doi: 10.1111/j.1460-2695.2010.01533.x Comparison of 3P-Weibull parameters based on J C and K J C values C. LARRAINZAR 1 , C. BEREJNOI 2 and J.E. PEREZ IPI ˜ NA 3 1 UN Comahue - U.N.Comahue/ANPCyT, Calle Buenos Aires N ◦ 1400, Neuqu´ en 8300, Argentina, 2 Facultad de Ingenier´ ıa, U.N.Salta, Avda. Bolivia N ◦ 5150, Salta 4400, Argentina, 3 GMF/LPM, U.N.Comahue/CONICET, Calle Buenos Aires N ◦ 1400, Neuqu´ en 8300, Argentina Received in final form 13 September 2010 ABSTRACT The characterization of fracture toughness of ferritic steels in the ductile-to-brittle tran- sition 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. NOMENCLATURE 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. Correspondence: C. Berejnoi. E-mail: berejnoi@unsa.edu.ar 408 c  2010 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 34, 408–422 Fatigue & Fracture of Engineering Materials & Structures