21
of the material at the deformation rate 10
−4
s
−1
. The parameter B and n represents the isotropic work hardening constant
evaluated at strain rate 10
−4
s
−1
. The strain rate sensitivity and thermal softening parameters, denoted by C and m are calculated from the high strain rate and high- temperature experimental data. The experimentally obtained JC parameters of
Eq. (4.3) are given in Table 4.4.
4.6 Constitutive Model Error
To estimate the deviation between the experimental results and the model predictions, correlation coefficient and average
absolute error are also calculated. Average absolute error and correlation coefficient are expressed as
0.00
0.05
0.10
0.15
0.20
0
150
25
0
C
50
0
C
100
0
C
150
0
C
200
0
C
250
0
C
s
s
e
r
t
S
e
u
r
T
True Plastic Strain
300
450
600
Fig. 4.7 True stress-strain
curve at different temperature
0
5 0
1 00
150
2 00
250
0.6
0.7
0.8
0.9
1.0
YT / YRT
UT / URT
Temperature
0
C
YT /
YRT
0.5
0.6
0.7
0.8
0.9
1.0
UT /
URT
s
s
s s
s
s s
s
Fig. 4.8 Variation of
(σ YT /σ YRT ) and (σ UT /σ URT ) with
temperature. σ YRT , σ URT are
yield and ultimate strength at
room temperature. σ YT , σ UT are
yield and ultimate strength at
T temperature
4 Constitutive Behavior of AA7475-T7351 at High Strain Rate and Elevated Temperatures
of the material at the deformation rate 10
−4
s
−1
. The parameter B and n represents the isotropic work hardening constant
evaluated at strain rate 10
−4
s
−1
. The strain rate sensitivity and thermal softening parameters, denoted by C and m are calculated from the high strain rate and high- temperature experimental data. The experimentally obtained JC parameters of
Eq. (4.3) are given in Table 4.4.
4.6 Constitutive Model Error
To estimate the deviation between the experimental results and the model predictions, correlation coefficient and average
absolute error are also calculated. Average absolute error and correlation coefficient are expressed as
0.00
0.05
0.10
0.15
0.20
0
150
25
0
C
50
0
C
100
0
C
150
0
C
200
0
C
250
0
C
s
s
e
r
t
S
e
u
r
T
True Plastic Strain
300
450
600
Fig. 4.7 True stress-strain
curve at different temperature
0
5 0
1 00
150
2 00
250
0.6
0.7
0.8
0.9
1.0
YT / YRT
UT / URT
Temperature
0
C
YT /
YRT
0.5
0.6
0.7
0.8
0.9
1.0
UT /
URT
s
s
s s
s
s s
s
Fig. 4.8 Variation of
(σ YT /σ YRT ) and (σ UT /σ URT ) with
temperature. σ YRT , σ URT are
yield and ultimate strength at
room temperature. σ YT , σ UT are
yield and ultimate strength at
T temperature
4 Constitutive Behavior of AA7475-T7351 at High Strain Rate and Elevated Temperatures