Application non-Gaussian probability distributions to describe the properties of high-strength fibers

Abstract

This article deals with the model for applying the 3-parameter Weibull distribution to describe the tensile strength of a bundle of parallel fibers (complex thread). This is important because high-strength fibers are usually produced in the form of strands rather than single fibers. For modelling the fiber bundle, fibers with a deformation diagram similar to linear were selected: carbon, glass and aramid (Kevlar-49). The test data of single carbon and glass fibers were obtained by F. Mesquita and colleagues, and the authors’ data obtained from tests of single Kevlar-49 fibers were used to model the aramid fiber bundle. The test data of single fibers of different types were divided into equal ranges of destructive stress and the number of fibers whose strength fell within a given range of values was calculated. The use of a 2-parameter Weibull distribution to predict the strength of reinforced plastics suggests the possibility of accumulation of breaks from the very beginning of deformation, which further leads to the prediction of the appearance of a cluster of fiber breaks of infinite size in the composite under any load, which contradicts observations. It is shown that the 3-parameter distribution better describes the results obtained, and does not require the assumption of fiber destruction at zero voltage. It was found that in the case of glass fibers, destruction begins almost from the start of loading, and the two-parameter Weibull distribution describes their destruction well.