Issue 49

M. Hadj Miloud et alii, Frattura ed Integrità Strutturale, 49 (2019) 630-642; DOI: 10.3221/IGF-ESIS.49.57

Initial parameters

Interval of variation Identified parameters

420.00 350.00

300.0 to 450.0 150.0 to 600.0 0.150 to 0.50 0.01 to 0.05

339.70

0  (MPa) K (MPa)

428.6

n

0.20

0.3

0.015

0.026



L

Fixed f F

0.1

0.1

0.1

f C f N

0.010 0.0040

0.005 to 0.08 0.0005 to 0.007 ----------------------

0.052 0.0088 4.13%

Cost function

18%

Table 3. Identified GTN and Ludwick parameters.

Figure 7: Global comparison between experimental data and numerical results.

GTN parameters with predefined σ(ε)

Voce and GTN parameters

Ludwick and GTN parameters

Ref. [9]

------- ------- ------- -------

------- ------- ------- -------

0  = 339.8 MPa

0  = 339.7 MPa K = 428.6 MPa

Hardening law prameters

 = 9.380

n =0.3

S  = 659 MPa

L  = 0.0214

L  =0.026

Fixed f F

0.1

0.1

0.1

0.1

f C f N

0.0100 0.0012 5.51%

0.048 0.0065 4.01%

0.052 0.0088 4.13%

0.06 0.004 -------

Cost function

Table 4. Identified material parameters. The comparison in the Fig. 7 shows a good agreement between the experimental curve and those obtained for GTN model with Voce and Ludwick hardening laws rather than with predefined hardening σ(ε). The Fig. 8 presents the evolution of cost function with the iteration number. As it is indicated below, the number of identified parameters, in the case of GTN model identification with tabulated hardening law is lower than the other cases. Therefore, the number of iterations allowing a stagnation of cost function (of 5%) is reached after only two iterations, but low parameters accuracy is observed (Tab. 4). In the two other cases (GTN-Ludwick/Voce) of identification, a high parameters precision is obtained relatively to those found in Ref. [9]. The cost function stagnation is reached after five iterations. We note that, on the one hand, the number of iterations for GTN model identification with predefined σ(ε) is less than with Voce and Ludwick hardening laws, but on the other hand, the obtained parameters are more accurate.

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