Markov process model for the strength and reliability of ceramic matrix composites reinforced with continuous fibers

摘要

The previously proposed stochastic model for predicting the strength and reliability of a fiber-reinforced ceramic matrix composite is improved. The present model is applicable for the case that the stress of a broken fiber is perfectly recovered along the fiber-axis, and its recovery length is increased as the fiber stress increases. The analysis is based on the Markov process, in which it is assumed that a state of damage in the composite evolves with each fiber breakage. If the Weibull distribution is used as a strength distribution of the fiber, each state probability is analytically obtained as a function of fiber stress. The expected value and variance of the composite's nominal stress are estimated from the state probabilities, but these are available only for a unit composite with an increasing stress recovery length. It was then verified that the nominal stress of the unit composite follows a Gaussian distribution. The whole composite structure is given as the chain-of-bundles model, and the composite strength distribution is finally predicted from a minimum value distribution.