Size/Effect Modeling of Weibull Jc Cumulative Distribution Function Based on a Scalling Approach

Abstract

Ever since the 1980s there have been a surge of 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 CDF of the critical value of the J-integral (Jc) under constraint of a small sample size in the transition temperatrure range. Specifically, the Jc experimental data correspond to the CT specimen testing of the reactor pressure-vessel steel 20MnMoNi55 at only two sizes and temperature of 60°C. Thus, a simple approximate scaling algorithm has been developed to tackle the effect of the CT specimen size on the J c CDF for such small sample size. 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 J c -scaling is performed to ensure the approximate overlap of the points that correspond to the CDF values F(Jc = η) = 1 – 1/e ≈ 0.632 for different CT specimen widths (W), which assumes η·W κ = const. Second, the F-scaling is performed to ensure the equality of the slopes of the CDF in the scaled (F·W ξ vs. J c ·W κ ) space. The objective of the sketched approach is to obtain a conservative estimate of J c CDF that encapsulates the CT specimen size.