13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- is smaller than the high-constraint m (assuming that σu is not dependent on constraint), see e.g. [5]. This suggests that the excess of plastic deformations introduced by the lower constraint require reduction of m to make reliable predictions. The methodology proposed in [5] for cross-calibration of m between high and low constraint geometries has shown promise [5, 6], but remains limited to temperatures well below T0, where the lower constraint conditions do not introduce substantial increase in plastic deformations relative to the high constraint case. This may prove problematic when used to predict cleavage fracture toughness for short cracks in irradiated material, where the reference temperature is shifted to higher values. To predict the irradiation effects on cleavage one needs a reliable model for the ductile-to-brittle transition (DBT) regime. Here, however, the Weibull parameters need to be varied to match experimental data. One possibility is to keep the shape parameter constant, which leads to temperature dependence of the scale, σu [7, 8]. Another possibility is to keep the scale parameter constant, which leads to temperature dependence of the shape, m [9, 10]. As for the low-constraint situation, m needs to be reduced with increasing temperature, i.e. with enhanced plasticity. Considering the physical basis for the Beremin LA [2, 3], the current state of affairs is not satisfactory, because the Weibull parameters must depend exclusively on the material microstructure. If the model for individual failure probability accounted adequately for the local fields and microstructure effects on particle failure, and the global failure were a weakest-link event, then the changes in plasticity due to constraint reduction or temperature increase should be already accounted for, leaving the Weibull parameters constants. In particular, m should be linked to the shape of size distribution of cleavage initiation particles, while σu should depend on the elastic properties and surface energy of the material as well as on the scale of the particle size distribution. Since these parameters do not change noticeably with constraint or temperature, the need to vary m and σu at increasing plastic deformations suggests that the link between physics and mechanics breaks. One possibility is that the individual failure probability model does not account adequately for the mechanical and particle size effects. A second possibility is that with the increase of plastic deformations the population of micro-cracks that needs to be accounted for in the weakest-link statistics becomes larger than the tail of the distribution, approximated by power-law in the Weibull-stress models. A third possibility is that the weakest-link assumption becomes increasingly invalid with increasing plasticity and micro-crack interaction effects need to be accounted for. To improve the individual failure probability, the effect of the plastic strain has been introduced in modifications of the Beremin model [11, 12] as well as in incremental formulations [13]. Recently, in addition to plastic strains the effect of stress triaxiality has also been introduced [14]. In a previous work [15], we have compared these models with the original Beremin and demonstrated that they provide improvements in the predicted failure probability profiles ahead of cracks with different constraints. This comparison has been done against a large set of experimental data for the locations of cleavage initiation sites reported in [16]. However, the prediction of the cleavage fracture toughness temperature dependence with these models remained unsatisfactory when performed with single set of Weibull parameters calibrated at T0. The effect of particle size on local failure probability was first proposed in [17]. The model now known as WST, however, remained as a microstructure-informed local model and to our knowledge had not been applied for global failure predictions. A different direction of work considers ductile damage prior to cleavage in the DBT regime, employing damage models for the material behaviour coupled with subsequent calculation of failure probability following Beremin [18, 19]. This approach has the potential to capture better the fracture behaviour in the DBT, but the models are presently too simplified with no interaction of void growth and micro-cracking at microstructure level [20]. Until advanced coupled models are developed and tested, the wider engineering community would benefit from a simpler uncoupled cleavage fracture model for the DBT region.
RkJQdWJsaXNoZXIy MjM0NDE=