A Statistical Approach to the Prediction of Brittle Fracture in Heat-Affected Zones of A707 Steel Welds

Abstract This article presents a statistical approach to the prediction of the variations in fracture toughness of the heat-affected zones in A707 steel welds. Fractographic analyses were first used to determine the inclusion size distributions from the ductile fracture regions that precede the onset of cleavage fracture. The inclusion size distributions were shown to be well characterized by the three-parameter Weibull distribution. Based on the inclusion size distribution, a modified version of the model by Lin, Evans, and Ritchie was used to estimate the statistical variability of the crack-tip opening displacement (fracture toughness). The modification involves the use of a polynomial function in the determination of the dimensionless stress parameter, in the Hutchinson-Rice-Rasengren (HRR) field solution. This enables a fully analytical solution to be obtained for the critical driving forces associated with specified failure/survival probabilities under elastic-plastic fracture conditions. The comparison showed that the modified model prediction was in good agreement with measured crack-tip opening displacement (fracture toughness) data. Finally, the implications of the results are discussed for the probabilistic design of damage tolerant structures in which cleavage fracture can occur, following an initial stage of ductile tearing by microvoid coalescence.