13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Cleavage modelling with experimental particle size distribution and novel particle failure criterion Andrey P Jivkov1,*, Peter James2 1 School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester M13 9PL, UK. 2 AMEC, Walton House, Birchwood, Warrington WA3 6GN, UK. * Corresponding author: andrey.jivkov@manchester.ac.uk Abstract Most of the existing local approaches for cleavage fracture derive from the assumptions that global failure is a weakest-link event and that only the tail of the size distribution of micro-crack initiating features is significant. This appears to be sufficient in predicting lower shelf toughness under high constraint conditions, but may fail when attempting to predict toughness in the transition region or for low constraint conditions when using the same parameters. While coupled ductile damage models with Beremin-like failure probability could be useful in the transition region, uncoupled models with “a posteriori” probability calculations are advantageous to the engineering community. Cleavage toughness predictions in the transition regime, which can be extended to low constraint conditions, are here made with improved criterion for particle failure and experimentally based size distribution of initiators for specific RPV steel. The model is shown to predict experimentally measured locations of cleavage initiators. Further, the model predicts the fracture toughness in a large part of the transition region and accurately predicts a measured shift with irradiation. All results are obtained without changes in model parameters. This suggests that the model can be used for assessing toughness changes due to constraint- and temperature-driven plasticity changes. Keywords RPV steel; local failure criterion; global failure probability; transition temperature regime 1. Introduction Safety assessment and life extension decisions in nuclear plant require reliable methodologies for predicting changes in cleavage fracture toughness behaviour of ferritic RPV steels due to irradiation and defect geometry effects. Local approaches (LA) to cleavage fracture are promising as these could account for the micro-mechanisms involved in the cleavage failure phenomenon, such as the nucleation of micro-cracks at second-phase brittle particles, the propagation of such micro-cracks within grains and the propagation of a critical micro-crack leading to component failure [1]. The pioneering LA to cleavage, proposed by the Beremin group [2], is based on two main assumptions: that the global failure probability is a weakest-link event and that the individual failure probabilities are dictated by local mechanical fields and specific microstructure data such as the size distribution and number density of cleavage-initiating particles. Assuming that the tail of the size distribution can be approximated by a power-law, the weakest-link statistics leads to a global failure probability expressed as a Weibull-type function of a generalised stress, the Weibull stress σw [2, 3]: ( ) ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = − − m u w fP V σ σ 1 exp (1) The shape, m, and scale, σu, of the Weibull function can be calibrated using fracture toughness data obtained with particular crack geometry at a given temperature and corresponding FE analysis [4]. For calibrations performed with high-constraint crack geometries at or below the ductile-to-brittle transition temperature, T0, the shape and scale obtained can be used with sufficiently good accuracy to predict cleavage fracture toughness of other high-constraint geometries at temperatures below T0 [2-4]. However, an attempt to use the same parameters to calculate cleavage toughness under lower constraint conditions or higher temperatures leads to predictions that do not match experimental values. For cleavage fracture toughness data obtained at a given temperature with low- and high-constraint geometries, independent calibrations would typically show that the low-constraint m
RkJQdWJsaXNoZXIy MjM0NDE=