Non-deterministic Calibration
167
with comparison to the commonly used finite element model updating (FEMU)
method [26]. Local DIC strain data was also used to calibrate spatial variations
of yield stress within a weld nugget and heat-affected zone using uniform stress
and virtual fields methods [39]. Recently, Rokoš et al. [32] addressed the known
issue of boundary condition sensitivity within the IDIC method, by formulating a
procedure to combine material parameters with kinematic boundary conditions as
degrees of freedom at the model boundary. For an in-depth description of parameter
identification methods using local DIC strain and global stress data, see [1].
The application of parameter identification methods to CP models is relatively
limited. Early work of Hoc et al. [17] studied the calibration of CP parameters for
an ARMCO oligocrystal specimen using deterministic optimization. In that work,
the local DIC strain field was homogenized to produce a statistical distribution of
their component values. Additionally, global stress values were measured during
experiment. A cost function was formed by a weighted sum of both sets of data:
summing the differences between the measured and computed strain distributions,
at eight sampling points, and the measured and computed global stresses. More
recently, local DIC strain and global stress data have been used to calibrate CP
parameters from in situ tensile tests. By comparing two different CP models with
experimental data at various length scales (global stress-strain curve and strain map
from DIC), Sangid et al. [37] showed that although the two CP models agreed with
each other and the experimental data with regard to the global stress-strain behavior,
their local agreement was relatively poor at the spatial length scale of the slip
system. Guery et al. [15] used FEMU to calibrate CP parameters for AISI 316LN
steel using 2D simulations of microstructures with varying grain size. Grain sizedependent CP parameters were calibrated and illustrated the ability to reproduce the
expected Hall-Petch behavior. Bertin et al. [2] also studied CP parameter calibration,
using the IDIC method. In comparison with the study previously mentioned, the
work of Bertin et al. was on a smaller scale, focused on the deformation of a bicrystal
tensile sample fabricated using a focused ion beam (FIB).
The use of CP models within the finite element framework has largely focused
on the propagation of uncertainty via representative volume elements (RVEs),
formed by statistical instantiations of microstructure morphology. In these studies,
the CP model parameters are, however, deterministic, and their variations are
not considered in the ultimate prediction of variation in mechanical behavior.
This is likely due to two fundamental difficulties. First, there are currently no
proven methods for the non-deterministic identification of CP model parameters,
and preliminary developments are required. Second, the inclusion of CP model
parameter uncertainties adds to an already computationally intensive problem, when
considering variations in microstructure morphology. A goal of this chapter is to
illustrate that there are now methods available for the non-deterministic calibration
of CP model parameters and that those parameters can be considered in the forward
propagation from microscale uncertainties to predicted variation in component scale
mechanical behavior.
167
with comparison to the commonly used finite element model updating (FEMU)
method [26]. Local DIC strain data was also used to calibrate spatial variations
of yield stress within a weld nugget and heat-affected zone using uniform stress
and virtual fields methods [39]. Recently, Rokoš et al. [32] addressed the known
issue of boundary condition sensitivity within the IDIC method, by formulating a
procedure to combine material parameters with kinematic boundary conditions as
degrees of freedom at the model boundary. For an in-depth description of parameter
identification methods using local DIC strain and global stress data, see [1].
The application of parameter identification methods to CP models is relatively
limited. Early work of Hoc et al. [17] studied the calibration of CP parameters for
an ARMCO oligocrystal specimen using deterministic optimization. In that work,
the local DIC strain field was homogenized to produce a statistical distribution of
their component values. Additionally, global stress values were measured during
experiment. A cost function was formed by a weighted sum of both sets of data:
summing the differences between the measured and computed strain distributions,
at eight sampling points, and the measured and computed global stresses. More
recently, local DIC strain and global stress data have been used to calibrate CP
parameters from in situ tensile tests. By comparing two different CP models with
experimental data at various length scales (global stress-strain curve and strain map
from DIC), Sangid et al. [37] showed that although the two CP models agreed with
each other and the experimental data with regard to the global stress-strain behavior,
their local agreement was relatively poor at the spatial length scale of the slip
system. Guery et al. [15] used FEMU to calibrate CP parameters for AISI 316LN
steel using 2D simulations of microstructures with varying grain size. Grain sizedependent CP parameters were calibrated and illustrated the ability to reproduce the
expected Hall-Petch behavior. Bertin et al. [2] also studied CP parameter calibration,
using the IDIC method. In comparison with the study previously mentioned, the
work of Bertin et al. was on a smaller scale, focused on the deformation of a bicrystal
tensile sample fabricated using a focused ion beam (FIB).
The use of CP models within the finite element framework has largely focused
on the propagation of uncertainty via representative volume elements (RVEs),
formed by statistical instantiations of microstructure morphology. In these studies,
the CP model parameters are, however, deterministic, and their variations are
not considered in the ultimate prediction of variation in mechanical behavior.
This is likely due to two fundamental difficulties. First, there are currently no
proven methods for the non-deterministic identification of CP model parameters,
and preliminary developments are required. Second, the inclusion of CP model
parameter uncertainties adds to an already computationally intensive problem, when
considering variations in microstructure morphology. A goal of this chapter is to
illustrate that there are now methods available for the non-deterministic calibration
of CP model parameters and that those parameters can be considered in the forward
propagation from microscale uncertainties to predicted variation in component scale
mechanical behavior.