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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3

where σ and ϵ p are the flow stress and plastic strain, respectively. However, σ 0 , Q , and β are material constants. Eq. 1 can be rearranged into the expression Eq. 2 :

σ = σ s − k v e

( − n v ϵ p )

(2)

The material hardening parameters were identified as: σ s = 149 . 831MPa, k v = 33 . 136 MPa, and n v = 1077 . 35. The corresponding true stress–strain curve used for simulation is shown in Fig. 1.

Fig. 1: True stress-plastic strain curve.

2.2. FE model

The finite element methods (FEM) is a powerful tool that enable the simulation of ISF process and therefore capture the qualitative and quantitative trends. In the current study, a fully 3D elasto-plastic FE model was considered. Therefore, a truncated cone has been adopted as a benchmark part. FE simulations were conducted in ABAQUS 6.13 Explicit solver considering the high material non-linearities and large deformation. Fig. 2 depicts the numerical model developed for the SPIF process. To be close to reality and experimental setup, three main instances were considered, the blank sheet which was assumed to have isotropic property and meshed with shell elements (S4R) with reduced integration points. Five reduced integrations points were applied through the sheet thickness. The tool and the binder were treated as a rigid bodies surfaces. The interaction at the interface sheet / tool and sheet / binder is governed by the Coulomb’s friction law expressed in EQ. 3. Without any indication, in addition to the profile toolpath, the standard process parameters are as follows: step size ∆ z = 0 . 6 mm, wall angle ψ = 60 ◦ , maximum drawing depth h = 43 . 3mm,