PSI - Issue 72

Levente Tatár et al. / Procedia Structural Integrity 72 (2025) 345–353

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Fig. 6. Input flowcurves (a) and simulated engineering stress-strain curves (b) at extensometer location for first three FEM simulations

The results of these simulations show that the exponential true strain true strass curve derived from the Considère criterion results indeed a constant force. Quite small deviations from this curve lead to pronounced premature necking. 3.2. Primitive correction approach As a primitive correction approach we simply lengthened the curve providing from the pictures to be closer to the Considère curve by the formula:     mod pict pict 0 1 K          (6) In this equation ε mod is modified engineering strain, ε pict is engineering strain from pictures, ε 0 is engineering strain at maximum force, K is a constant. True strain true stress curves are derived from the engineering curves. The transformed curves and the corresponding results are shown in Fig. 7 for the precise, idealized model.

Fig. 7. Transformed input (a) and output (b) for the idealized model

3.3. Simulation results for the realistic model

To obtain a realistic model Bezier surfaces have been created using the microscopic irregularities. The nodes of the mesh have been distorted to match the Bezier surfaces. The same kind of correction has been applied as for the idealistic model. Out-of-centre necking has been observed. The value of the K constant matching the target curve is completely different from the idealized model. The best fit values: K = 2.5 for idealized model, K = 4.5 for realistic model. See Fig. 8b.