PSI - Issue 61

Toros Arda Akşen et al. / Procedia Structural Integrity 61 (2024) 260 – 267 Toros Arda Akşen, Bora Şener, Emre Esener, Mehmet Firat / Structural Integrity Procedia 00 (2019) 000 – 000

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can be calibrated by only one mechanical test. In this regard, this criterion is opted for in different industries. To investigate the effect of the calibration, uniaxial tensile and bulge tests were considered, and the critical damage indicator was separately calculated based on these tests. Firstly, uniaxial tensile test was considered. A mesh sensitivity study was performed to accurately capture strain localization after the diffuse necking and uniaxial tensile test was modelled with different element sizes. Due to the symmetrical conditions, only quarter models using hexahedral solid elements were developed as shown in Fig. 2.

a

b

c

Fig. 2. Finite element models of uniaxial tensile test specimens. (a) model 1; (b) model 2; (c) model 3

The inverse method was adopted to attain true stress-strain curve beyond the diffuse necking and force displacement curves (through the experimental and numerical approaches) were compared with each other as shown in Fig. 3. Numerical analyses were done with the implicit finite element (FE) solver Marc. The number of elements for each model and the CPU solution times were listed in Table 3 as well.

0 1000 2000 3000 4000 5000 6000 7000 8000

Experiment (Mean) Model 1 Model 2 Model 3

Force (N)

0

3

6

9

12 15 18

Displacement (mm)

Fig. 3. Comparison of force-displacement responses attained by different mesh layouts.

Table 3. Element numbers for each mesh layout and the CPU solution times. Total elements In-plane elements

Through-thickness elements

Solution time (sec)

Model 1 Model 2 Model 3

624

312 675

2 4 8

2359 9829

2700 9504

1188

40705

As it is seen from Fig. 3 that the predicted force-displacement curves for the FE models are well matched with the experiment. On the contrary, the solution time was remarkably elevated, especially for the model 3 despite the force displacement results being almost identical. Comprising the solution time and the mesh layout performance, Model 2 was selected to determine the fracture in the study. The reason why the Model 2 was used is that a similar in-plane mesh layout sizes will be regarded for the blank’s region interacting with the punch radius in the rectangular cup drawing simulations, since crack initiation is expected to emerge at this region of interest. The computed true stress strain curve from Model 2 was used for the determination of the critical damage indicator. After the calibration of the