PSI - Issue 82

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

87

4

feed rate F = 2000mm / min, and initial sheet thickness t 0 = 1mm.

τ f = f σ n

(3)

where τ f represents the frictional shear stress, σ n is the normal stress at the contact interface, and f = 0 . 05 is the friction coe ffi cient.

Fig. 2: Numerical model formulation of SPIF.

3. Results and Discussions

3.1. Validation of the FE model

The forming forces components in the three direction x , y , and z denoted by F x , F y , and F z during the forming process of frustums cone were presented in Fig. 3. The axial force F z has shown the highest magnitude compared to the in-plane forces F x and F y . F z reaches 600 N in the steady-state regime. While the in-plane forces varies with oscillations pattern between [ − 250N , 250 N]. The variability of F x and F y along with the relative stability of F z is an intrinsic characteristic of the SPIF process. The numerical results were validated against empirical formulae introduced by Behera et al. (2017) to predict the magnitude of the forming force in the steady-state regime.

1 . 57 0 d

0 . 41

0 . 09 ψ cos ψ

F zs = 0 . 0716 R m t

∆ h

(4)

where ∆ h is the scallop height measured in mm, given as:

∆ z 2 4 d

sin 2 ( ψ )

(5)

∆ h =