Comparison of 3P-Weibull parameters based on JC and KJC values

Abstract

The characterization of fracture toughness of ferritic steels in the ductile-to-brittle transition is problematic due to the scatter of test results. Several proposals using Weibull statistics have been made, some of them in terms of J and others in terms of K; some authors employ a two parameters Weibull function (2P-W), while others use a three parameters function (3P-W), although ASTM E1921 uses 3P-W in terms of K with two fixed parameters to determine the Reference Temperature To. An analysis about the relationship between Weibull distributions expressed in terms of J and K is presented in this paper. It is shown that if the JC results follow a 3P-W, their equivalent KJC values do not exactly fit a 3P-W function obtained by means of a simple transformation of the three parameters. Nevertheless, an approximated 3P-W function in K terms is proposed in this work. It fits very well with the transformed values and their parameters are related to the ones expressed in J terms. In case the experimental results follow a 3P-W in KJC, a similar analysis can be performed. For the particular situation of a 2P-W, there is an exact equivalence between the distributions in terms of J and K, being the Weibull slope in terms of K twice the slope in terms of J.