Computational Micromechanics Modeling of Polycrystalline Superalloys. . .
155
-1.5 -1 -0.5 0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Experiment
Simulation
-1.5 -1 -0.5 0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Experiment
Simulation
-1.5 -1 -0.5 0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Experiment
Simulation
-1.5 -1 -0.5 0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Experiment
Simulation
(a)
(b)
(c)
(d)
Fig. 15 Experimental results and numerical predictions of the stabilized cyclic stress-strain
loops of Inconel 718 alloy at 400 ◦ C tested under uniaxial cyclic deformation with R ε = −1. (a)
ε//ε min = 3 for ASTM 8.5 grain size. (b) Idem as (a) for ASTM 3 grain size. (c) ε//ε min = 1.5
for ASTM 3 grain size. (d) Idem as (c) for ASTM 3 grain size
cycle. The simulation accounts for the alloy microstructure through the RVE
and is performed for the particular cyclic loading condition studied (strain/stress
range, strain rates, R ratio, etc.). The evolution during the stable cycle of the
mechanical fields and internal variables at the microscopic level is used then to
obtain some fatigue indicator parameters (FIP) which describe the main driving
force that controls crack formation. These parameters are finally linked, using
phenomenological relations, to some stage of the fatigue life of the alloy under
study. Opposite to the homogenization of the averaged response, a large set of
RVEs should be used since the microscopic fields are very sensitive to the particular
RVE [64]. The reason is that the FIP of a RVE is based on the extreme value of
the FIP distribution inside that RVE, and the tail of this distribution is strongly
dependent on the particular RVE. This RVE ensemble is sometimes called SVE
(statistical volume element, [64]) or M-SERVES (microstructure representative
155
-1.5 -1 -0.5 0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Experiment
Simulation
-1.5 -1 -0.5 0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Experiment
Simulation
-1.5 -1 -0.5 0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Experiment
Simulation
-1.5 -1 -0.5 0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Experiment
Simulation
(a)
(b)
(c)
(d)
Fig. 15 Experimental results and numerical predictions of the stabilized cyclic stress-strain
loops of Inconel 718 alloy at 400 ◦ C tested under uniaxial cyclic deformation with R ε = −1. (a)
ε//ε min = 3 for ASTM 8.5 grain size. (b) Idem as (a) for ASTM 3 grain size. (c) ε//ε min = 1.5
for ASTM 3 grain size. (d) Idem as (c) for ASTM 3 grain size
cycle. The simulation accounts for the alloy microstructure through the RVE
and is performed for the particular cyclic loading condition studied (strain/stress
range, strain rates, R ratio, etc.). The evolution during the stable cycle of the
mechanical fields and internal variables at the microscopic level is used then to
obtain some fatigue indicator parameters (FIP) which describe the main driving
force that controls crack formation. These parameters are finally linked, using
phenomenological relations, to some stage of the fatigue life of the alloy under
study. Opposite to the homogenization of the averaged response, a large set of
RVEs should be used since the microscopic fields are very sensitive to the particular
RVE [64]. The reason is that the FIP of a RVE is based on the extreme value of
the FIP distribution inside that RVE, and the tail of this distribution is strongly
dependent on the particular RVE. This RVE ensemble is sometimes called SVE
(statistical volume element, [64]) or M-SERVES (microstructure representative