Analysis of Size Dependence of Ceramic Fiber and Whisker Strength

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Abstract
The strengths of ceramic fibers and whiskers have been observed to increase with decreasing fiber diameter and length. Typically, both surface flaws and volume flaws exist in ceramic fibers and whiskers, which makes it impossible to characterize the strength dependence of both the diameter and the length with a single‐modal Weibull distribution function. Our data also show that the single‐modal Weibull distribution is inadequate to characterize the strength of fibers with varying diameters even in the case of a constant fiber length. In addition, experimental data also show that, for sapphire whiskers whose surface flaws were removed by chemical polishing, the whisker strength has a much stronger size dependence on diameter than predicted by the single‐modal Weibull function, which indicates that factors other than those characterized by the Weibull function also play a role in the strength of sapphire whiskers. In this paper, the factors affecting the strengths of ceramic fibers and whiskers are analyzed in terms of Weibull statistics, fracture mechanics, and flaw size density variation with varying fiber diameters. A three‐parameter modified Weibull distribution, which combines the above strength‐affecting factors, is proposed to characterize both the diameter and the length dependence for ceramic fibers and whiskers with or without surface flaws. Characterization of the strength data of sapphire whiskers and Nicalon SiC fibers with varying diameters shows the validity of the modified Weibull distribution function.

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