fiber composites for which the processing conditions were varied at the same fiber content, the proposed function captures the experimental data as well as the Weibull distribution. The obtained λa shows a good correlation with the mechanical properties of the composites to hint the relation to the processing conditions. For the carbon fiber composites for which the fiber content was varied, the proposed distribution better captures the long tail decay than the Weibull distribution whereas the Weibull distribution better captures the data around the sharp peak for high fiber contents than the proposed distribution. It so appears that the proposed function provides a straightforward analysis of the fiber length distribution in polymer composites, in particular for the long tail decay that is of importance for the material properties.