Fig. 9: (a) Dependence of final ρ and f on stress variation rate under t c andt t=0 s; (b) ρ value at the end of 1st cycle and (c) the related minimum σ n in the compression phase of 2nd cycle.
Fig. 9b shows that ρ decreases rapidly with the decrease of in the range of <0.4 MPa/s. This implies that a too low stress variation rate reduces the nucleation ability. This seems to agree with the previous one-cycle creep-fatigue modelling work19, where the local normal stress relaxation was found to occur during the load reversal with low . On the other hand, theρ curve decreases with the increase of when >0.4 MPa/s. At first glance, this might be attributed to the lack of nucleation time when becomes sufficiently high. However, a closer examination of the change of final ρ in Fig. 9a in comparison with the ρ curve in Fig. 9b does not support the above explanation. It is evident that the final ρ quickly decreases to a value of 10-20 mm-2 with increased , Fig. 9a, whereas the ρ at the end of 1st cycle decreases moderately to 10-12 mm-2, Fig. 9b.
We thereby hypothesised that the enhanced cavity sintering effect contributed to the rapid decrease in the high range. Fig. 9c shows that the absolute value of the minimum σ n has a monotonically increasing trend with the increase of . This suggests that the sintering effect becomes more pronounced in the high range, causing the final ρ to decrease, as revealed in Fig. 9a. To this end, our hypothesis is supported by the observation.
Finally, it can be seen in Fig. 9b that the optimum does not coincide with the value of producing the maximum ρ value. It is the combined effect of sintering and nucleation over the course of 10 cycles that determines the optimum value leading to the highest final ρin Fig. 9a (for brevity not shown here).