Procedure for Uncertainty Estimation in Determining the Master Curve Reference Temperature1

Abstract

The master curve reference temperature, T0, characterizes the fracture performance of structural steels in the ductile-to-brittle transition region. For a given material, this reference temperature is estimated via fracture toughness testing. A methodology is presented to compute the standard error of an estimated T0 value from a finite sample of toughness data, in a unified manner for both single temperature and multiple temperature test methods. Using the asymptotic properties of maximum likelihood estimators, closed-form expressions for the standard error of the estimate of T0 are presented for both test methods. This methodology includes statistically rigorous treatment of censored data, which represents an advance over the current ASTM E1921 methodology (“E1921-10, Standard Test Method for Determination of Reference Temperature, T0, for Ferritic Steels in the Transition Range,” ASTM International, West Conshohocken, PA, 2010). Through Monte Carlo simulations of realistic single temperature and multiple temperature test plans, the recommended likelihood-based procedure is shown to provide better statistical performance than the methods in the ASTM E1921 standard.