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.