PSI - Issue 18

L. Collini et al. / Procedia Structural Integrity 18 (2019) 671–687 L. Collini / Structural Integrity Procedia 00 (2019) 000–000

678 8

 f , ij pl l j

pl

 f



(4)

T i

Table 4. Triaxiality ratios imposed on the RVE at the meso-scale.

T

Σ 11

Σ 22

Σ 33

-0.333 -0.126 0.000 0.126 0.218 0.333 0.577 1.000 1.667

-1 -1

0

0 0 0 0 0 0 0

0.5

1 1 1 1 1 1 1

-1

-1/2 -1/4

0

1/2

1

1/4

1/2

1

4.2. Plastic flow In this work a classical plasticity model is chosen to reproduce the plastic flow of the two phases. Isotropic hardening with a Mises-type yield surface, associated flow rule and a Johnson-Cook hardening law is used, where the yield stress, σ 0 , is assumed to be of the form:  0  A  B  pl   n     1  ˆ  m   (5) The parameters A, B and the hardening exponent n are taken from the literature for a α-ferrite Fe-Si matrix, Springer (2012), and for fine pearlite structure, Hyzak et al. (1976), Gensamer et al. (2012), Toribio et al. (2016). The values are reported in Tab. 5 and in a graphical form in Fig. 4. Since neither strain rate nor temperature dependence are considered, the related parameters are set to zero.

Fig. 4. Model of plastic flow for the matrix constituents.