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.
4.2 Cycle frequency range
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.