PSI - Issue 82

Marwen Habbachi et al. / Procedia Structural Integrity 82 (2026) 84–90 Habbachi et al. / Structural Integrity Procedia 00 (2026) 000–000

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5

The relative error between the analytical and numerical results was approximately 9 %, demonstrating a high level of agreement between the two findings:

F Num − F Ana F Ana

600 − 549 . 28 549 . 28

= 9 . 23%

(6)

∆ F (%) =

=

Fig. 3: The forming forces F x , F y , and F z .

3.2. Interaction e ff ect

An attempt was performed to investigate the interaction e ff ects on the maximal axial forming force in the steady state regime after filtering the unwanted noise signal. The influence of the interaction of step size ∆ z and wall angle ψ is depicted in Fig. 4a. The maximal force F z max is increased drastically when the steepness of the wall shape increases due to the fact that larger step size causes a proportional rise on the forming due to the fact that a large amount of material is deformed at that instant. However, a combination of these two factors results in a rapid increase and therefore render it to be a critical factor of the forming. Notably, F z max has shown a decrease when the wall angle reaches ψ = 60 ◦ . Above that the forming under high drawing angle result in high risk of material fracture even before reaching the targeted forming height. The combination of step size ∆ z and sheet thickness t 0 (Fig. 4b) shows a gradual increase following the same trend at di ff erent step depths. However, for thicker sheets t 0 = 2 mm, the forming force rapidly reaches an amplitude above 2 kN, regardless of the selected step size. This behavior can be attributed to the larger amount of material that must be formed at each contour. To ensure accurate results, the number of integration points through the sheet thickness was intentionally increased to seven and ten. Consequently, seven integration points (IP7) were selected, as the relative error compared to ten integration points (IP10) was approximately 3%.