Modeling the tensile strains of non-uniform fibers

The maximum strain experienced by the thinnest segment of a non-uniform fiber governs fiber breakage, yet this maximum strain can not be obtained from a normal single fiber test. Only the average strain of the whole fiber specimen can be obtained from a normal single fiber tensile test. This study has examined the relationship between the average strain, the maximum strain and the degree of fiber non-uniformity, expressed in coefficient of variation (CV) of fiber diameters along fiber length. The tensile strain of irregular fibers has been simulated using the finite element method (FEM). Using this method, average and maximum tensile strains of non-uniform fibers were calculated. The results indicate that for irregular fibers such as wool, there is an exponential relationship (i.e. ε_ave/ε_max = ae ^{-v CV}) between the ratio of average breaking strain and maximum breaking strain (ε_ave/ε_max) and the along-fiber diameter variation (CV). The strain ratio decreases with the increase of the along-fiber diameter variation.