Markov process model for the strength and reliability of unidirectional fiber-reinforced ceramic matrix composites

A stochastic model for predicting the strength and reliability of a unidirectional fiber-reinforced ceramic matrix composite is proposed, based on the Markov process model. In the proposed model, stress distributions in the composite follow the Curtin's assumptions, of which validity is examined by using the FEM model consisting of fiber, matrix and interface elements. It is further assumed that a state of damage in the composite is evolved with each fiber breakage. Then, the damage evolution process is governed by simultaneous first-order differential equations. When the Weibull distribution is used as a strength distribution of the fiber, each state probability is analytically obtained as a function of stress. The expected value and variance of the composite stress were estimated from the state probabilities. Additionally the maximum stress of the expected value, i.e. the strength, was predicted together with the coefficient of variation. The results showed that, even if broken fibers are imperfectly recovered in stress on the fiber-axis away from the breakage points, the composite exhibits a higher strength and reliability than that of bundle structure. Finally, it is concluded that stress recovery in broken fibers is a significant mechanism to increase the strength and reliability of the composite.