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

Abstract

A B S T R A C T 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 J C results follow a 3P-W, their equivalent K JC 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 K JC , 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.Keywords ductile-brittle transition; J C to K JC transformation; Weibull function. N O M E N C L A T U R E b = shape parameter or Weibull slope. b J = shape parameter or Weibull slope in J values. b JAp = approximated shape parameter or Weibull slope in J values. b K = shape parameter or Weibull slope in K values. b KAp = approximated shape parameter or Weibull slope in K values. B = specimen thickness B 0 = reference specimen thickness J = J-integral value. J C = J-integral at the point of onset of cleavage fracture. J i = an individual value of a set of J values. J min = threshold parameter or lowest value of J in the population.J 0 = scale parameter of the Weibull distribution in J values (J 0 = J for P = 0.632). K = linear elastic stress intensity factor. K J = an elastic-plastic equivalent stress intensity factor derived from a J value. K JC = an elastic-plastic equivalent stress intensity factor derived from J C value. K min = threshold parameter or lowest value of K in the population. K 0 = scale parameter of the Weibull distribution in K values (K 0 = K for P = 0.632). K 1 = an individual value of stress intensity factor. LRM = linear regression method.

Fracture Toughness of Ferritic Steels in the Ductile-to-Brittle Transition Region

“…An analysis about the relationship between Weibull distributions expressed in terms of J and K was presented in reference [7]. It was shown that if the J C results follow a 3P-W, their equivalent K JC values do not exactly fit a 3P-W function obtained by means of a simple transformation of the three parameters.…”

“…Figure 1 shows the fracture behavior of different materials with temperature, including some that don't have a transition zone. The characterization of fracture resistance of ferritic steels in this region is problematic due to scatter in results, as well as size and temperature dependences [2][3][4][5][6][7][8][9].…”

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

“…Substantial research efforts over the last few decades have developed statistical treatments of cleavage fracture based both on macroscopic approaches and on local approaches . The master curve approach has evolved into a standard procedure in characterizing the temperature dependence of the macroscopic fracture toughness over the DBT regime.…”

“…Integrity assessments based on such approaches for realistic structural details require a simplified and reliable approach to determine these key material parameters for engineering applications. Substantial research efforts over the last few decades have developed statistical treatments of cleavage fracture based both on macroscopic approaches [11][12][13][14][15] and on local approaches. [16][17][18][19] The master curve approach 7,12,14 has evolved into a standard procedure 20 in characterizing the temperature dependence of the macroscopic fracture toughness over the DBT regime.…”

Estimation of the Fracture Toughness Threshold of a Ferritic Steel at the Lower Ductile to Brittle Transition Region

“…The fracture toughness of materials working at the ductile to brittle transition usually shows considerable scatter [1][2][3][4][5][6][7][8] . It is believed that the relative position of the crack tip related to microstructural heterogeneities causes the scatter, this theory is known as the weakest link theory [2][3][4] .…”