## 3 Experimental Validation and Results Discussion  
Some experimental tests were planned and carried out in order to validate the developed finite element model. The experimental activity consisted of stretching some sheets of aluminium-based alloy on a punch whose shape was a hemisphere with a radius of 60 mm. Each sheet had a rectangular shape of 220 mm \(\times\) 190 mm, and it was locked on the die through a blank holder with a circular hole of 83 mm radius (see Figure 6a). Figure 5: Numerical trend of the sheet thickness for different values of the friction coefficient \(\mu\) with a punch stroke of (**a**) 10 mm, (**b**) 20 mm and (**c**) sheet breaking. The tests were carried out by means of the equipment designed at the Technology and Manufacturing Systems Laboratory of the University of Cassino (see Figure 6b). It is constituted of an interface, to acquire data, made up of a PC, a multimeter KEITHLEY 2700, and a power supply ATTEN TPR3003T (1 in Figure 6b), an interface to manage the test parameters and to translate the punch (2 in Figure 6b), a mould creep (3 in Figure 6b), a punch and a load cell LUNITEK FT (4 in Figure 6b), a crossbar (5 in Figure 6b) actuated by a rotating screw jack (6 in Figure 6b), and an electric motor (7 in Figure 6b). [PERSON] et al. [19] further details on the experimental equipment that was used to perform the forming process on an AA6060 aluminium vessel are presented. The sheet was fixed on the die by means of a blank holder and eight screws, using a torque wrench and imposing a tightening torque of 45 Nm. During the tests, each sheet was stretched up to a predetermined value of the punch stroke. Three values of the punch stroke (10 mm, 20 mm and sheet breaking, as shown in Figure 7) were considered. Three sheets for each punch stroke were considered. Each stretched sheet was oriented and locked on the coordinate measuring machine Prismo Vast MPS of Zeiss(r) by means of standardized fixturing elements, as shown in Figure 8a. The inner and outer surfaces were measured by a probe with a tip radius of 3 mm, while a stylus length of 48 mm and 40 mm was used for the inner and the outer surfaces, respectively, of each stretched sheet. The part reference system was defined by measuring both the plane of the fixturing equipment on which the sheet was supported  
Figure 6: (**a**) Dimensions of the considered sheets (mm); (**b**) stretching equipment. Figure 7: Stretched sheets with a punch stroke of (**a**) 10 mm, (**b**) 20 mm and (**c**) sheet breaking. and the cylindrical surface of the sheet that was in contact with the blank holder, as shown in Figure 8b. Therefore, five measurement profiles at 1.5 mm from each other were measured along the \(y\) and \(z\) directions of the part reference frame (PRF) in the centre of each sheet inner or outer surface in order to underline the maximum value reached by the sheet during the stretching along the \(x\)-direction in the part reference frame (see Figure 9). Each profile had a length of 150 mm and it was constituted by about 150 measurements points. Therefore, 1500 points were measured on both the inner and the outer surface of each sheet. It was planned to measure a set of profiles on each outer and inner surface, instead of the whole 3D surfaces, in order to experimentally reproduce the two semi-profiles binding the generic section of the deformed sheet obtained through the numerical model. Figure 8: (**a**) Sheet location and fixturing on the coordinate measuring machine (CMM); (**b**) part reference system. Figure 9: Measurement strategy. The developed geometric algorithm was applied to the 1500 points measured on both the inner and the outer sides of each sheet experimentally stretched. The first step (see Figure 10) chose, among the five profiles measured along a single direction on the outer surface, the one characterized by the highest value of the \(x\)-coordinate in the part reference frame (PRF), because it corresponded to the apex of the semi-spherical samples.