PSI - Issue 5
L.F.P. Borrego et al. / Procedia Structural Integrity 5 (2017) 239–246 Borrego et al./ Structural Integrity Procedia 00 (2017) 000 – 000
242
4
2
2
2
2 13 12 3 3 3 2 Y 2 2 22 33 33 11 11 22 23
2
(1)
where Σ 11 , Σ 22 , Σ 33 , Σ 12 , Σ 13 , and Σ 23 are the components of the effective stress tensor, Σ (Σ = σ´ - Χ, where σ´ is the deviatoric component of the Cauchy stress tensor and Χ is the backstress tensor); Y is the yield stress, and its evolution with plastic strain is modeled by the Voce hardening law:
p ( ) Y Y Y Y (
p
)[1 exp( C
)]
(2)
0
Sat
0
Y
p is the equivalent plastic strain. The Lemaître-Chaboche
where Y 0 , Y Sat and C Y are material parameters and
kinematic hardening law is:
σ X
p
X
X
X Sat C X
(3)
1 200
800
400
0
-1
-0.5
0
0.5
1
Stress [MPa]
-400
-800
-1 200
Stra in [%]
Fig. 2. Stress-strain plot ( = 0.8%).
where p is the equivalent plastic strain rate. The identification of the material parameters that best describe the plastic behaviour of AA7050-T6 was carried out by minimizing the cost function F (A): X C and Sat X are material parameters and
2
Fit
Exp
( ) A
N
( ) A
F
Exp
i
1
(4)
i
where Fit ( ) A and Exp are the fitted and the experimentally measured values of true stress, respectively; A is the set of Voce and Lemaitre-Chaboche parameters that minimises F (A); N is the total number of experimental points.
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