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.