316
M. R. Karamooz-Ravari et al.
Fig. 17.4 Transformation surface in plane stress state for different typical values of α
asymmetry into the model. However, as its value increases, the level of asymmetry
increases too. The level of asymmetry might be different in loading and unloading.
Without loss of generality, the value of this parameter can be distinguished for these
two loading strategies:
α =
α 1 if ˙
σ > 0
α 2 if ˙
σ < 0
(17.51)
By applying the principle of complementary virtual work, the following relation
is obtained for the strain tensor:
ε i j = −
ν
E
σ mm δ i j +
1 + ν
E
σ mn ·
3
2π
Ω
N mn N i j + T mn T i j
dΩ
+
ε
∗
+ ξ
+
s + ε
∗
− ξ
−
s
·
3
2π
Ω
T i j dΩ
(17.52)
To find how efficient the model is for simulating the tension–compression asymmetry, tension–compression uniaxial test, and four-point bending are simulated and
the obtained results are compared against experimental measurements. Here, all the
simulations are considered at constant temperature so that there is no temperatureinduced martensite and the value of E
T
M is optional. For the sake of brevity, only one
M. R. Karamooz-Ravari et al.
Fig. 17.4 Transformation surface in plane stress state for different typical values of α
asymmetry into the model. However, as its value increases, the level of asymmetry
increases too. The level of asymmetry might be different in loading and unloading.
Without loss of generality, the value of this parameter can be distinguished for these
two loading strategies:
α =
α 1 if ˙
σ > 0
α 2 if ˙
σ < 0
(17.51)
By applying the principle of complementary virtual work, the following relation
is obtained for the strain tensor:
ε i j = −
ν
E
σ mm δ i j +
1 + ν
E
σ mn ·
3
2π
Ω
N mn N i j + T mn T i j
dΩ
+
ε
∗
+ ξ
+
s + ε
∗
− ξ
−
s
·
3
2π
Ω
T i j dΩ
(17.52)
To find how efficient the model is for simulating the tension–compression asymmetry, tension–compression uniaxial test, and four-point bending are simulated and
the obtained results are compared against experimental measurements. Here, all the
simulations are considered at constant temperature so that there is no temperatureinduced martensite and the value of E
T
M is optional. For the sake of brevity, only one