Prediction of cleavage failure probabilities using the Weibull stress

Abstract

In this work, the use of the Weibull stress as a measure of the failure probability of a cracked body is examined. Closed form expressions for the Weibull stress are presented for linear elastic and power law materials. These expressions allow Weibull stress values and failure probabilities to be estimated without the need for finite element analyses and provide insight into the use of the Weibull stress as a parameter for the prediction of cleavage failure of cracked bodies. Application of the Weibull stress to the prediction of transition region and upper shelf cleavage failure probabilities of ferritic steel welds is also discussed. The effect of ductile tearing, described by a Gurson-type material model, is examined. Numerical analyses of compact tension fracture tests are carried out and used to interpret experimental fracture toughness data for ferritic steel welds. A comparison between the finite element results and the experimental data indicates that the scatter in the cleavage fracture toughness values in the transition region are quite well captured by the Weibull stress. However, cleavage failure probabilities close to the upper shelf using the two parameter Weibull model are considerably higher than those observed in practice. A number of reasons for this discrepancy and suggestions to improve the predictions are proposed.