Mechanical Engineering Faculty Research


Analysis of Material Inhomogeneity in the European Round Robin Fracture Toughness Data Set

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The European fracture toughness dataset was developed by ten European laboratories in order to provide an experimental data base sufficiently large to study specimen size and temperature effects on cleavage fracture toughness in the ductile-to-brittle transition regime. The initial Master Curve analysis of this data set was presented by Wallin [Eng. Fract. Mech., Vol. 69, 2002, pp. 451–481. showing a range of T0 reference values ranging from −80°C to −110°C, with −90°C as an average and a standard deviation of 6.7°C. The initial round robin data set included all scaled C(T) specimens ranging from 1/2T to 4T in scale, but more recently additional specimens have been tested using this material including deep and shallow crack bend specimens (SE(B)) [Link, R. E., unpublished], precracked Charpy size specimens [Wallin, K., Fracture, Fatigue, and Residual stress—PVP, Vol. 393, J. Pan, Ed., ASME, New York (1999)], and even some biaxially loaded cruciform specimens [Lidbury, D. P. G., Fatigue Fract. Eng. Mater. Struct., Vol. 29, 2006, pp. 829–849]. These specimens are being analyzed to develop and test constraint analysis tools essential in the application of the Master Curve method to structural applications in the commercial nuclear power industry. The present authors have also developed fracture toughness data on this material over a range of loading rates to investigate the sensitivity of the calibrated Weibull coefficients used in the constraint correction models of Gao and Dodds [Eng. Fract. Mech., Vol., 68, 2001, pp. 263–284] to material loading rates in typical nuclear pressure vessel steels. Clear material inhomogeneity characteristics have developed in this data, and it was felt that a more complete investigation of the inhomogenity in the Euro forging data set should be conducted. Following the proposal of Wallin [Eng. Fract. Mech., Vol. 71, No. 16, 2004, pp. 2392–2346], software was written to investigate whether the subject data set could best be expressed as a bimodal distribution of two combined Master Curve distributions, and this software was then applied to the various individual data sets in the European round robin data. The output of each analysis (e.g., the 2T data set) was two Tx values and a probability value pa, where Ta and Tb are the T0 values for the two constituents and pa is the probability of Ta. Using a procedure being developed as an annex to ASTM E1921 which is based on suggestions of Wallin, standard deviations of each of these quantities are estimated and used to judge if the dataset represents inhomogeneous material. The results show that several of the data sets obtained in the original round robin test program are better described by bimodal probability distributions than by the single Weibull distribution of ASTM E1921. Both single specimen datasets, and multi-temperature analysis of the various size specimens appear to show a preference for bimodal probability distributions. Additional sets of precracked Charpy size specimens were then machined from slices of the cross section and the results of testing these specimens shows that some cross sections of the Euro forging demonstrate a clear pattern of toughness variation across the forging cross section, while other cross sections show nearly constant fracture toughness with crack position. A major conclusion of this work is that making “mechanics based” conclusions comparing constraint effects using the Euro forging material is going to be more difficult given the apparent presence of material inhomogeneity in this material as demonstrated very convincingly by the data and analysis presented in this paper

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Journal of ASTM International