A K₀‐based calibration procedure for the Weibull stress cleavage model

Abstract

This paper presents a simplified calibration procedure for the microscopic Weibull stress model to estimate the cumulative probability of cleavage fracture for ferritic steels. The proposed method requires two discrete values of the macroscopic Weibull scale parameter (K0) in contrast to the two sets of statistically significant fracture toughness data mandated in previous calibration schemes. The proposed approach predicates on the fundamental assumption that the macroscopic toughness, for specimens dominated by cleavage mechanisms, follow the three‐parameter Weibull model outlined in the testing standards. The calibration procedure thus generates two sets of fictitious toughness data corresponding to two sets of specimens with marked differences in crack‐front constraints. The calibrated Weibull parameters agree closely with the calibration results based on the conventional approach for the Euro steels. The proposed calibration also leads to an improved method to determine a limiting load level, beyond which extensive plastic deformation propagates in the specimen.

Effect of experimental sample size on local Weibull assessment of cleavage fracture for steel

“…A large Weibull modulus m increases the constraint correction function g ( M ) based on Eq. , as also confirmed by previous researchers, and thereby leads to higher corrected fracture toughness values [Eq. ].…”

“…Table indicates that neither of the two datasets at −110 °C contains any K Jc value with M < 10. The calibration using the full data sets leads to a calibrated value of m true = 17, similar to the previous calibration efforts …”

“…The confidence level P m thus follows: where N m ,true denotes the number of subset pairs that yield a calibrated m within the specified confidence interval m ∈ [ m true − 4, m true + 4]. Qian and Chen have proposed a simplified K 0 ‐based calibration to determine the Weibull modulus m and demonstrated the relatively strong effect on the calibrated m value by a deviation of more than 5% in the K 0 value [Eq. ].…”

“…Wasiluk et al 21 have confirmed the temperature independence of the Weibull modulus m based on the 'Euro' fracture toughness datasets and reported a calibrated value of m = 20. Qian and Chen 43 and Qian et al 44 have calibrated the Weibull modulus m using various sets of 'Euro' fracture toughness datasets at three different temperatures. The maximum deviation of the calibrated m values from the calibrated m = 20 by Wasiluk et al 21 equals 3.…”

“…The calibration using the full data sets leads to a calibrated value of m true = 17, similar to the previous calibration efforts. 43,44 Figure 8a displays the mean value μ m of the calibrated Weibull modulus m at À 110 o C. The mean value μ m decreases with a decreasing subset size n. Figure 8b illustrates the increasing standard deviations S m of the calibrated Weibull modulus m with respect to the subset size n which ranges from 6 to 49. Figure 8c shows the confidence level for the calibrated Weibull modulus, P m , based on a specified Weibull modulus confidence interval from 13 to 21.…”