Computational Micromechanics Modeling of Polycrystalline Superalloys. . .
143
The texture is included in any of the two RVE typologies by assigning to each
grain a given initial orientation defined by a rotation tensor. The rotation of each
grain is selected to fulfill statistically the orientation distribution function experimentally obtained [27, 62]. In the case of the Inconel 718, all the microstructures
studied presented a random texture, and therefore, grain orientations have been
randomly generated in the rotation group SO(3).
The computational cost and local accuracy of the two RVEs typologies are
different, and their use depends on the application. For simulating the monotonic
response, only a small number of different RVEs are needed, and each simulation
requires only a limited number of load increments. In this case, Voronoi RVEs
are used because they are computationally affordable and the local solution near
grain boundaries can be more accurate. On the contrary, for simulating of the
cyclic response and fatigue performance, many different RVEs have to be simulated, and each simulation comprises a large number of cycles. In this situation,
voxelized RVEs are preferred due to their simple generation and better numerical
performance.
4.3 Single Crystal Behavior
The behavior of the Inconel 718 grains is accounted using crystal plasticity theory.
A unified kinematic crystal plasticity framework is used for all the regimes studied,
but, for simplicity, slightly different flow and hardening rules are used for monotonic
and cyclic behavior. In this section, we will review the general equations of the
crystal plasticity models used, while the particular flow and hardening rules will be
incorporated in each section.
With respect to the number and type of slip systems available in Inconel 718,
slip trace analysis performed in [4] and the micromechanical tests presented in the
previous section indicate that plastic deformation only takes place in octahedral
111 < 110 > slip systems, as in a single-phase FCC alloy. This is due to the low
volume fraction (<20%) of γ and γ , and, therefore, only those 12 slip systems are
considered in the crystal plasticity modeling of the alloy.
The kinematic description of the model is based on the multiplicative decomposition of the deformation gradient, F, into the elastic F e and plastic components
F p ,
F = F
e F
p
(7)
The plastic velocity gradient in the intermediate configuration, L p , is given by the
sum of the shear rates ˙
γ α on all the slip systems α, according to
L
p
= ˙
F
p F
p −1 =
α
˙
γ
α s
α
⊗ m
α
(8)
143
The texture is included in any of the two RVE typologies by assigning to each
grain a given initial orientation defined by a rotation tensor. The rotation of each
grain is selected to fulfill statistically the orientation distribution function experimentally obtained [27, 62]. In the case of the Inconel 718, all the microstructures
studied presented a random texture, and therefore, grain orientations have been
randomly generated in the rotation group SO(3).
The computational cost and local accuracy of the two RVEs typologies are
different, and their use depends on the application. For simulating the monotonic
response, only a small number of different RVEs are needed, and each simulation
requires only a limited number of load increments. In this case, Voronoi RVEs
are used because they are computationally affordable and the local solution near
grain boundaries can be more accurate. On the contrary, for simulating of the
cyclic response and fatigue performance, many different RVEs have to be simulated, and each simulation comprises a large number of cycles. In this situation,
voxelized RVEs are preferred due to their simple generation and better numerical
performance.
4.3 Single Crystal Behavior
The behavior of the Inconel 718 grains is accounted using crystal plasticity theory.
A unified kinematic crystal plasticity framework is used for all the regimes studied,
but, for simplicity, slightly different flow and hardening rules are used for monotonic
and cyclic behavior. In this section, we will review the general equations of the
crystal plasticity models used, while the particular flow and hardening rules will be
incorporated in each section.
With respect to the number and type of slip systems available in Inconel 718,
slip trace analysis performed in [4] and the micromechanical tests presented in the
previous section indicate that plastic deformation only takes place in octahedral
111 < 110 > slip systems, as in a single-phase FCC alloy. This is due to the low
volume fraction (<20%) of γ and γ , and, therefore, only those 12 slip systems are
considered in the crystal plasticity modeling of the alloy.
The kinematic description of the model is based on the multiplicative decomposition of the deformation gradient, F, into the elastic F e and plastic components
F p ,
F = F
e F
p
(7)
The plastic velocity gradient in the intermediate configuration, L p , is given by the
sum of the shear rates ˙
γ α on all the slip systems α, according to
L
p
= ˙
F
p F
p −1 =
α
˙
γ
α s
α
⊗ m
α
(8)