Computational Micromechanics Modeling of Polycrystalline Superalloys. . .
157
N i =
W NL
crit
(W b
cyc ) m
(29)
where the fatigue life depends on the stabilized cyclic FIP, W b
cyc , through two
material parameters, W NL
crit and m. In order to obtain the stabilized cyclic FIP,
it was observed that 5 cycles were enough, except for the smallest strain range
ε//ε min = 1 and the strain ratio of R ε = −1 in which cyclic simulations were
extended up to ≈12% of the fatigue life. This slow convergence to the stable
cyclic behavior is a consequence of the cyclic softening that, for the small amount
of plasticity accommodated in each cycle, extends the reduction of the stress
range until a large number of cycles. It must be noted that the parameters of the
crack initiation law should be in principle independent of the alloy microstructure
and therefore the effect of the grain size distribution and other microstructural
features enter in the model through the FIP values, obtained in the polycrystalline
simulations.
7.2 Results
The parameters of the fatigue initiation law described in Eq. 29 were fitted
using two different fatigue tests (ε//ε min = 1 and 3.5) performed in an alloy
with fine-grained microstructure (ASTM 8.5). The cyclic FIP, W b
cyc , for the two
loading conditions was obtained from the average value of the simulation of
a RVE ensemble (SVE) with 20 different RVEs. The resulting parameters are
W NL
crit = 4.8485 × 10 4 MJ/m 3 and m = 1.4755.
As in the rest of the chapter, two microstructures are considered, ASTM 3 and
ASTM 8.5, in order to check the ability of the model to reproduce size effects in the
fatigue life. The cyclic response of four different RVEs (selected to be representative
of the SVE distribution of FIPs) for each strain range and microstructure is simulated
using the framework previously presented. A value of the FIP, W b
cyc , is obtained
from each simulation. The life estimation for each RVE and load condition is
obtained then by introducing the FIP in Eq. (29), so four different values are
computed for each loading conditions that represent somehow the scatter in life.
The resulting fatigue life initiation predictions for the two grain sizes considered
are summarized in Fig. 16. Figure 16a, b shows the predictions of the LCF life for
the fine-grained microstructure and R ε = −1 and R ε = 0, respectively. The bars in
the graph represent the scatter of the 20 models used for fitting the fatigue life
initiation law, and the stars represent each of the 4 individual realizations of a fatigue
simulation. It is shown that the model is able to predict very accurately the fatigue
life for very different strain ranges and also under different strain ratios. Moreover,
considering that the two tests necessary for fitting the model were obtained from
tests at R ε = −1, the results with R ε = 0 are pure predictions and perfectly capture
the experimental response.
157
N i =
W NL
crit
(W b
cyc ) m
(29)
where the fatigue life depends on the stabilized cyclic FIP, W b
cyc , through two
material parameters, W NL
crit and m. In order to obtain the stabilized cyclic FIP,
it was observed that 5 cycles were enough, except for the smallest strain range
ε//ε min = 1 and the strain ratio of R ε = −1 in which cyclic simulations were
extended up to ≈12% of the fatigue life. This slow convergence to the stable
cyclic behavior is a consequence of the cyclic softening that, for the small amount
of plasticity accommodated in each cycle, extends the reduction of the stress
range until a large number of cycles. It must be noted that the parameters of the
crack initiation law should be in principle independent of the alloy microstructure
and therefore the effect of the grain size distribution and other microstructural
features enter in the model through the FIP values, obtained in the polycrystalline
simulations.
7.2 Results
The parameters of the fatigue initiation law described in Eq. 29 were fitted
using two different fatigue tests (ε//ε min = 1 and 3.5) performed in an alloy
with fine-grained microstructure (ASTM 8.5). The cyclic FIP, W b
cyc , for the two
loading conditions was obtained from the average value of the simulation of
a RVE ensemble (SVE) with 20 different RVEs. The resulting parameters are
W NL
crit = 4.8485 × 10 4 MJ/m 3 and m = 1.4755.
As in the rest of the chapter, two microstructures are considered, ASTM 3 and
ASTM 8.5, in order to check the ability of the model to reproduce size effects in the
fatigue life. The cyclic response of four different RVEs (selected to be representative
of the SVE distribution of FIPs) for each strain range and microstructure is simulated
using the framework previously presented. A value of the FIP, W b
cyc , is obtained
from each simulation. The life estimation for each RVE and load condition is
obtained then by introducing the FIP in Eq. (29), so four different values are
computed for each loading conditions that represent somehow the scatter in life.
The resulting fatigue life initiation predictions for the two grain sizes considered
are summarized in Fig. 16. Figure 16a, b shows the predictions of the LCF life for
the fine-grained microstructure and R ε = −1 and R ε = 0, respectively. The bars in
the graph represent the scatter of the 20 models used for fitting the fatigue life
initiation law, and the stars represent each of the 4 individual realizations of a fatigue
simulation. It is shown that the model is able to predict very accurately the fatigue
life for very different strain ranges and also under different strain ratios. Moreover,
considering that the two tests necessary for fitting the model were obtained from
tests at R ε = −1, the results with R ε = 0 are pure predictions and perfectly capture
the experimental response.