Modeling brittle and tough stress–strain behavior in unidirectional ceramic matrix composites

Abstract

A new simple model for predicting the uniaxial stress–strain behavior of a unidirectional ceramic matrix composite, including stochastic matrix crack evolution, stochastic fiber damage and ultimate failure, is presented. The model demonstrates an important transition in composite behavior. “Brittle” (low failure strain) behavior occurs when the matrix cracking stresses are sufficiently high; the composite fails during the matrix cracking regime of deformation and at a strain that is controlled by the matrix flaw population and elastic properties. “Tough” (high failure strain) behavior occurs when the matrix cracking stresses are lower; matrix cracking is completed prior to failure and the failure strain of the composite is controlled by the fibers. In both cases, the failure strength is fiber-controlled. The model is applied to study SiC/SiC 500-fiber minicomposite deformation, using data recently obtained by Lissart and Lamon on two material types, “B” and “C”. Parameters for the matrix flaw population are used to fit the experimental stress–strain data but the failure is controlled by the measured fiber strength statistics. Excellent agreement is found for the “C” materials, which are in the transition regime between the brittle and tough limits and variations in fiber strength are postulated to be responsible for the wide range of behaviors found in the “B” materials. The fitted matrix flaw parameters are then used to predict the fiber/matrix interfacial sliding resistance and the values obtained are in excellent agreement with independent values determined from both unload/reload hysteresis loops and fiber pullout lengths. The new model provides a useful tool for understanding the interplay matrix and fiber flaw distributions and the overall dependence of stress–strain behavior on all the underlying constituent material properties.