Load-sharing and Monte Carlo models of defects in a bundle of fibres

Abstract

Two methods for modelling and random simulation of progressive deformation and breaks in a bundle of parallel fibres are proposed. First, a stochastic load-sharing reliability model of a parallel system and of its resistance against a stress is utilized. The method of its statistical analysis is presented, too. In order to improve certain limitations of such model, a complementary method based on the Monte Carlo simulation is introduced. The bundle of fibres is modelled as a grid consisting of a set of nodes and connecting arcs. The deformation and breaks are caused by an external load stretching the grid. The first objective is to find an optimal, stabilized, states of the grid corresponding to each load level. Optimal configuration is found with the help of Markov Chain Monte Carlo (MCMC) procedures. In order to model the breaking process, the load is increased sequentially. It is shown that the model is applicable also to other structures, namely to the plain weave fabric and its defects simulation. The results with bundle of fibres are compared with real stress–strain curves. The parameters for simulation were selected in such a way that obtained stress–strain curve corresponds to a real experiment with carbon fibres.