322
M. R. Karamooz-Ravari et al.
Table 17.3 Utilized material parameters for simulation of cyclic loading in superelastic regime
(Karamooz-Ravari et al. 2018)
M f ( ◦ C) σ cr
s0 (MPa) C M0 (MPa/ ◦ C) C Af0 (MPa/ ◦ C) E M0 (MPa) σ M0
ye (MPa) ε ∗
0
36.17
220
11.03
11.0
74,000
NA
0.035
M s ( ◦ C) σ cr
se (MPa) C Me (MPa/ ◦ C) C Afe (MPa/ ◦ C) E Me (MPa) σ A0
ye (MPa) ε ∗
e
47.87
50
8.0
1.0
34,000
1002
0.013
A s ( ◦ C)
σ cr
f 0 (MPa)
C As0 (MPa/ ◦ C)
E A0 (MPa)
σ M0
y0 (MPa)
h(MPa)
μ
21.52
650
12.0
60,000
NA
75,000
0.5
A f ( ◦ C)
σ cr
fe (MPa)
C Ase (MPa/ ◦ C)
E Ae (MPa)
σ A0
y0 (MPa)
ε
(max)
p
m
51.0
950
14.0
30,000
750
0.019
3.5
Fig. 17.8 Comparison of the obtained stress–strain responses with experimental ones (KaramoozRavari et al. 2018)
by further increasing, no significant changes are observed, demonstrating that the
stress–strain response accumulates.
Evolution of the residual strain, peak strain, and dissipation energy during cycling
loading is depicted in Fig. 17.9a–c both experimentally and numerically. The prediction of the model is well validated by the first nine experimental cycles. In addition,
all the quantities converge to specific values as the number of cycles increase.
Table 17.4 shows the material parameters used for the shape memory regime cyclic
loading. The test temperature is about 23 °C which is lower than M f , so that ξ s0 = 0
and ξ T 0 = 1. The prediction of the model is compared against the experimental
findings for the first and eighth cycles as presented in Fig. 17.10 which shows a good
agreement.
M. R. Karamooz-Ravari et al.
Table 17.3 Utilized material parameters for simulation of cyclic loading in superelastic regime
(Karamooz-Ravari et al. 2018)
M f ( ◦ C) σ cr
s0 (MPa) C M0 (MPa/ ◦ C) C Af0 (MPa/ ◦ C) E M0 (MPa) σ M0
ye (MPa) ε ∗
0
36.17
220
11.03
11.0
74,000
NA
0.035
M s ( ◦ C) σ cr
se (MPa) C Me (MPa/ ◦ C) C Afe (MPa/ ◦ C) E Me (MPa) σ A0
ye (MPa) ε ∗
e
47.87
50
8.0
1.0
34,000
1002
0.013
A s ( ◦ C)
σ cr
f 0 (MPa)
C As0 (MPa/ ◦ C)
E A0 (MPa)
σ M0
y0 (MPa)
h(MPa)
μ
21.52
650
12.0
60,000
NA
75,000
0.5
A f ( ◦ C)
σ cr
fe (MPa)
C Ase (MPa/ ◦ C)
E Ae (MPa)
σ A0
y0 (MPa)
ε
(max)
p
m
51.0
950
14.0
30,000
750
0.019
3.5
Fig. 17.8 Comparison of the obtained stress–strain responses with experimental ones (KaramoozRavari et al. 2018)
by further increasing, no significant changes are observed, demonstrating that the
stress–strain response accumulates.
Evolution of the residual strain, peak strain, and dissipation energy during cycling
loading is depicted in Fig. 17.9a–c both experimentally and numerically. The prediction of the model is well validated by the first nine experimental cycles. In addition,
all the quantities converge to specific values as the number of cycles increase.
Table 17.4 shows the material parameters used for the shape memory regime cyclic
loading. The test temperature is about 23 °C which is lower than M f , so that ξ s0 = 0
and ξ T 0 = 1. The prediction of the model is compared against the experimental
findings for the first and eighth cycles as presented in Fig. 17.10 which shows a good
agreement.