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.
A B S T R A C TThe crack length measurements of both the original crack length and the stable crack extension are requested by several fracture toughness test methods, wherein which high accuracy measurement instruments are demanded. Low magnification optical microscopes as well as travelling-stage microscopes are used to achieve the accuracy requirements, although many times these time-consuming techniques present some experimental difficulties, especially when a great number of specimens have to be measured. A methodology to measure crack length from high-resolution images acquired by means of a desktop flatbed-scanner is presented in this paper. The acquired images are analysed by means of software that allows obtaining the crack length. Several aspects were studied to demonstrate the suitability of the method: the optical resolution, the depth of field and the effects of possible optical aberrations. Finally, an uncertainty balance was performed to demonstrate that the methodology is able to reach the necessary accuracy required by the fracture toughness test methods.
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