Simplified Method for Adjusting the Shape and Characteristic Strength Parameters of the Weibull Strength Distribution of Graphite Materials

Abstract

Abstract The 2021 version of the ASME Boiler and Pressure Vessel Code Section III, Division 5, Paragraph HHA-3217 utilizes a 3-parameter Weibull distribution to characterize the strength of graphite materials. Subparagraph (g)(2) thereof requires that the designer modify the threshold parameter (S0). However, no guidance is provided to update the other parameters of the Weibull distribution following an update of S0 (i.e., Sc, the characteristic strength parameter, and m, the Weibull modulus or also referred to as the shape parameter). This paper illustrates why failing to update the other parameters results in an unrealistic and overly conservative distribution. This paper provides a simple method to update the shape and characteristic strength parameters of the Weibull distribution. This method relies on a straightforward, algebraic formulation that is easy to implement and does not require access to the underlying experimental datasets. The performance of the method is evaluated and shown to compare favorably with maximum likelihood estimate (MLE) optimization using both simulated and experimental data. Differences between methods tend to be on the order of a few percent and are negligible for small changes to S0. Moreover, any deviations are further shown to be conservative for the purposes of stress analysis of graphite.