Fig. 10: Model predicted nucleation incubation time (with stress amplitude and temperature indicated) in comparison with experimental data. Experimental data points are collected from creep-fatigue tests on Type 316 stainless steel.

Overall, our cavitation model informs that temperature and tensile stress are two influencing factors for the nucleation incubation time. For comparison purposes, experimental results are plotted as red data points in Fig. 10. The ‘no cavity’ data was obtained from the work by Shi and Pluvinage ⁴². The creep-fatigue test was conducted at 500 ˚C on Type 316L stainless steel under total strain range of 1.60% (stress amplitude of 350 MPa) together with tensile hold of t _t=10 s. They observed no creep cavitation damage, being consistent with the transgranular crack propagation mode. In addition, the 600 ˚C ‘cavity’ data point was obtained from the creep-fatigue test on Type 316 stainless steel conducted by Hales⁴³. They found cavitation damage under the test condition of total strain range of 0.5% andt _t=60 s. No stress-strain hysteresis loop was given, and hence the stress amplitude has been calculated as 140 MPa using relevant database in ³⁸. The 593 ˚C ‘cavity’ data point was obtained from the creep-fatigue crack growth test on Type 316 stainless steel conducted by Michel and Smith ⁴⁴. The test was performed with the initial stress intensity factor range of 20 MPa.m^-2, and they reported the presence of intergranular creep damage. In summary, our model prediction agrees with the experimental observation.

Cavitation can also be found in high-temperature fatigue tests under certain range of cycle frequencies ⁴⁵. The cycle frequency that is positively correlated with the stress variation rate can be defined as . The optimum for final ρ has been calculated under the condition of without stress hold (i.e.t _c and t _t=0 s indicative of pure fatigue) has been presented in Fig. 9a. Hence, it is possible to extend our model prediction to examine the nucleation ability under different cycle frequency range for high-temperature fatigue.

The frequency range for cavity nucleation depends on both the temperature and stress amplitude. Fig. 11 presents the predicted nucleation field in the stress amplitude and frequency space at 550 and 600 ˚C. Here, the nucleation criterion is defined as the final ρof ≥10^-20 mm^-2. In other words, if the condition of ρ <10^-20mm^-2 is met, the combination of stress amplitude and frequency is judged as being unable to create cavitation. The shape of the nucleation field looks like the upside-down hills. This means that the load waveform with a higher stress amplitude has a wider range of cycle frequencies to promote cavitation. Also, an optimum frequency is found at each temperature, allowing the lowest stress amplitude to meet the cavitation criterion. The presence of optimum frequency shares the same mechanism as the optimum in Fig. 9. In low frequency, the lack of nucleation ability is the reason, whereas enhanced sintering is responsible for the reduced cavities in the high frequency.