Statistical Analysis of Master Curve Sampling, Screening, and Weighting Methodologies

The master curve methodology is used to define the scatter and temperature dependence of ferritic steel fracture toughness in the ductile-to-brittle transition region, described by a single parameter, the reference temperature, T_o. The primary objectives of this study are to investigate the effect that different processes have on bias and precision of the reference temperature estimation, as well as the effect on the required dataset size. Analyses were performed through Monte Carlo simulations using a synthetic dataset consisting of 17,600 artificial single-edge bend K_Jc values censored by applicable specimen capacity limits. Reference temperature assessments were performed using both multi- and single-temperature analyses, and the effects of temperature selection, data validity weighting factors, and material homogeneity screening processes were evaluated. Multi-temperature analyses were based on a selected initial test temperature, with data sampled from subsequent temperatures based on provisionally calculated T_o values. The obtained reference temperature values are normally distributed with the average value remaining relatively constant regardless of test temperature. Standard deviations of reference temperatures were also relatively constant when evaluating data from test temperatures within ± 50°C (± 90°F) of the final calculated T_o, exhibiting less variability than predicted by the current specification. When sampling data are more than 50°C (90°F) below T_o, however, larger datasets are needed to obtain similar levels of precision. Guidance is provided for the modification of weighting factors to incorporate multiple confidence intervals into the validation procedure. Finally, recommendations are given on the assessment of an anomaly caused by all K_Jc data lying above the median master curve.