Fig. 13. A schematic diagram of cavitation with particular emphasis on
the difference between early- and late-stage cavity growth: (a)
nucleation; (b) early-stage; (c) late-stage and (d) coalescence.
In the late-stage cavitation, damage increase is manifested by the
radius increase of large sized cavities. According to the traditional
growth model, the growth rate is positively correlated with the cavity
radius 24, 51, 52. Also, the late-stage growth rate is
controlled by applied stress σ s. Therefore, the
time integral of σ s can be used to assess the
propensity of late-stage growth under a given load-waveform shape. In
this sense, a positive value of the integral ofσ s indicates that the cavities would continue
growing up, whereas a negative value indicating shrinkage in size.
Bearing the difference between the early- and late-stage in mind, theρ curves in Fig. 12b for the fast-slow and slow-fast
load-waveforms can be reconciled as below.
The time integral of σ s (red curves) for the two
scenarios are superimposed in Fig. 12b with their values indicated by
the secondary y-axis. The slow-fast one shows a positive value of theσ s integral, whereas the fast-slow one shows a
negative value. This implies that cavities in the case of fast-slow is
difficult to grow up under the negative value ofσ s integral. By contrast, cavities formed in the
slow-fast cycling is more likely to continue growing up, although their
number density is much less compared to that in the fast-slow one. This
eventually leads to an increased cavitated GB fraction f in the
case of slow-fast. The cavity coalescence occurs when f becomes
sufficiently large, causing the formation of intergranular cracks in
macroscopic scale. Hence, cavitation associated intergranular fracture
was most likely to occur in the case of slow-fast compared to the
fast-slow, as experimentally observed in 5, 48.