13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- If assessed in terms of a shift in the Master Curve T0 value the proposed model provides a +33 oC reference temperature shift, whereas the Master Curve assessment provides a +29oC shift. This means that the model has, for this case, accurately predicted the shift in toughness with irradiation with some additional safety margin. The strong side of the proposed model is that it offers a microstructure-property relation that remains as true to the physics as presently possible within the constraints of the uncoupled material behaviour and the weakest-link assumption. The model takes directly microstructure data: the density of initiators and the probability distribution of their sizes, which can be determined by metallography. It basically requires the calibration of a single parameter: the rupture energy density scale, for which the additional information for positions of cleavage initiators can be determined by fractography. In the particular case reported here, the surface energy was also calibrated. This however was necessary to study a distribution with a higher than the experimental shape, while the scale parameter and density of initiators remained the same. It should be noted that the shape, scale and density are intrinsically related for a given material, so that the need to calibrate the surface energy could be eliminated for accurate experimental data. We have shown, at least in principle, that by advancing the local failure probability expression and accounting for a “real” size distribution data, one can achieve improved predictions for cleavage fracture toughness, certainly in the lower transition region. The outcome at higher temperatures is not yet satisfactory, but the reason for this could be the third possibility described in the introduction: interactions between micro-cracks, the density of which increases with plasticity, may become strong enough to invalidate the weakest-link assumption behind the current model. This will be a subject of future investigations. 4. Conclusions • The proposal offers a microstructure-informed strategy for calculating the probability of failure in a large part of the DBT region. • The calibration provides an estimate of surface energy that is close to values available in the literature, indicating that if all available parameters were well defined, the model would provide meaningful predictions of fracture toughness. • The predicted initiation sites (individual probability profiles) correspond very well with experimentally determined initiation sites for this material. • Cleavage toughness predictions in the DBT regime correlate well with both experimental data and Master Curve fits in the un-irradiated state. • On changing the tensile properties to consider irradiation, the shift in fracture toughness and spread of experimental results are well predicted. This is achieved with a single calibration at one temperature in the unirradiated state. Acknowledgements The support from BNFL to Jivkov is gratefully acknowledged. James would also like to acknowledge assistance from colleagues at AMEC in the FEA and to PERFORM60 for data. References [1] A. Pineau, Development of the local approach to fracture over the past 25 years: theory and applications. Int J Fract 138 (2006) 139–166. [2] F.M. Beremin, A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metal Trans 14A (1983) 2277-2287. [3] F. Mudry, A local approach to cleavage fracture. Nucl Eng Design 105 (1987) 65-76.
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