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

摘要

The strength and reliability analysis model for unidirectional fiber-reinforced ceramic matrix composites is proposed, in order to investigate theoretically if this material can be applied for practical use from the viewpoint of materials reliability engineering. The 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. Then, the 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 in the stress-strain relation of the composite are estimated from the state probabilities. Also the maximum stress of the expected value, i.e. the strength, is predicted together with the coefficient of variation. It is proved that, if broken fibers are recovered in stress along the fiber-axis away from the breakage points due to sliding force, the composite exhibits a higher strength and reliability than that of a bundle structure. Finally, it is concluded that ceramic matrix composites are theoretically a highly-reliable material.