A strength reliability model of fiber-reinforced ceramic matrix composites including individual constituent damages given by Markov process

A new strength reliability model of fiber-reinforced ceramic matrix composites is proposed, in which both the processes of multiple matrix cracks and fiber breaks are taken into account, based on Markov process model. It is assumed that damages due to the cracks and breaks accumulate discretely and independently in the composite in accordance with change in transition probabilities with an increase in matrix and fiber stresses, respectively. Both the processes were finally described by simultaneous ordinary different equations, and the probabilities being in states were solved numerically. The results show that, first, the proposed reliability model can predict means and variances in fiber and matrix stresses, with an increase in strain. Next, this model predicts well strength data, obtained experimentally from various ceramic matrix composites. In addition, when the composite stress is subject to the mixed rule, the mean and variance in the composite stress can be obtained from the first-order second-moment method. The analyzed stress-strain curve of the composite can be simulated well, as been in actual behavior. According to this modeling, combination of large scatter matrix strength to small scatter fiber strength, brings an increase in strength of the composites.