PSI - Issue 13

J Beswick et al. / Procedia Structural Integrity 13 (2018) 63–68 Beswick et al. / Structural Integrity Procedia 00 (2018) 000 – 000

67

5

Figure 4 shows the predictions for the high- and intermediate-constraint geometries starting from the average toughness of the low-constraint geometry, while Fig. 5 shows the cumulative probabilities of failure to illustrate the model predictions for the spread of toughness values. Despite the slight over-prediction of the intermediate constraint toughness the agreement with experiment is acceptable. It is clear that for all geometries the Weibull stress model over-predicts the probability of failure at lower loads (  w <  u ) and under-predicts the probability of failure at higher loads (  w >  u ). This outcome needs to be addressed in future developments of the model, particularly through modification of the micro-crack density correction factor to include characteristics of the stress and strain fields in addition to plastic strains.

Fig. 4. Predicted average fracture toughness values for high- (left) and intermediate- (right) constraint geometries, using the low-constraint geometry as a starting point.

Fig. 5. Calculated and experimental cumulative probabilities of failure for the calibrated high- and low-constraint (left) and predicted intermediate (right) constraint geometries.

The calibrated models were applied directly to the fracture toughness data for PS material. The average measured toughness values were J c ,0.4 =21.8 kJ/m 2 , J c ,0.2 =21.0 kJ/m 2 , J c ,0.05 =31.4 kJ/m 2 . The observed substantial toughness reduction is attributed to damage introduced during pre-straining to 5% plastic strain. The measured reductions of the Young’s modulus and proportionality stress, noted in Section 2, suggest that a fraction of the second phase particles has been converted to micro-cracks during pre-straining. This apparently has a strong effect on the predictions of the local approaches shown in Fig. 6. The results for the three levels of constraint over-predict significantly the measured fracture toughness values. This suggests that the change of deformation properties – elastic, yield and flow – due to pre-service or service-related plasticity is not sufficient for the tested LA to make reliable predictions for the change of fracture toughness. By extension, this also suggests that the change of deformation properties due to other effects, e.g. radiation, is not sufficient for these LA to infer the correct change in fracture toughness properties.