56
S. Ghosh et al.
Sub-Grain
Grain Scale
Analysis
Homogenized
Single Crystal
Homogenized
Polycrystal
L1 Ordered
2
Al
Ni
Fig. 1 Schematic representation of multiple scales in the development of a crystal plasticity finite
element model for Ni-based superalloys: polycrystalline microstructure, subgrain microstructure
in a single grain, discretized subgrain microstructural RVE, and homogenized crystal plasticity FE
model for a grain
The continuous γ -matrix phase has a face-centered cubic (FCC) lattice structure
and is an alloy of Ni and Cr with a small fraction of other alloying elements. The
γ precipitate phase is a coherent, ordered intermetallic Ni 3 Al reinforcing phase
of L1 2 crystal structure, which appears as a distribution of cuboidal precipitates in
a solid solution. The presence of the γ precipitate phase in the γ matrix causes
strengthening mechanisms for the two-phase system. In FCC and L1 2 crystal
structures, dislocations have Burgers vectors with the same 101 directions but
different magnitudes. A full dislocation in the L1 2 structure must transverse twice
the distance compared to that of FCC in order to maintain the ordered lattice, which
creates many additional consequences for the dislocation core. Figure 1 shows the
polycrystalline microstructure, the subgrain γ − γ microstructure in a single grain,
the discretized subgrain γ − γ microstructural representative volume element or
RVE, and the homogenized crystal plasticity finite element model for a grain.
The shape and size of the γ -phase depend largely on the cooling rate and internal
stress gradients during processing [3–5]. Slower cooling rates lead to the formation
of bimodal populations of large (≥500 nm) secondary and small (≤50 nm) tertiary
γ precipitates, while higher cooling rates yield a predominantly unimodal distribution of secondary γ precipitates (∼50–500 nm). The γ precipitates act as effective
obstacles to the motion of dislocations by virtue of their shape and ordered structure.
The volume fraction of γ precipitates, their mean size, and spacing have a major
effect on the mechanical properties of these superalloys [6, 7]. Micro-mechanisms
controlling creep in polycrystalline Ni-based superalloys are complex [6, 8]. At
intermediate temperatures 650 ◦ C ≤ θ ≤ 800 ◦ C and moderate stress levels
650 MPa, dominant deformation mechanisms include antiphase boundary (APB)
shearing and micro-twinning. The probability of occurrence of a given mechanism
depends on the load, crystal orientation, and microstructural morphology. At lower
S. Ghosh et al.
Sub-Grain
Grain Scale
Analysis
Homogenized
Single Crystal
Homogenized
Polycrystal
L1 Ordered
2
Al
Ni
Fig. 1 Schematic representation of multiple scales in the development of a crystal plasticity finite
element model for Ni-based superalloys: polycrystalline microstructure, subgrain microstructure
in a single grain, discretized subgrain microstructural RVE, and homogenized crystal plasticity FE
model for a grain
The continuous γ -matrix phase has a face-centered cubic (FCC) lattice structure
and is an alloy of Ni and Cr with a small fraction of other alloying elements. The
γ precipitate phase is a coherent, ordered intermetallic Ni 3 Al reinforcing phase
of L1 2 crystal structure, which appears as a distribution of cuboidal precipitates in
a solid solution. The presence of the γ precipitate phase in the γ matrix causes
strengthening mechanisms for the two-phase system. In FCC and L1 2 crystal
structures, dislocations have Burgers vectors with the same 101 directions but
different magnitudes. A full dislocation in the L1 2 structure must transverse twice
the distance compared to that of FCC in order to maintain the ordered lattice, which
creates many additional consequences for the dislocation core. Figure 1 shows the
polycrystalline microstructure, the subgrain γ − γ microstructure in a single grain,
the discretized subgrain γ − γ microstructural representative volume element or
RVE, and the homogenized crystal plasticity finite element model for a grain.
The shape and size of the γ -phase depend largely on the cooling rate and internal
stress gradients during processing [3–5]. Slower cooling rates lead to the formation
of bimodal populations of large (≥500 nm) secondary and small (≤50 nm) tertiary
γ precipitates, while higher cooling rates yield a predominantly unimodal distribution of secondary γ precipitates (∼50–500 nm). The γ precipitates act as effective
obstacles to the motion of dislocations by virtue of their shape and ordered structure.
The volume fraction of γ precipitates, their mean size, and spacing have a major
effect on the mechanical properties of these superalloys [6, 7]. Micro-mechanisms
controlling creep in polycrystalline Ni-based superalloys are complex [6, 8]. At
intermediate temperatures 650 ◦ C ≤ θ ≤ 800 ◦ C and moderate stress levels
650 MPa, dominant deformation mechanisms include antiphase boundary (APB)
shearing and micro-twinning. The probability of occurrence of a given mechanism
depends on the load, crystal orientation, and microstructural morphology. At lower