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carried out by using cylindrical punch diameters of 20, 12and 10 mm, allowed verifying the likely enhancement of formability due to the bending effect by means of t0/R ratio. The specimen geometry for those tests was chosen in order to obtain a deformation state near plane strain,which also occurs in SPIF.2.2. Single point incremental forming testsA series of SPIF tests were carried out within the experimental plan exposed in Table 1. The setup described in Pérez-Santiago et al. (2011) was used to perform the tests following this testing methodology. The geometry was a conical frustum with circular generatrix, with the initial diameter of the truncated cone set to 70 mm, being theinitial drawing angle 20º and the generatrix radius 40 mm. The step down was set to 0.2 mm per pass. Tooldiameters of 10 and 20 mm were used. The rotation of the tool was free and the feed rate used for all tests was setto 3000 mm/min. Special lubricant Houghton TD-52 for metal forming applications was used in order to minimizefriction effects. The final depth and final forming angle were recorded just in the instant in which the failure took place. Three replicates of each SPIF test were carried out in order to provide statistical meaning to the results. Ascan be observed in Table 1, almost the same final depths, and consequently final forming angles, were repetitiveachieved for each case.Table 1. Series of SPIF tests carried outTool diameter T (mm)Final depthZf (mm)Final forming anglef (mm)20 13.4 / 13.4 / 13.4 52.79 / 52.79 / 52.7910 14.4 / 13.8 / 13.8 54.57 / 53.51 / 53.51The strain state was measured in the light of circle grid analysis, within a similar methodology to that latterlyperformed in Centeno et al (2012c), by using the 3D deformation digital measurement system ARGUS®. With this aim, a point pattern had to be created on every undeformed sheet blank by an electrolytic etching process. The Fig.5 (left) depicts the point pattern after deforming a metal sheet by SPIF until failure with a hemispherical formingtool of 10 mm diameter. This analysis provides the contour of principal strains at the outer surface of the final part, as shown in Fig. 5 (right). As said before, this was performed using the commercial software ARGUS®. As can beseen, the area of maximum logarithmic major strain is obviously located at the vicinity of the crack (notice thatorientation of the final part coincides in Fig. 5 left and right).1,() fff 2, 3,( 2, 3, It must also be observed that the crack develops from a certain depth at the forming wall having an upwarddevelopment to both sides, which was accurately captured by the measurement system. In fact, the measurementsystem was able to measure the deformation of the ellipses both above and below it, and therefore able tointerpolate the strains throughout the crack, providing the continuous contour map as depicted in Fig. 5 (right). As has been commonly observed, as for example in Silva et al. (2011) and Centeno et al. (2012c), metal sheets formed by incremental forming present a trend of principal strains within the forming limit diagram (FLD) that grows inthe first quadrant towards failure close to plane strain condition. In fact, the Fig. 6 depicts the principal strains atthe FLD of the previous final part formed by SPIF corresponding to the colored contour of major strain representedin Fig. 5 (right).Fig. 6. Principal strains at the FLD of the final part formed by SPIF.At this point it must be said that the points corresponding to the maximum level of major strains, those in red at Fig. 6, are processed by ARGUS® as mentioned above by means of an interpolation throughout the crack. In thissense, these points might represent the level of principal strains at fracture with certain feasibility. Nevertheless,the validity of these fracture strains must be verified with microscopic measurements. In fact, both the formabilityand the fracture strains were verified using microscopic thickness measurements by applying the samemethodology that was previously used with the stretch-bending tests. Actually, sheet thickness at fracture wasmeasured at several places around the final part formed in SPIF. As can be seen in Fig. 7 (left), the average thickness strain was evaluated at both sides just where the crack occurs, and therefore the average major strain at fracture was calculated. This evaluation was also carried out at the opposite wall with respect to that where thecrack appears, as can be seen in Fig. 7 (right), in order to validate the higher levels of achievable principal strains,corresponding to the points colored in yellow and orange in Fig. 6. 3. Results and discussion Based on the results of the series of Nakazima tests corresponding to the three different specimen geometries utilized (i.e. uniaxial, plane strain and biaxial strain), and using the fracture strains calculated respectively by ARAMIS® and from thickness measurements at the microscope, the conventional forming limits EFL and FFL are constructed. Finally, the Fig. 8 depicts the EFL and the FFL in a range of minor strains from -0.15 to 0.05 approximately. As can be seen, the EFL presents a straight evolution while the FFL seems to present the V-shape evolution expected for this kind of low-ductility materials, as was mentioned above. On the contrary, the level of major strains at fracture within the FFL at the first quadrant and close to plane strain condition differs to those formability levels shown in Fig. 6 for the case of SPIF. In any case, the validity of this fracture curve must be checked against other forming processes, such as the case of SPIF or stretch-bending by using small cylindrical punches. Actually, fracture strains, evaluated by measuring thickness at the microscope, for the highest formability corresponding to both series of SPIF and stretch-bending tests respectively (which in both cases coincides with the smallest forming tool considered, i.e. a forming tool of 10 mm diameter) are represented in Fig. 9. First of all, for the case of SPIF, the fracture strains calculated by applying this methodology are consistent with those registered by ARGUS® for the same case. Moreover, it can be easily noticed that this fracture strains are well above the FFL. It is well known that in the case of ductile materials, failure strains are above the FLC, being failure controlled by fracture with absence of necking, as discussed for instance in Silva et al. (2011) and Centeno et al. (2012c). In those cases, and depending on certain process parameters, the metal sheet deformed by SPIF could increase formability until the FFL. But the phenomenon captured for this low-ductility aluminum alloy consists on an upward displacement of the fracture limit of the metal sheet when it is deformed by SPIF.