Markov process analysis for the strength of ceramic matrix composites reinforced with continuous fibers

A stochastic model for predicting the strength and reliability of unidirectional fiber-reinforced ceramic matrix composites is proposed, in order to find theoretically statistical properties in strength of the composites, composed of constituents with large variations in strength. In the proposed model, mechanical behaviors of the composites follows the Curtin's assumptions, of which validity was examined by a FEM analysis. The proposed model is based on a Markov process, in which it is assumed that a damage state in the composite is developed with each fiber breakage. When the Weibull distribution is used as a strength distribution of the fiber, the probability of being in each state is analytically solved as a function of stress. The expected value and variance in the composite stress were then estimated from the probabilities of being in states. Furthermore, the maximum stress of the expected value, i.e. the strength, is predicted together with the coefficient of variation. The results showed that, even if broken fibers are imperfectly recovered in stress along the fiber-axis from the breakage points, the composite exhibits a higher strength and reliability than that of a dry bundle. Finally, it is concluded that stress recovery in broken fibers is a significant mechanism to determine the strength and reliability of the composites.