Fig. 12: (a) Applied stress as a function of time for the fast-slow and slow-fast creep-fatigue load waveforms; (b) predicted time evolution ofρ and the time integral of σ s at 600 ˚C.
Now let’s consider the unequal ramp rate scenarios from the modelling perspective. Fig. 12a presents the time-evolution curves ofσ s for both the fast-slow and slow-fast cycling, and they were used as the model input. The corresponding ρ curves in black are shown in Fig. 12b. It can be seen that the ρ in fast-slow test gradually increases after a few cycles, whereas that of the slow-fast test accumulates negligible number of cavities. This is in conflict with the experimental results as the failure of slow-fast test was dominated by creep cavitation. To reconcile this seemingly contradictory phenomenon, it is important to recollect the concept of our cavity nucleation and early-stage growth model.
Schematic diagram in Fig. 13 depicts the whole process of creep cavitation. The respective nucleation and subsequent early-stage growth in Fig. 13a and 13b are the main focus of the present work. Since the nucleated cavities are extremely small (<0.1 μm) compared with the particles at GB, they are surrounded by a highly localised and time-dependent stress field σ n, induced by the GB sliding with the rate of , Fig. 13b. However, the growth mechanism of large sized cavities would be completely different. Fig. 13c shows that the large cavity is surrounded by a uniform stress field under the far-field stress σ s. The cavity coalescence shown in Fig. 13d is also affected by the stress concentration, but this stress concentration is due to the reduction in effective load-bearing area 49, which approximately equalsσ s/(1-f ) 50. Therefore, it can be considered that the local normal stressσ n is key to early-stage creep cavitation, whereas the far-field stress σ s controls its late-stage.