STRAIN AND HYSTERESIS BY STOCHASTIC MATRIX CRACKING IN CERAMIC-MATRIXCOMPOSITES

A theory is presented to predict the stress/strain relations and unloa d/reload hysteresis behavior during the evolution of multiple matrix c racking in unidirectional fiber reinforced ceramic matrix composites ( CMCs). The theory is based on the similarity between multiple matrix c racking and fiber fragmentation in a single fiber composite, and deter mines the crack and strain evolution as a function of the statistical distribution of initial flaws in the material, the interfacial sliding resistance tau, and the thermal residual stresses in the composite. T he model properly includes matrix fragments of all lengths, from lengt hs smaller than the current slip length delta(sigma) to larger than 2 delta(sigma), at applied stress sigma, and accounts for their respecti ve and differing contributions to the overall strain and hysteresis be havior of the composite. The procedure by which experimental stress/st rain and hysteresis data can be interpreted to derive values for the i nterfacial shear stress, thermal stresses, and intrinsic matrix flaw d istribution is discussed. The actual physical crack spacing needs only to be determined at one load level, such as post-fracture, which grea tly simplifies the data acquisition and analysis. Several detailed exa mples are presented, and the results compared with a widely-used appro ach in which the crack spacing is assumed constant and equal to the av erage spacing obtained directly from experiment. The discrepancy betwe en the previous and present theories is manifest in an incorrect estim ate for the interfacial sliding, but only by approximately 10%. The ef fect of changing temperature, and hence residual stresses, without cha nging either matrix flaws or interfacial sliding resistance, is studie d. (C) 1997 Elsevier Science Ltd.