Fig. 8: The dependence of final ρ on (a)
Δσ t and (b) Δσ c witht t= 60/100 s; the evolution of ρ in (c)
and f in (d) as a function of fatigue cycles calculated with
different stress magnitudes of Δσ c=30/60/140/170
MPa but under the same tensile hold time of t t=60
s.
In terms of the effect of Δσ c on the finalρ , a positive correlation is found between the two until
Δσ c reaching the breakdown value, Fig. 8b. Such
breakdown of the positive correlation can be seen when
Δσ c>120 MPa under the condition oft t=60 s. This is followed by a sharp drop of
final ρ when Δσ c>160 MPa.
With the increase of tensile hold time to t t=100
s, the breakdown occurs at a higher compressive stress of when
Δσ c>270 MPa.
To explain this interesting phenomenon, the change of ρ andf as a function of cycles are presented in Fig. 8c and 8d,
respectively. Four different stress levels of
Δσ c=30/60/140/170 MPa are considered, and they
represent different characteristic regions as highlighted by using
different colours in Fig. 8b. Comparing the values of ρ at the
end of the 1st cycle, the test with Δσ c=170 MPa
has the largest ρ of 3.6×10-9mm-2, whereas that with Δσ c=30
MPa shows the smallest ρ of 0.7×10-9mm-2, Fig. 8c. This indicates that a higher
Δσ c helps to produce more creep cavities in the
subsequent tension phase. However, in the next compression phase of the
2nd cycle, these nucleated cavities would be sintered to different
extents depending on the stress level of Δσ c. For
example, the ρ value reduction is found to be
-0.2×10-9, -0.3×10-9,
-1.9×10-9 and -3.6×10-9mm-2 for Δσ c=30, 60, 140 and
170 MPa, respectively, Fig. 8c. Thus, the competing effect of
Δσ c on ρ through the cavity nucleation and
sintering leads to the fact that an intermediate level of
Δσ c is more likely to create more cavities.
For the same reason, the breakdown of the positive correlation between
the final ρ and Δσ c as revealed in Fig.
8b, can be explained by the sintering effect that becomes predominant
when the compressive stress is sufficiently large. In terms of the
cavitated GB fraction f , its value increases with the number of
cycles, Fig. 8d. The zigzag shape in the f curves reflect the
alternating nucleation and sintering events. In summary, increasing the
stress level of Δσ t is more effective in
enhancing the final ρ when compared to
Δσ c. The underlying mechanism is the side effect
associated with the cavity sintering due to the increased
Δσ c.
3.5 Effect of stress variation
rate
After elaborating the effects of four input parameters
(t t, t c,
Δσ t and Δσ c), we now
consider the effect of stress variation rate , Fig. 4. To limit the
effect of hold time on the prediction results, botht c and t t are set to 0 s
for calculations. Fig. 9a shows the effect of on the final ρ andf after 10 cycles. There is an optimum value of
(~0.4 MPa/s) that leads to the maximum final ρand f . To explain its presence, the ρ values as calculated
at the end of 1st cycle (i.e. the moment of finishing the tension phase)
are presented in Fig. 9b, while the minimum σ n as
calculated in the 2nd cycle (i.e. the following compression phase) are
shown in Fig. 9c. Note that the magnitude of ρ at the end of 1st
cycle can be regarded as the evaluation of the nucleation ability in the
considered load-waveform shape. Equally, the absolute value of the
minimum σ n in the 2nd cycle can be regarded as
the evaluation of the sintering ability.