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.