Computational Micromechanics Modeling of Polycrystalline Superalloys. . .
141
4.2 Microstructure Representation
In computational homogenization of polycrystals, the RVEs should contain a
statistical representation of the most important features of the actual microstructure
[63]. For the same composition and precipitate content, the microstructural aspects
that mostly influence the elastoplastic response of Inconel 718 are the grain size,
shape, and orientation distributions of the alloy. In the case of the fatigue response,
the effect of second phases or twin boundaries can also be determinant under
small loads (high cycle fatigue). However, for relatively large deformations (low
cycle fatigue), range in which we will study Inconel 718, the effect of these
microstructural features is negligible compared with the strain localization due to
grain orientation and neighborhood. Therefore, all the RVEs generated for this study
are representative of the grain distributions experimentally measured but do not
explicitly include other microstructural features.
Two wrought microstructures are analyzed in this study, containing both a
relatively homogeneous grain size distributions – well represented using lognormal grain size distributions – but with different average grain size. For a given
microstructure, the grain size distribution was measured using optical images of
cross sections of the material including approximately 300 grains. The experimental
2D grain size distributions were transformed to a 3D distribution assuming spherical
grains [26], and these 3D grain radii distribution were approximated by a lognormal function. An example of the resulting 3D grain size distribution obtained
for one of the Inconel 718 microstructures studied is represented in Fig. 9, where
the parameters obtained for the log-normal distribution were σ = 0.70862, μ = 3.65
and a correlation coefficient of 0.93 [14].
Two different types of RVEs are generated, tessellation-based RVE with unstructured meshes (Fig. 10a) and voxelized RVEs (Fig. 10b). The first type of RVEs was
Fig. 9 Log-normal grain size
distribution of polycrystalline
Inconel 718 (solid line) and
the corresponding grain size
distribution in the RVE of the
microstructure, from [14]
0
4
8
12
16
20
0
30
60
90
120
150
180
lognormal experimental
grain size distribution
Grain size distribution
in the RVE
Fraction of grains (%)
Grain size (mm)
141
4.2 Microstructure Representation
In computational homogenization of polycrystals, the RVEs should contain a
statistical representation of the most important features of the actual microstructure
[63]. For the same composition and precipitate content, the microstructural aspects
that mostly influence the elastoplastic response of Inconel 718 are the grain size,
shape, and orientation distributions of the alloy. In the case of the fatigue response,
the effect of second phases or twin boundaries can also be determinant under
small loads (high cycle fatigue). However, for relatively large deformations (low
cycle fatigue), range in which we will study Inconel 718, the effect of these
microstructural features is negligible compared with the strain localization due to
grain orientation and neighborhood. Therefore, all the RVEs generated for this study
are representative of the grain distributions experimentally measured but do not
explicitly include other microstructural features.
Two wrought microstructures are analyzed in this study, containing both a
relatively homogeneous grain size distributions – well represented using lognormal grain size distributions – but with different average grain size. For a given
microstructure, the grain size distribution was measured using optical images of
cross sections of the material including approximately 300 grains. The experimental
2D grain size distributions were transformed to a 3D distribution assuming spherical
grains [26], and these 3D grain radii distribution were approximated by a lognormal function. An example of the resulting 3D grain size distribution obtained
for one of the Inconel 718 microstructures studied is represented in Fig. 9, where
the parameters obtained for the log-normal distribution were σ = 0.70862, μ = 3.65
and a correlation coefficient of 0.93 [14].
Two different types of RVEs are generated, tessellation-based RVE with unstructured meshes (Fig. 10a) and voxelized RVEs (Fig. 10b). The first type of RVEs was
Fig. 9 Log-normal grain size
distribution of polycrystalline
Inconel 718 (solid line) and
the corresponding grain size
distribution in the RVE of the
microstructure, from [14]
0
4
8
12
16
20
0
30
60
90
120
150
180
lognormal experimental
grain size distribution
Grain size distribution
in the RVE
Fraction of grains (%)
Grain size (mm)