Theory of Mechanical Properties of Ceramic‐Matrix Composites

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Abstract
A theory is presented to predict the pullout work and ultimate tensile strength of ceramic‐matrix composite (CMC) materials tested under uniaxial tension as functions of the underlying material properties. By assuming that the fibers fracture independently and that global load redistribution occurs upon fiber fracture, the successive fragmentation of each fiber in the multifiber composite becomes identical to that of a single fiber embedded in a homogeneous large‐failure‐strain matrix, which has recently been solved exactly by the present author. From single‐fiber fragmentation, the multifiber composite distribution of pullout lengths, work of pullout, and ultimate tensile strength are easily obtained. The trends in these composite properties as a function of the statistical fiber strength, the fiber radius and fill fraction, and the sliding resistance τ between the fibers and the matrix easily emerge from this approach. All these properties are proportional to a characteristic gauge length δc and/or the associated characteristic stress σ, with proportionality constants depending only very weakly on the fiber Weibull modulus: the pullout lengths scale with δc, the work of pullout scales with σcδc, and the ultimate strength scales with σc. The key length δc is the generalization of the “critical length,” defined by Kelly for single‐strength fibers, to fibers with a statistical distribution of strengths. The theory also provides an interpretation of fracture‐mirror measurements of pulled‐out fiber strengths so that the in situ key strength σc and Weibull modulus of the fibers can be determined directly. Comparisons of the theoretical predictions of the ultimate tensile strength to literature data on Nicalon/lithium aluminum silicate (LAS) composites generally show good agreement.