*2.3. Incremental Tube Expansion*

The experiments in incremental tube expansion were performed in a Deckel Maho CNC machining center equipped with a single point hemispherical tool (*rtool* = 5 mm) made from a cold working tool steel (120WV4-DIN) hardened and tempered to 60 HRc. The bottom tube end of the specimens was fixed to prevent sliding and rotation, and the tool path was programmed to perform a multi-stage incremental forming sequence consisting of an upward helical trajectory with a constant semi-angle Ψ = 15 ◦ (Figure 4a). The pitch *p* between two consecutive stages was set to 2 mm and the initial tool depth at the beginning of the first stage was set to 2 mm with respect to the upper tube end (Figure 3b). Table 1 summarizes the main process parameters. Ψ ° 

Three different tests were performed under the above-mentioned experimental conditions and a total of eight forming stages were needed for each test to observe of an incipient failure by fracture close to the plastically deformed tube end (Figure 3c), as is later discussed in the paper.

**Figure 4.** Schematic representation of incremental tube expansion showing (**a**) the single point hemispherical tool path and (**b**) the multi-stage forming strategy. A photograph of a specimen after eight forming stages is included in (**c**) together with a detail showing the final cracked surface.

**Table 1.** Main parameters used in the incremental tube expansion tests.

