Weibull Analysis of the Strength of Carbon Fibers Using Linear and Power Law Models for the Length Effect

Abstract

The single-filament test measurements for strength of carbon fibers obtained by Bader and Priest [5] are analyzed using a broader class of Weibull models with the scale parameter assumed to be a function of fiber gauge length. Two specific models are proposed for the fiber gauge length effect on tensile strength: The power law model and a linear model. The methods of maximum likelihood estimation and Weibull plots provide tools for the parameter estimation and assessment of the fitted models. In particular, the models provide excellent prediction of the fiber strength distributions at longer gauge lengths not tested, but illustrate that extrapolation to very short gauge lengths yield larger predicted fiber strengths than those actually observed experimentally, and extrapolation to very long gauge lengths yield smaller predicted fiber strength than observed experimentally. Analysis of the Bader-Priest data using the proposed models supports the observed "end effects" (or "clamp effects) for short gauge lengths studied initially by Phoenix and Sexsmith [3] and reported also by Stoner, Edie and Durham [4].