ANALYSIS OF SIZE DEPENDENCE OF CERAMIC FIBER AND WHISKER STRENGTH

The strengths of ceramic fibers and whiskers have been observed to inc rease with decreasing fiber diameter and length, Typically, both surfa ce flaws and volume hams exist in ceramic fibers and whiskers, which m akes it impossible to characterize the strength dependence of both the diameter and the length with a single-modal Weibull distribution func tion, Our data also show that the single-modal Weibull distribution is inadequate to characterize the strength of fibers with varying diamet ers even in the case of a constant fiber length, In addition, experime ntal data also show that, for sapphire whiskers whose surface flaws me re removed by chemical polishing, the whisker strength has a much stro nger size dependence on diameter than predicted by the single-modal We ibull function, which indicates that factors other than those characte rized by the Weibull function also play a role in the strength of sapp hire whiskers, In this paper, the factors affecting the strengths of c eramic fibers and whiskers are analyzed in terms of Weibull statistics , fracture mechanics, and ham size density variation with varying fibe r diameters, A three-parameter modified Weibull distribution, which co mbines the above strength-affecting factors, is proposed to characteri ze both the diameter and the length dependence for ceramic fibers and whiskers with or without surface flaws, Characterization of the streng th data of sapphire whiskers and Nicalon SiC fibers with varying diame ters shows the validity of the modified Weibull distribution function.