A Framework for Quantifying Effects of Characterization Error on the. . .
241
arises from potential ambiguity in the diffraction pattern associated with a finite
sampling volume. However, if the dwell time is not increased, then this would result
in a decrease in the overall strength of the output signal, which will diminish the
quality of the diffraction patterns. If there are resource limitations that limit the total
characterization time, then the choice to increase dwell time would have to be offset
by a decreased number of interrogation points. This could be achieved by decreasing
resolution or decreasing sample size, both of which can increase error. Given typical
constraints on instrumentation time, this interaction illustrates the balance and tradeoffs that must be made during the data collection process.
4 Case Study: Application to Finite Element Model
To this point the work has focused on purely geometric measures of the error of the
simulated microstructure compared to the ground truth phantom. While this form of
error is important, it might not fully reflect how these reconstructions are ultimately
used. In practice these reconstructions are often used to inform computational
models, either as direct inputs or through the extraction of key statistics. To analyze
this interaction requires extending the analysis to apply the microstructural data to
a computational model. The extension is relatively straightforward, because data
processing tools such as DREAM.3D that perform meshing allow direct modeling
of the simulated microstructures. This addition allows computational models to
serve as the context for measuring error. Given that the results from computational
models are the primary outcome, evaluating their sensitivity to microstructural data
set inputs and subsequently the data collection processes used to collect them is
clearly of interest. This is shown in this section through an example case study.
To illustrate how the proposed framework can help in determining the error
associated with resolution, a simple example was performed. An outline of the
computational framework is shown in Fig. 14. For this example, a 500 × 500 × 500
voxel equiaxed phantom encompassing ∼1500 interior grains, with an average grain
diameter of 18.2 voxels, was generated using DREAM.3D. Data collection was
then performed at various interrogation point spacings, over various volumes, and
with different levels of noise. A pictorial representation of the problem is shown in
Fig. 15. Each simulated microstructure and the larger phantom were meshed using
standard DREAM.3D filters and exported as ABAQUS input files. Individual grains
were assigned elastic material properties based on their crystallographic orientation.
The average von Mises stress in each interior grain at a global strain of 2% was
evaluated. The error in this average grain stress between the phantom microstructure
and the simulated microstructure was then averaged across all interior grains.
Results are shown in Fig. 16 for various normalized sample sizes and resolutions.
Figure 16 shows a greater dependence of the mean average stress on the total
number of grains resolved (i.e., sample size). In small samples, boundary conditions
dominate the grain-averaged stresses. For this reason, increasing the total number of
interrogation points without also increasing the volume over which they were placed
241
arises from potential ambiguity in the diffraction pattern associated with a finite
sampling volume. However, if the dwell time is not increased, then this would result
in a decrease in the overall strength of the output signal, which will diminish the
quality of the diffraction patterns. If there are resource limitations that limit the total
characterization time, then the choice to increase dwell time would have to be offset
by a decreased number of interrogation points. This could be achieved by decreasing
resolution or decreasing sample size, both of which can increase error. Given typical
constraints on instrumentation time, this interaction illustrates the balance and tradeoffs that must be made during the data collection process.
4 Case Study: Application to Finite Element Model
To this point the work has focused on purely geometric measures of the error of the
simulated microstructure compared to the ground truth phantom. While this form of
error is important, it might not fully reflect how these reconstructions are ultimately
used. In practice these reconstructions are often used to inform computational
models, either as direct inputs or through the extraction of key statistics. To analyze
this interaction requires extending the analysis to apply the microstructural data to
a computational model. The extension is relatively straightforward, because data
processing tools such as DREAM.3D that perform meshing allow direct modeling
of the simulated microstructures. This addition allows computational models to
serve as the context for measuring error. Given that the results from computational
models are the primary outcome, evaluating their sensitivity to microstructural data
set inputs and subsequently the data collection processes used to collect them is
clearly of interest. This is shown in this section through an example case study.
To illustrate how the proposed framework can help in determining the error
associated with resolution, a simple example was performed. An outline of the
computational framework is shown in Fig. 14. For this example, a 500 × 500 × 500
voxel equiaxed phantom encompassing ∼1500 interior grains, with an average grain
diameter of 18.2 voxels, was generated using DREAM.3D. Data collection was
then performed at various interrogation point spacings, over various volumes, and
with different levels of noise. A pictorial representation of the problem is shown in
Fig. 15. Each simulated microstructure and the larger phantom were meshed using
standard DREAM.3D filters and exported as ABAQUS input files. Individual grains
were assigned elastic material properties based on their crystallographic orientation.
The average von Mises stress in each interior grain at a global strain of 2% was
evaluated. The error in this average grain stress between the phantom microstructure
and the simulated microstructure was then averaged across all interior grains.
Results are shown in Fig. 16 for various normalized sample sizes and resolutions.
Figure 16 shows a greater dependence of the mean average stress on the total
number of grains resolved (i.e., sample size). In small samples, boundary conditions
dominate the grain-averaged stresses. For this reason, increasing the total number of
interrogation points without also increasing the volume over which they were placed