Fig. 6: Creep-fatigue test with initial compression is compared with that with initial tension: (a) and (b) the time evolution ofσ n and ρ for the test condition oft t=100 s, t c=20 s (i.e.t t>t c); (c) and (d) the time evolution of σ n and ρ for the test condition of t t=20 s,t c=100 s (i.e.t t<t c)
Fig. 6d depicts the time evolution of ρ curves for these two test conditions. After each cycle, the ρ curves drop to 0, indicating that all of the cavities nucleated in the tension phase are sintered during the subsequent long compressive hold (t c=100 s). By comparison of Fig. 6b with 6d, it can be known that the nucleation rate in the tests witht c=100 s is almost ten orders of magnitude higher than that in the tests with t c=20 s. This is due to the fact that the maximum σ n is higher in the test with t c=100 s (1043 MPa in Fig.6a) when compared with that test with t c=20 s (761 MPa in Fig.6c). However, this does not necessarily lead to the overall increase of cavitation damage as the prolonged compressive hold would also cause sintering and close all cavities nucleated in the previous tension phase.

3.3 Combined effect of tensile and compressive holds

Combined effect of t t andt c on the final ρ after 10 cycles is presented in Fig. 7a by the contour plot. Note that except for thet t and t c, the default value as given in Table 2 is used for all the other load-waveform parameters and temperature. The contour curves of 0.1 and 0.0001 in Fig. 7a are very close to each other, suggesting that the contour curve of 0.1 can be used as the lower bound value. In other words, below this value, the final ρ is negligible. There is a threshold value oft t for cavitation whent c=0 s, indicating that the nucleated cavities can be sintered by the load reversal from tension to compression. In addition, under the condition of t c=0 s, the contour curves with values of 0.5 and beyond do not intercept with the x-axis. This indicates that there is an upper bound value fort t; any prolonged tensile holdt t than this critical value would not further contributing to the final ρ . This is probably attributed to the rapid decrease of σ n during tensile hold as informed by the exponential decay function in Eq.(2).
Now let’s focus on the changing values of t c. When t t is less than 60 s, increasingt c helps to reduce the final ρ . But whent t is greater than 60 s, an increasedt c promotes the increased final ρ until reaching the allowable value as highlighted by the magenta dash curve in Fig. 7a. It is also evident that the allowable t cincreases with the increasing t t. The presence of allowable t c is the result of two competing effects: (i) the increased t c can promote the cavity nucleation rate by affecting the maximumσ n in the next tension phase; (ii) the prolongedt c increases the likelihood of cavity sintering process, given the compressive stress.
Furthermore, the combined effect of t t andt c on the final f is presented in Fig. 7b. The distribution of contour curves looks similar by the comparison of Fig. 7a with 7b, suggesting that the dependence of final ρ andf on the load waveform parameters are highly consistent, i.e. both are positively correlated with the maximumσ n.