Non-deterministic Calibration
193
0.0495
0.0500
0.0505
m
0
1000
2000
3000
4000
Probability density
0
500
1000
g *
s
[MPa]
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
Probability density
129.5
130.0
130.5
g 0 [MPa]
0
2
4
6
Probability density
90
100
110
120
G 0 [MPa]
0.00
0.05
0.10
0.15
Probability density
24.8
25.0
25.2
σ
2
[MPa
2 ]
0
2
4
6
8
Probability density
Fig. 16 The results of local calibration. The marginal probability density functions of the
calibration parameters, including the estimate of the variance of the error. The triangle denotes
the true values of each calibration parameter
for this parameter. The σ 2 probability density functions in Fig. 16 should not be
compared to those shown in Fig. 13 because they correspond to noise estimates of
different data sets (i.e., noise in homogenized stress vs. noise in HREBSD stress).
7 Summary
The objective of this chapter is to motivate the use of CP models in microstructuredependent engineering problems and to provide a comprehensive study of calibrating CP model parameters. Historical perspective and background is provided for
understanding what methods have been published, in terms of both generalized