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N. Wade et al.
enabled the study of many fine- and ultrafine-grained alloys. Materials scientists
have been tasked with the challenge of using this improved resolution to evaluate
materials that have property-structure relationships that scale across several orders
of magnitude. For example, Rene-88 DT has parent grain sizes on the order of 20–
100 μm but has features that exist at smaller length scales, like annealing twins that
are approximately 100 nm–1 μm thick and precipitate phases that are approximately
10 nm–1 μm in diameter. Previous work has shown that all of these features,
as well as the overall grain boundary networks, play a role in crack initiation
and propagation [13], meaning that microstructural data needs to be collected at
100 nm–1 μm resolutions across 1 mm length scales, pushing the limits of FIB and
mechanical serial sectioning.
As research continues to advance this technology, there is a growing tendency
toward generating large data sets, without a full understanding of the associated
limitations. For example, high-resolution data sets provide more detailed information about small-scale features, but they may not capture a representative volume
due to resource limitations. This trade-off must be reconciled in the context of the
properties one hopes to infer from the data set. In fact, a whole field of research has
emerged studying the effects of various properties as a function of the representative
volume element from which they are derived, with the ultimate goal of determining
the minimum volume from which to collect data without bias. Early data collection
efforts provided rough guidelines such as collecting enough slices to encompass a
volume at least twice the diameter of the largest grain [14], although more recent
efforts have suggested that larger volumes than this are needed. One common
statistical approach is to compare the variance of apparent properties through
a Monte Carlo (MC) simulation of increasing RVE sizes [15, 16] or stochastic
characterization of response quantities [17].
Other efforts have looked at how the spatial resolution should be selected to
ensure good convergence of properties, with some suggesting a minimum of ten
samples across a feature diameter is a reasonable resolution to resolve statistical
properties [18]. A later study looked at the effect of voxel resolution on the accuracy
of ensemble statistics by systematic downsampling of a synthetic microstructure,
suggesting different values for various types of desired statistics [19].
In other circumstances, researchers have looked at ways to improve interpretation
of the data, thereby reducing the overall experimental cost. For example, DeGraef
et al. introduced a dictionary-based indexing of diffraction patterns, which reduces
the number of unindexed or misindexed pixels resulting from the lack of clearly
identifiable Kikuchi bands [20].
In summary, each of these efforts has tried to identify ways of optimally
allocating resources to obtain the highest-quality data sets. This can be recast as
an effort to reduce the error in collecting data from a physical sample and building a
digital reconstruction of the material. Any error introduced during the generation of
these digital reconstructions is propagated to the material model. Understanding the
effects of this error will help in the effort to develop more accurate computational
models.
N. Wade et al.
enabled the study of many fine- and ultrafine-grained alloys. Materials scientists
have been tasked with the challenge of using this improved resolution to evaluate
materials that have property-structure relationships that scale across several orders
of magnitude. For example, Rene-88 DT has parent grain sizes on the order of 20–
100 μm but has features that exist at smaller length scales, like annealing twins that
are approximately 100 nm–1 μm thick and precipitate phases that are approximately
10 nm–1 μm in diameter. Previous work has shown that all of these features,
as well as the overall grain boundary networks, play a role in crack initiation
and propagation [13], meaning that microstructural data needs to be collected at
100 nm–1 μm resolutions across 1 mm length scales, pushing the limits of FIB and
mechanical serial sectioning.
As research continues to advance this technology, there is a growing tendency
toward generating large data sets, without a full understanding of the associated
limitations. For example, high-resolution data sets provide more detailed information about small-scale features, but they may not capture a representative volume
due to resource limitations. This trade-off must be reconciled in the context of the
properties one hopes to infer from the data set. In fact, a whole field of research has
emerged studying the effects of various properties as a function of the representative
volume element from which they are derived, with the ultimate goal of determining
the minimum volume from which to collect data without bias. Early data collection
efforts provided rough guidelines such as collecting enough slices to encompass a
volume at least twice the diameter of the largest grain [14], although more recent
efforts have suggested that larger volumes than this are needed. One common
statistical approach is to compare the variance of apparent properties through
a Monte Carlo (MC) simulation of increasing RVE sizes [15, 16] or stochastic
characterization of response quantities [17].
Other efforts have looked at how the spatial resolution should be selected to
ensure good convergence of properties, with some suggesting a minimum of ten
samples across a feature diameter is a reasonable resolution to resolve statistical
properties [18]. A later study looked at the effect of voxel resolution on the accuracy
of ensemble statistics by systematic downsampling of a synthetic microstructure,
suggesting different values for various types of desired statistics [19].
In other circumstances, researchers have looked at ways to improve interpretation
of the data, thereby reducing the overall experimental cost. For example, DeGraef
et al. introduced a dictionary-based indexing of diffraction patterns, which reduces
the number of unindexed or misindexed pixels resulting from the lack of clearly
identifiable Kikuchi bands [20].
In summary, each of these efforts has tried to identify ways of optimally
allocating resources to obtain the highest-quality data sets. This can be recast as
an effort to reduce the error in collecting data from a physical sample and building a
digital reconstruction of the material. Any error introduced during the generation of
these digital reconstructions is propagated to the material model. Understanding the
effects of this error will help in the effort to develop more accurate computational
models.