Application of Markov process to chain-of-bundles probability model and lifetime distribution analysis for fibrous composites

摘要

Markov process was applied to the chain-of-bundles probability model which is often used for the axial strength analysis of a unidirectional fibrous composite. It was assumed to the process that a group consisting of fiber breakage points, theso-called cluster, evolves in time intermittently subject to two kinds of local load shares around a cluster, and that the composite fractures if the cluster achieves a critical size. Then, the two kinds of cluster evolution processes are governed bysimultaneous first-order differential equations. A time-dependent Weibull distribution was used as a lifetime distribution function of the fiber, and the cumulative probability solutions for rupture-time of the critical cluster were analytically obtained. The results showed that the larger clusters reduce the width of distribution and form a master-like distribution curve, similarly to the results predicted from a conventional numerical method, the so-called recursion analysis technique. The proposedMarkov process analyses were in a relatively good agreement with the distribution curves predicted by the conventional one. In addition, the effect of ineffective length which is gradually increased in time due to the shear stress relaxation of the matrix in metal matrix composites, was taken into the analysis.