154
A. Cruzado et al.
and the simulations is excellent in all cases, with the only exception of the cyclic
stress amplitude in the tests carried out at min = 1.5, which was slightly
underestimated.
6.3 Grain Size-Dependent Cyclic Behavior
The approach followed to include grain size dependency in the cyclic behavior of
Inconel 718 alloy is an extension of the phenomenological approach introduced to
reproduce grain size dependency in the monotonic behavior. In this case, in addition
to the modification of the initial CRSS (Eq. 18), the dependency on the grain size
D is also introduced in the backstress. The parameters c and d controlling the
kinematic hardening evolution, given by Eq. (20), are redefined as
c = c
+
k c
√
D
(25)
c
d
=
c
d
+
k c/d
√
D
(26)
where c and (c/d) stand for the direct hardening modulus and saturation hardening,
respectively, corresponding to a very large grain (where no dislocation pileups are
formed) and k c and k c/d stand for the Hall-Petch parameters that introduce the effect
of grain size. The fitting procedure and resulting values of these new parameters can
be found in [16]. The result of the cyclic deformation simulations for two different
strain ranges (ε//ε min = 3 and ε//ε min = 1.5) at T = 400 ◦ C and the two
different grain sizes considered, ASTM 3 and ASTM 8.5, are represented in Fig. 15
together with the experimental results.
The stabilized stress-strain hysteresis loops predicted by the model were able
to accurately reproduce the experimental behavior for both strain ranges. This
agreement supports the simplistic strategy to account for the grain size effect by
introducing Hall-Petch-type relations in both the initial critical resolved shear stress
and back stress evolution. Moreover, it is expected that the small effect of the grain
size at the macroscale level will be amplified at the microscopic level, providing a
non-negligible effect of grain size in the fatigue response.
7 Microstructure-Dependent Fatigue Life Simulation
7.1 Microstructure-Sensitive Crack Initiation Model
The prediction of crack initiation of Inconel 718 alloy as a function of its
microstructure is carried out using a micromechanics-based fatigue life estimation
approach. This approach consists first in simulating the cyclic response of the
alloy considered using computational homogenization until reaching the stabilized
A. Cruzado et al.
and the simulations is excellent in all cases, with the only exception of the cyclic
stress amplitude in the tests carried out at min = 1.5, which was slightly
underestimated.
6.3 Grain Size-Dependent Cyclic Behavior
The approach followed to include grain size dependency in the cyclic behavior of
Inconel 718 alloy is an extension of the phenomenological approach introduced to
reproduce grain size dependency in the monotonic behavior. In this case, in addition
to the modification of the initial CRSS (Eq. 18), the dependency on the grain size
D is also introduced in the backstress. The parameters c and d controlling the
kinematic hardening evolution, given by Eq. (20), are redefined as
c = c
+
k c
√
D
(25)
c
d
=
c
d
+
k c/d
√
D
(26)
where c and (c/d) stand for the direct hardening modulus and saturation hardening,
respectively, corresponding to a very large grain (where no dislocation pileups are
formed) and k c and k c/d stand for the Hall-Petch parameters that introduce the effect
of grain size. The fitting procedure and resulting values of these new parameters can
be found in [16]. The result of the cyclic deformation simulations for two different
strain ranges (ε//ε min = 3 and ε//ε min = 1.5) at T = 400 ◦ C and the two
different grain sizes considered, ASTM 3 and ASTM 8.5, are represented in Fig. 15
together with the experimental results.
The stabilized stress-strain hysteresis loops predicted by the model were able
to accurately reproduce the experimental behavior for both strain ranges. This
agreement supports the simplistic strategy to account for the grain size effect by
introducing Hall-Petch-type relations in both the initial critical resolved shear stress
and back stress evolution. Moreover, it is expected that the small effect of the grain
size at the macroscale level will be amplified at the microscopic level, providing a
non-negligible effect of grain size in the fatigue response.
7 Microstructure-Dependent Fatigue Life Simulation
7.1 Microstructure-Sensitive Crack Initiation Model
The prediction of crack initiation of Inconel 718 alloy as a function of its
microstructure is carried out using a micromechanics-based fatigue life estimation
approach. This approach consists first in simulating the cyclic response of the
alloy considered using computational homogenization until reaching the stabilized