Influence of Individual Specimens, Estimation Accuracy, and Round-off Errors on the Master Curve Reference Temperature

Abstract Fracture toughness of ferritic steels in the ductile-to-brittle transition region can be probabilistically described using the Master Curve approach standardized as ASTM E1921, Standard Test Method for Determination of Reference Temperature, T0, for Ferritic Steels in the Transition Range. The Master Curve reference temperature, T0, is a point estimate based on direct fracture toughness testing results and can be used to generate lower bound fracture toughness values to be used in structural integrity assessments. Understanding the factors affecting the accuracy and variability of the T0 estimation is crucial to comprehensively quantifying uncertainty in the T0-based lower bound fracture toughness. In this work, simulated data were used to investigate the influence of individual specimens, which can exhibit vastly different fracture toughness levels, on the T0 estimate. This was quantified with a simple novel leave-one-out statistic—DFT0. The effect of rounding errors in the ASTM E1921 equations, data set size, and test temperatures on the T0 estimation accuracy were also assessed. It was found that high fracture toughness specimens shift the T0 to lower values with considerably larger magnitude than the upward shifts caused by correspondingly low fracture toughness specimens. Specimens tested at lower temperatures tend to have stronger influence on T0 than those tested at higher temperatures. The average DFT0 values rarely exceeded 4°C in single-temperature datasets. The rounding errors in ASTM E1921 introduce a positive bias of around 0.2°C. The root mean square error of the reference temperature estimates can be reduced by increasing data set size, temperature, or both.