PSI - Issue 33

Naoya Oie et al. / Procedia Structural Integrity 33 (2021) 586–597 Oie, N. / Structural Integrity Procedia 00 (2019) 000–000 Bordet model, explains the fracture phenomenon more accurately than the Beremin model that assumes an initial defect. However, considering the distribution of � in this three-point bending test, as shown in Fig. 10, and the cumulative probability of crack nucleation, as shown in equation (15), it is doubtful that only � is involved in crack nucleation. If we fully accept this local approach, it means that the number of cracks increases explosively as they approach the notch tip. Shibanuma et al. (2013) formulated the probability of cementite cracking in ferritic cementite steel as depending not only on plastic strain but also on stress. In the next section, we will further examine factors other than � that contribute to crack nucleation. ���� ��� � � ���� � � � � � � �15� 595 10

Fig. 9. Distribution of P(x) for each Weibull stress model.

Fig. 10. Gradient of ε p near the notch tip.

4.3. Reformulation of the local approach Fig. 11 shows an optical microscope image of a microcrack at the grain boundary of ferritic-pearlitic steel. Smith (1966) considered the initiation point of brittle fracture to be the pile-up of dislocations into carbides at grain boundaries. Shibanuma et al. (2018) developed a fracture toughness prediction model for ferritic-pearlitic steel based on the mechanism that cracks in pearlite colonies break through grain boundaries and enter ferrite grains, resulting in crack growth. The microcrack on the grain boundary as shown in Fig. 11 may well be the initiation point of brittle fracture. The figure shows that the microcrack is a little meandering. This suggests that plastic strain, not simple shear stress, contributes to crack nucleation. The microcrack also has a volume, not a sheer line. This suggests that tensile stresses from some directions also contribute to crack nucleation. That is, not only the stress but also the equivalent plastic strain and the triaxiality of tensile stress may contribute to crack growth. Void growth, which may be the initiation point of brittle fracture, has also been studied for a long time. McClintock (1968) considered a model of the deformation of a hole in a material and showed that the strain leading to failure of a plastic body decreases as the hydrostatic pressure increases. Rice and Tracey (1969) solved the problem of void growth as a continuum plasticity problem and formulated that voids grow more when the stress triaxiality is large. Therefore, in this study, a factor of triaxiality is introduced for the probability density function f for simplicity, as shown in equations (16)-(17). ���� � � ��� � � � � � ��� � ��� � � �16�