A scaling approach to size effect modeling of Jc CDF for 20MnMoNi55 reactor steel in transition temperature region

Abstract

Ever since the 1980s there is a sustained interest in the size effect, as one of the most pronounced consequences of fracture mechanics. In the present study, the investigation of the size effect is focused on estimation of the Weibull cumulative distribution function (CDF) of the critical value of the J-integral (Jc) in the transition temperature region under constraint of a small statistical sample size. Specifically, the Jc experimental data correspond to the C(T) specimen testing of the reactor pressure-vessel steel 20MnMoNi55 at only two geometrically-similar sizes. Thus, a simple approximate scaling algorithm has been developed to tackle the effect of the C(T) specimen size on the Jc CDF under these circumstances. Due to the specific form of the two-parameter Weibull CDF, F(Jc|β,η), the scaling procedure is applied according to a two-step scheme. First, the Jc-scaling is performed to ensure the approximate overlap of the points that correspond to the CDF value F(Jc = η) = 1 − 1/e ≈ 0.632 for different C(T) specimen widths (W), which assumes η·Wκ = const. Second, the F-scaling is performed to ensure the equality of the slopes of the CDF in the scaled (F·Wξ vs. Jc·Wκ) space. The objective of the sketched approach is to obtain a size-dependent Jc CDF that encapsulates a reasonably conservative data extrapolation.