74
S. Ghosh et al.
with a relative error of 5% in the second moment of the distribution corresponds to
a P-SERVE of approximately 100–200 precipitates. This is much larger than that
for the yield strength and hardening rate, due to the requirements of convergence of
higher order moments of the distribution.
2.6 Summary of the Subgrain-Scale Analysis
This section develops the microstructure and property-based SERVEs, viz., MSERVE and P-SERVE for intragranular microstructures of Ni-based superalloys,
characterized by γ -γ phase distribution. Steps to the development of the MSERVE and P-SERVE include the development of statistically equivalent virtual
microstructures or SEVMs, for which statistical distribution functions are equivalent
to those from experimental data. The main difference between the M-SERVE and
the SEVMs is that the M-SERVE is the optimal domain with respect to a chosen
microstructural feature.
An important outcome of parametric representation of the morphology, e.g.,
in Eq. (4), is the capability of explicit representation of these parameters in parametrically homogenized constitutive models [20]. These constitutive models can
relate the sensitivity of various response fields to these morphological parameters
and hence facilitate material design. P-SERVEs are established with respect to
a few global and local material properties from evolving variables in dislocation
density-based crystal plasticity FE (DD-CPFE) simulations. It is observed that
the convergence with respect to the global properties occurs in the vicinity of
≈10–20 precipitates for relative error bounds of 5%. When local variables are
considered, a higher number of precipitates with N p ≈ 100–200 becomes necessary
for convergence. Spatially averaged quantities converge quicker than the local distributions, independent of whether the quantity is microstructure or property-based.
The convergence characteristics of the M-SERVE and P-SERVE can generally be
used to delineate the relation between morphological characteristics and certain
response functions in the microstructure.
3 M-SERVE and P-SERVE for Polycrystalline
Microstructures of Ni-Based Superalloys
This section establishes M-SERVEs and P-SERVEs for the scale corresponding to
polycrystalline microstructures of Ni-based superalloys, as shown in Fig. 10. This
scale is characterized by an ensemble of grains containing annealing twins that
are generated as a consequence of the thermomechanical process. An algorithmic
development is pursued to generate 3D statistically equivalent virtual polycrystalline
microstructures (3D-SEVMs) from experimental observations by employing sta-
S. Ghosh et al.
with a relative error of 5% in the second moment of the distribution corresponds to
a P-SERVE of approximately 100–200 precipitates. This is much larger than that
for the yield strength and hardening rate, due to the requirements of convergence of
higher order moments of the distribution.
2.6 Summary of the Subgrain-Scale Analysis
This section develops the microstructure and property-based SERVEs, viz., MSERVE and P-SERVE for intragranular microstructures of Ni-based superalloys,
characterized by γ -γ phase distribution. Steps to the development of the MSERVE and P-SERVE include the development of statistically equivalent virtual
microstructures or SEVMs, for which statistical distribution functions are equivalent
to those from experimental data. The main difference between the M-SERVE and
the SEVMs is that the M-SERVE is the optimal domain with respect to a chosen
microstructural feature.
An important outcome of parametric representation of the morphology, e.g.,
in Eq. (4), is the capability of explicit representation of these parameters in parametrically homogenized constitutive models [20]. These constitutive models can
relate the sensitivity of various response fields to these morphological parameters
and hence facilitate material design. P-SERVEs are established with respect to
a few global and local material properties from evolving variables in dislocation
density-based crystal plasticity FE (DD-CPFE) simulations. It is observed that
the convergence with respect to the global properties occurs in the vicinity of
≈10–20 precipitates for relative error bounds of 5%. When local variables are
considered, a higher number of precipitates with N p ≈ 100–200 becomes necessary
for convergence. Spatially averaged quantities converge quicker than the local distributions, independent of whether the quantity is microstructure or property-based.
The convergence characteristics of the M-SERVE and P-SERVE can generally be
used to delineate the relation between morphological characteristics and certain
response functions in the microstructure.
3 M-SERVE and P-SERVE for Polycrystalline
Microstructures of Ni-Based Superalloys
This section establishes M-SERVEs and P-SERVEs for the scale corresponding to
polycrystalline microstructures of Ni-based superalloys, as shown in Fig. 10. This
scale is characterized by an ensemble of grains containing annealing twins that
are generated as a consequence of the thermomechanical process. An algorithmic
development is pursued to generate 3D statistically equivalent virtual polycrystalline
microstructures (3D-SEVMs) from experimental observations by employing sta-