Strain and hysteresis by stochastic matrix cracking in ceramic matrix composites

Abstract

A theory is presented to predict the stress/strain relations and unload/reload hysteresis behavior during the evolution of multiple matrix cracking in unidirectional fiber reinforced ceramic matrix composites (CMCs). The theory is based on the similarity between multiple matrix cracking and fiber fragmentation in a single fiber composite, and determines the crack and strain evolution as a function of the statistical distribution of initial flaws in the material, the interfacial sliding resistance τ, and the thermal residual stresses in the composite. The model properly includes matrix fragments of all lengths, from lengths smaller than the current slip length δ(σ) to larger than 2δ(σ), at applied stress σ, and accounts for their respective and differing contributions to the overall strain and hysteresis behavior of the composite. The procedure by which experimental stress/strain and hysteresis data can be interpreted to derive values for the interfacial shear stress, thermal stresses, and intrinsic matrix flaw distribution is discussed. The actual physical crack spacing needs only to be determined at one load level, such as post-fracture, which greatly simplifies the data acquisition and analysis. Several detailed examples are presented, and the results compared with a widely-used approach in which the crack spacing is assumed constant and equal to the average spacing obtained directly from experiment. The discrepancy between the previous and present theories is manifest in an incorrect estimate for the interfacial sliding, but only by approximately 10%. The effect of changing temperature, and hence residual stresses, without changing either matrix flaws or interfacial sliding resistance, is studied.