PSI - Issue 82

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

85

2

(Alaswad et al.(2012); Habbachi et al. (2024)). This alternative has been adopted in many research applications, including automotive Peter et al. (2019), aerospace Gupta et al. (2021), and biomedical implants Marzouki et al. (2023). The forming force in SPIF is essential for the proper selection and design of forming platforms such robots and milling centers, which could be a critical design consideration Petek et al. (2009a). Tremendous research has been devoted to determining the e ff ect of individual input parameters on the forming force magnitude Iseki (2001) predicted the forming force based on plane-strain deformation using approximated deformation analysis. Dabwan et al. (2016) claimed that the sheet thickness is the predominant factor impacting the forming force, followed sequentially by the tool diameter and the step depth, however the influence of the feed rate is negligible based on experimental investigation. Recently Habbachi and Baksa (2024a,b) performed a parametric numerical-experimental approach to depict the e ff ect of four process parameters on the forming force amplitude. Results indicated that the sheet thickness has the major impact followed by the tool diameter, wall angle, and step size during the SPIF of Al 3003-O. A Taguchi method and analysis of variance were conducted by Kumar and Gulati (2018) to study and optimize the e ff ect of input factors. Findings outlined that the forming trend after reaching the peak strongly depend of the selected parameters, classified as safe, severe, and crucial. An autonomous on-line system was developed for fracture prediction in terms of location and time, relying mainly on the shape of the forming force time series based on skewness and statistical estimators as presented in Petek et al. (2009b). The authors insisted on the robustness and the reliability of the proposed system to respond well to di ff erent workpiece shapes, material types, etc. Fiorentino (2013) introduced a failure criterion based on the forming force. The interaction e ff ect has been rarely discussed. Indeed, Kumar et al. (2020) evaluated the interaction between the step size, wall angle, and the tool rotational speed. Outcomes indicated that the combination at high levels of two of these factors resulted in rapid increase of the forming force, which can adversely a ff ect the forming tool and associated hardware, and therefore must be avoided. It was presented that components designed with a higher wall angle can be formed with reduced forming force in case a higher spindle speed was coordinated. Based on the reviewed literature and the established connection between the forming process, hardware selection, and fracture occurrence in the formed part, the present study aims to investigate the interaction e ff ects of step size, wall angle, and sheet thickness on the maximum axial downward forming force.

2. Materials and methods

2.1. Materials

A tensile test based on ASTM E-8 standard tensile testing machine was carried out to derive the material properties for the commercial pure aluminum alloy Al 1050A-H16 sheets using dog-bone specimens with a thickness of 1 mm in accordance with ISO 6892-1. The average value of tensile specimens till the break was calculated and recorded as presented in Fig. 1. Thereafter, the Young modulus is E = 69 . 5 GPa, Poisson’s ratio ν = 0 . 33, and YS = 112 . 88MPa at 0.02%o ff set. The Voce hardening law was used to extrapolate the material behavior beyond the necking point, with the true stress–strain relationship defined as:

σ = σ 0 + Q 1 − e

( − βϵ p )

(1)