M-SERVE and P-SERVE
69
O
O
O
O
O
X
X
X
X
(a)
X
X
X
X
X
(b)
X
X
X
X
X
|
2
(c)
(d)
Fig. 7 (a) 50th and 95th percentile expected KS test statistic for various N p (red and blue lines
indicate the number of samples required to achieve a 95% probability of observing a KS test
statistic of less than 0.2 and 0.1, respectively); (b) ensemble error metric between SEVMs with
N p = 200 and those with N p = 10, 20, 50, 100, 200 respectively; (c) variability related to the
differences in S 2 ; and (d) ensemble CDFs of the local volume fraction for SEVMs with N p =
10, 20, 50, 100, 200. (Reprinted from: Pinz et al. [30], with permission from Elsevier)
2.5 Determining the Property-Based Statistically Equivalent
RVE (P-SERVE)
The mechanical response of Ni-based superalloys is highly dependent on the
subgrain-scale intragranular γ − γ microstructure. Microstructural simulations
for evolving variables and overall response fields must incorporate large-enough
computational RVEs to account for variabilities in evolving fields caused by spatial and morphological heterogeneities. The property-based statistically equivalent
representative volume element (P-SERVE) corresponds to the minimum simulation