Markov Process Model for the Strength and Reliability of Unidirectional Fiber-Reinforced Ceramic Matrix Composites
Koichi GODA
Abstract:A stochastic model for predicting the strength and reliability of a unidirectional fiber-reinforced ceramic matrix composite is proposed, in order to find theoretically a reliability system in strength of the composite, which is composed of the 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 the FEM analysis. The proposed model is based on the Markov process, in which it is assumed that a state of damage in the composite is developed with each fiber breakage. 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 in the composite stress are estimated from the state probabilities. Additionally 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 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 determine the strength and reliability of the composite. Key Words:Brittle Materials, Ceramic Matrix Composites, Fiber Reinforcement, Interface, Strength and Reliability, Markov Process, Weibull Distribution, Finite Element Method.