232
N. Wade et al.
Fig. 5 Slice of (a) Phantom microstructure and (b) simulation sampled with normalized resolution
of 0.14
surprising that these grains exhibit the most error, in terms of mismatched volume,
grain size distribution, and lost features.
More complex error metrics can be defined such as the PDF of the grain aspect
ratio distribution. For most data sets, the most appropriate error metric is typically
dependent on the desired application. For data collection, efforts seeking to identify
unique sites within a microstructure might prefer a counting metric, such as the
number of triple lines or quad points where three or more grains meet. In each
case any desired error metric can be computed directly by examining the difference
between phantom and simulation volumes. For microstructures collected to support
computational models, the best error metric might be differences between the
predicted response from the model based on the phantom and the model based on
the simulated microstructure, as will be described in Sect. 4.
3.2 Resolution
One of the most important parameters in data collection is the resolution at which
data is collected. The resolution or spacing between interrogation points sets a
minimum feature size threshold, which in practice should be larger than the spacing
itself, in order to resolve that feature. The accuracy resolving shape, size, and feature
boundaries is dependent on the resolution. Moreover, the appropriate resolution
should be determined relative to microstructural features of interest, and for this
reason the current discussion normalizes resolution by the average feature size.
Often a minimum of ten samples across a feature diameter is recommended to
resolve statistical properties [18]. By varying the spacing of interrogation points,
we can examine in more detail this rule of thumb and develop an estimate of the
error associated with changing resolution.
Figure 6 shows the effect of varying resolution in a single coordinate direction for
various material types. This is analogous to varying the slice thickness during serial
N. Wade et al.
Fig. 5 Slice of (a) Phantom microstructure and (b) simulation sampled with normalized resolution
of 0.14
surprising that these grains exhibit the most error, in terms of mismatched volume,
grain size distribution, and lost features.
More complex error metrics can be defined such as the PDF of the grain aspect
ratio distribution. For most data sets, the most appropriate error metric is typically
dependent on the desired application. For data collection, efforts seeking to identify
unique sites within a microstructure might prefer a counting metric, such as the
number of triple lines or quad points where three or more grains meet. In each
case any desired error metric can be computed directly by examining the difference
between phantom and simulation volumes. For microstructures collected to support
computational models, the best error metric might be differences between the
predicted response from the model based on the phantom and the model based on
the simulated microstructure, as will be described in Sect. 4.
3.2 Resolution
One of the most important parameters in data collection is the resolution at which
data is collected. The resolution or spacing between interrogation points sets a
minimum feature size threshold, which in practice should be larger than the spacing
itself, in order to resolve that feature. The accuracy resolving shape, size, and feature
boundaries is dependent on the resolution. Moreover, the appropriate resolution
should be determined relative to microstructural features of interest, and for this
reason the current discussion normalizes resolution by the average feature size.
Often a minimum of ten samples across a feature diameter is recommended to
resolve statistical properties [18]. By varying the spacing of interrogation points,
we can examine in more detail this rule of thumb and develop an estimate of the
error associated with changing resolution.
Figure 6 shows the effect of varying resolution in a single coordinate direction for
various material types. This is analogous to varying the slice thickness during serial