Statistical modelling of tensile properties of natural fiber yarns considering probability distributions of fiber crimping and effective yarn elastic modulus

Abstract

Unlike synthetic fiber yarns, due to limited fiber length, natural fiber yarns are made of twisted short natural fibers with various crimping status obeying certain probability distribution. Meanwhile, variations from fiber tensile properties and number of fibers in a yarn also result in scattering of mechanical properties of natural fiber yarns. An analytical model is proposed based on statistic theory to characterize the stochastic tensile properties of natural fiber yarns by defining crimp strain of fibers in a yarn and effective elastic modulus of yarns as random variables. The model is demonstrated on jute fiber yarns. Beta and normal probability distribution functions are selected to describe the statistical distributions of the crimp strain and effective elastic modulus, respectively. Parameters of the model are obtained from tensile testing results of jute yarns through inverse approach. The proposed model can provide accurate prediction bounds for tensile tests of jute yarns. Moreover, the proposed model is extended to predict the tensile response with progressive failure process of unidirectional fabric.