Theory of Mechanical Properties of Ceramic‐Matrix Composites

TLDR

The key length δc generalizes Kelly’s critical length to fibers with a statistical strength distribution. The study presents a theory to predict pullout work and ultimate tensile strength of ceramic‑matrix composites under uniaxial tension from material properties. Assuming independent fiber fracture and load redistribution, the multifiber composite reduces to a single fiber in a homogeneous matrix, whose exact fragmentation solution yields pullout length, work, and ultimate strength distributions. The theory predicts that pullout length, work, and ultimate strength scale with δc and σc, shows weak dependence on Weibull modulus, interprets fracture‑mirror data to extract σc and Weibull modulus, and agrees well with Nicalon/LAS composite data.

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 δ c and/or the associated characteristic stress σ, with proportionality constants depending only very weakly on the fiber Weibull modulus: the pullout lengths scale with δ c , the work of pullout scales with σ c δ c , and the ultimate strength scales with σ c . The key length δ c 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 σ c 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.