## 3 Results and Discussion
Single-point incremental forming process is a localized plastic forming process because the tool moves incrementally, forming the part in small steps. Usually, the punch follows a helical path and its movement causes compression or less elongation in the direction of motion (\(\varepsilon_{1}\)) and more stretching in the circumferential direction (\(\varepsilon_{2}\)) and therefore \(\varepsilon_{2}\) can exceed \(\varepsilon_{1}\). Figure 6: (**a**) Strain on x direction for FEM using material 89 for simulating PEHD 1000; (**b**) strain on x direction determined experimentally for PEHD 1000; (**c**) strain on y direction for FEM using material 89 for simulating PEHD 1000; (**d**) strain on y direction determined experimentally for PEHD 1000; (**e**) major strain for FEM using material 89 for simulating PEHD 1000; (**f**) major strain determined experimentally for PEHD 1000; (**g**) minor strain for FEM using material 89 for simulating PEHD 1000; (**h**) minor strain determined experimentally for PEHD 1000; (**i**) thickness reduction for FEM using material 89 for simulating PEHD 1000; (**j**) thickness reduction determined experimentally for PEHD 1000. Material 24 for polyamide gives the following differences: 2.55% for the specific strain \(\varepsilon_{\chi}\), 1.44% for the specific strain \(\varepsilon_{\chi}\), 0.52% for the major strain \(\varepsilon_{1}\), 14.7% for the minor strain \(\varepsilon_{2}\), and 0.52% for the relative thickness reduction, as presented in Table 2. Material 89 for polyamide gives the following differences: 4.21% for the specific strain \(\varepsilon_{\chi}\), 2.74% for the specific strain \(\varepsilon_{\chi}\), 2.84% for the major strain \(\varepsilon_{1}\), 15.55% for the minor strain \(\varepsilon_{2}\), and 2.99% for the thickness reduction. The differences given by material 24 for polyethylene are 4.63% for the specific strain \(\varepsilon_{\chi}\), 1.38% for the specific strain \(\varepsilon_{\chi}\), 4.63% for the major strain \(\varepsilon_{1}\), 6.58% for the minor strain \(\varepsilon_{2}\), and 4.52% for the relative thickness reduction. The differences given by material 89 for polyethylene are 4.21% for the specific strain \(\varepsilon_{\chi}\), 1.85% for the specific strain \(\varepsilon_{\chi}\), 1.59% for the major strain \(\varepsilon_{1}\), 9.29% for the minor strain \(\varepsilon_{2}\), and 3.27% for the thickness reduction. The analysis of the results shows that in all cases the largest difference between the data obtained experimentally and the data obtained by simulation occurs for the minor strain \(\varepsilon_{2}\). While 15.55% seems high, a closer look reveals that there is only a 1.28% difference in absolute value between the simulation and the experiment. Considering all these results, a good correlation is found between the experimental and theoretical results with regard to the strains. Figures 7 and 8 show the variation graphs of the forces in the forming process obtained by simulation and experiment for polyamide and polyethylene with material model 89. For the two figures, the left columns (Figures 7a,c,e and 8a,c,e) represent the results of the FEM simulation, while the right columns (Figures 7b,d,f and 8b,d,f) represent the experimental results. The figures present the results obtained for the simulations using material model 89, for which the results were closer to the ones obtained experimentally. A very close agreement between the curves obtained by simulation and those obtained experimentally in terms of the allure of the curves can be observed from the analysis of the graphs presented. It is worth mentioning that both the simulations and the experiments were performed using the same geometrical data (punch diameter, step, and wall angle of the part). When examining the graphs of the forces obtained by simulation, it can be seen that, especially in the case of the vertical force F\({}_{2}\), a \"noise\" is present on the graph. This noise occurs as a result of the loss of contact between the punch and the blank for very short sequences of time.