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J. Hochhalter et al.
parameter identification methods and specific methods studied for use with CP
models. A review of the literature illustrates that the methods for CP parameter
calibration studied to date have largely focused on global-local methods, where
a combination of global (homogenized) stresses are combined with local DIC
displacements or strain to form the comparison between measured and computed
data.
Various methods for acquiring and post-processing data are also overviewed.
Global data, as would come directly from test-stand data or attached gauges, are
relatively cheap and easy to apply. Consequently, especially when many tests are
being performed, acquiring global data may be the only affordable method. Acquiring local DIC displacement and strain data provides a significant improvement on
the measured data set. But, this comes with a cost of additional equipment and
setup time. Additionally, application of this data in the global-local approach also
implies the need to acquire EBSD data before testing. Local stress data can also
be measured using HREBSD to analyze shifts in diffraction patterns. Combining
both local methods, DIC and HREBSD, is now possible with selectively transparent
stamping as the means to apply a DIC speckle pattern to the test specimen surface.
However, this method requires the highest level of infrastructure and time since both
HREBSD and DIC must be completed multiple times during testing.
Three classes of calibration methods can be used, differing by the type of
acquired data. While global data is the easiest and cheapest to acquire, CP model
parameter calibration using that data has fundamental issues. Namely, because many
sets of CP model parameters can reproduce nearly equivalent global stress-strain
curves, there should be no expectation that the calibrated parameters are unique.
Adding local DIC displacement data aids in the mitigation of this uniqueness
issue, but there are still local minima that exist in this case. Because of the
hybrid approach, with both global and local data, the computational model in this
case must represent the particular microstructure being tested. Running these full
simulations, for example, as a finite element model, is computationally intensive
and intractable for a non-deterministic approach. Additionally, this leads to the need
for assumptions or direct measurement of the microstructure underlying the surface
and high sensitivities to applied boundary conditions. Purely local data enables a
computationally tractable method for non-deterministic calibration. Furthermore,
this method precludes issues of generating a model of the microstructure aggregate,
does not incorporate boundary conditions, and helps resolve the issue of uniqueness.
However, as illustrated by the calibration of g ∗
s , the model parameters cannot be
determined accurately without adequate data that has sensitivity to the parameter.
As complexity in acquiring data is added, the computational cost of the calibration and issues surrounding uniqueness can be resolved. The combination of
the results from Fig. 13, Table 3, and Fig. 16 is shown in Fig. 17; it illustrates the
calibrated parameters from each approach. The two distributions represent the calibrated parameters for the purely global (red) and purely local (blue) methods. This
clarifies the relative uncertainty and inaccuracy in calibrating CP model parameters
using only global data. On the other hand, the purely local method results in very
little uncertainty and accurately reproduces the correct parameters (black triangles).
J. Hochhalter et al.
parameter identification methods and specific methods studied for use with CP
models. A review of the literature illustrates that the methods for CP parameter
calibration studied to date have largely focused on global-local methods, where
a combination of global (homogenized) stresses are combined with local DIC
displacements or strain to form the comparison between measured and computed
data.
Various methods for acquiring and post-processing data are also overviewed.
Global data, as would come directly from test-stand data or attached gauges, are
relatively cheap and easy to apply. Consequently, especially when many tests are
being performed, acquiring global data may be the only affordable method. Acquiring local DIC displacement and strain data provides a significant improvement on
the measured data set. But, this comes with a cost of additional equipment and
setup time. Additionally, application of this data in the global-local approach also
implies the need to acquire EBSD data before testing. Local stress data can also
be measured using HREBSD to analyze shifts in diffraction patterns. Combining
both local methods, DIC and HREBSD, is now possible with selectively transparent
stamping as the means to apply a DIC speckle pattern to the test specimen surface.
However, this method requires the highest level of infrastructure and time since both
HREBSD and DIC must be completed multiple times during testing.
Three classes of calibration methods can be used, differing by the type of
acquired data. While global data is the easiest and cheapest to acquire, CP model
parameter calibration using that data has fundamental issues. Namely, because many
sets of CP model parameters can reproduce nearly equivalent global stress-strain
curves, there should be no expectation that the calibrated parameters are unique.
Adding local DIC displacement data aids in the mitigation of this uniqueness
issue, but there are still local minima that exist in this case. Because of the
hybrid approach, with both global and local data, the computational model in this
case must represent the particular microstructure being tested. Running these full
simulations, for example, as a finite element model, is computationally intensive
and intractable for a non-deterministic approach. Additionally, this leads to the need
for assumptions or direct measurement of the microstructure underlying the surface
and high sensitivities to applied boundary conditions. Purely local data enables a
computationally tractable method for non-deterministic calibration. Furthermore,
this method precludes issues of generating a model of the microstructure aggregate,
does not incorporate boundary conditions, and helps resolve the issue of uniqueness.
However, as illustrated by the calibration of g ∗
s , the model parameters cannot be
determined accurately without adequate data that has sensitivity to the parameter.
As complexity in acquiring data is added, the computational cost of the calibration and issues surrounding uniqueness can be resolved. The combination of
the results from Fig. 13, Table 3, and Fig. 16 is shown in Fig. 17; it illustrates the
calibrated parameters from each approach. The two distributions represent the calibrated parameters for the purely global (red) and purely local (blue) methods. This
clarifies the relative uncertainty and inaccuracy in calibrating CP model parameters
using only global data. On the other hand, the purely local method results in very
little uncertainty and accurately reproduces the correct parameters (black triangles).