Weibull parameters obtained from dependence of fiber strength on fiber length and area

Abstract

AbstractWeibull strength parameters of ceramic fibers can be inferred from variations in strength with fiber diameter or gauge length. The goal of this article is to provide a critical assessment of the efficacy of these methods. The issues are addressed using theorems in regression analysis and uncertainty propagation as well as Monte Carlo simulations. The results show that, when Weibull moduli are obtained from strength variations with fiber area, inordinately large sample sizes (>1000) are required to achieve reliable results. In contrast, Weibull moduli can be accurately estimated from the dependence of average fiber strength on gauge length for a modest sample size at each of two gauge lengths, provided the gauge length range is sufficiently large. The dependence of strengths of bundles containing many (ca. 500) fibers on gauge length yields yet more reliable results. The results are used to assess the fidelity of Weibull moduli obtained from these methods and provide guidance for preferred test methods.