3.1 Forming force
3.1.1 Hot-cracking characteristics
The straight groove experiments at different forming temperatures and ultrasonic amplitudes were carried out to study the forming force during the forming process. A piezoelectric quartz force sensor was used to determine the axial force. The evolution of the axial force at different temperatures and amplitudes is presented in Fig 6. To quantify the effect of temperatures and amplitudes on the axial force, the average axial force was calculated and compared (Fig 7). It shows that the axial force decreases with the rise in temperature. This might be ascribed to the activation of the non-basal slip systems, resulting in a decrease in the flow stress, as reflected in Fig. 2.
The application of UV during the process of warm incremental forming can also effectively reduce the axial force. The axial force decreases with an increase in the amplitude, as shown in Fig. 7. The average axial force was 139 N at 250 °C in the absence of UV. It decreases by 8% (128 N), 13% (121 N), and 20% (111 N) under UV amplitudes of 3.8 µm, 7.8 µm, and 11.2 µm, respectively. The rate of reduction is significantly high at high temperatures (e.g., 250 °C). This might be attributed to two reasons. On the one hand, with the activation of the non-basal slip systems, the application of UV can promote the movement of dislocation and reduce the deformation resistance of the material [25, 26] (Fig. 2). On the other hand, the friction coefficient and wear rate between the forming tool and the sheet increases with an increase in the temperature. The application of UV can reduce the extent of contact and friction between the friction pairs, thus, reducing the resistance during the forming process [27].
3.2 Formability
A truncated cone with varying wall angles was used as the target part to study the formability of the AZ31 Mg sheet under conditions of the UV-assisted warm SPIF. The forming angle at the cracked location P was considered as the maximum forming angle (θmax) (Fig. 8). The value of θmax is calculated based on the forming depth (h) at rupture, as demonstrated in Eq. (1).
The deformed parts under conditions of varying temperatures and amplitudes are shown in Fig. 9. The calculated θmax values are summarized in Table 2. The θmax at 150 °C in the absence of UV is used as the reference, and the increase in the value with other parameters is also summarized in Table 2. The average value of θmax was 40.8° at 150 °C. When the temperature increases to 200 °C and 250 °C, the value increases to 49.3° and 53.2°, respectively. A significant increase in the θmax value is observed when the temperature increases from 150 °C to 250 °C, which indicates an improvement of the formability of the sheet. The extent of activation of the non-basal slip systems increases with an increase in the temperature. In addition, dynamic recrystallization contributes to the increase in the plastic deformation ability of the magnesium alloy.
It can also be seen from Table 2 and Fig. 9 that the forming limit is improved significantly when UV of appropriate amplitude is applied in the warm incremental forming process. At all the three temperatures, the θmax values first globally increase and then decrease with an increase in the amplitude. The maximum value is reached when the amplitude of UV is 7.8 µm. The θmax value at 150 °C (40.8°) in the absence of UV was recorded, and a remarkable formability improvement of 54% (62.8°) was observed for the part at 250 °C under the UV amplitude of 7.8 µm. An increase in the rate by 18% was observed when the value was compared with the value recorded at the same temperature, 250 °C (53.2°), in the absence of UV. The results indicate that the extent of formability improvement depends on the effect of the temperature and the UV amplitude.
From previous studies, it can be inferred that under warm conditions, the non-basal slip systems of the magnesium alloy are activated. The plastic deformation continues to accumulate with the progress of the process of forming. When the plastic deformation accumulates to a certain degree, the aggregation and entanglement of dislocation occur, and the deformation resistance increases. UV can promote the movement of dislocations, reduce the deformation resistance of the material, and improve the plasticity of the material [25, 26]. However, there is a saturation value for the ultrasound energy absorbed by the material. On the other hand, the dynamic recrystallization (DRX) phenomenon can be observed during the process of warm deformation of the magnesium alloy. The application of UV can promote DRX [27-29]. It facilitates grain refinement and increases the number of grain boundaries. Thus, the progress of crack propagation is inhibited near the grain boundaries. Therefore, crack growth is suppressed, and the formability of the material is improved.
Table 2 Maximum forming angle.
Temperature (°C)
|
Amplitude
(µm)
|
Maximum forming angle (°)
|
Increasing rate
(%)
|
No.1
|
No.2
|
No.3
|
Average
|
150
|
0
|
40.1
|
41.4
|
40.8
|
40.8
|
--
|
3.8
|
42.6
|
42.6
|
41.7
|
42.3
|
3.7
|
7.8
|
42.6
|
43.1
|
43.5
|
43.1
|
5.6
|
11.2
|
39.6
|
41.0
|
39.5
|
40.0
|
-2.0
|
200
|
0
|
50.2
|
48.9
|
48.7
|
49.3
|
20.8
|
3.8
|
53.3
|
49.8
|
51.5
|
51.5
|
26.2
|
7.8
|
54.3
|
52.7
|
50.6
|
52.5
|
28.7
|
11.2
|
46.3
|
50.2
|
48.1
|
48.2
|
18.1
|
250
|
0
|
51.6
|
54.1
|
53.8
|
53.2
|
30.4
|
3.8
|
60.9
|
61.8
|
63.0
|
61.9
|
51.7
|
7.8
|
63.0
|
62.6
|
62.8
|
62.8
|
53.9
|
11.2
|
62.8
|
62.9
|
60.3
|
62.0
|
52.0
|
3.3 Geometry accuracy
Low geometry accuracy is the major disadvantage of the incremental forming process as the geometry accuracy obtained via incremental forming currently cannot reliably reach suitable levels specified by industrial users. The geometry inaccuracies are primarily caused by the sheet bending effect, continuous local springback around the tool, and global springback that occurs after the tool and clamping devices are released. The errors of the parts are primarily reflected by the springback angle of the blank holder area and the bulging of the side wall.
Considering the characteristics of the springback generated during the process of incremental forming, the springback angle θ1 and the sidewall curl radius ρ of the part are used for the accuracy evaluation of the part, as shown in Fig. 10. The springback angle θ1 reflects the springback of the blank holder area following the process of unloading. The target value of θ1 is 145°. The sidewall curl radius ρ reflects the degree of bulging of the part. After the experiments are completed, the cross-section of each deformed part is measured, and the values of θ1 and ρ are determined. Better part accuracy is reflected by smaller θ1 and larger ρ values. The θ1 and ρ values are summarized in Table 3 and compared in Fig. 11.
Fig. 11(a) shows that the springback angle θ1 decreases with an increase in the forming temperature. For instance, when the forming temperature increases from 150 °C to 200 °C and 250 °C under the amplitude of 0 µm, the errors of the θ1 values reduce from 3.9° to 2.2° and 1.8°, respectively. A similar trend is observed for all other UV-assisted samples, indicating that an increase in the forming temperature can improve the geometry accuracy in the blank holder area of the part. However, Figure 12(b) shows that the sidewall curl decreases with an increase in temperature. This indicates that the bulge of the sidewall becomes significant under these conditions, reducing the geometry accuracy of the part. This might be explained by the increased thermal gradient of the material layers under conditions of high temperature.
Figure 12 shows the temperature difference at the interior and the exterior of the sheet. The traced point is selected at the sidewall, and a flexible thermal couple is inserted into the platform to measure the temperature. The result indicates that the temperature difference is significant, and the difference increases with an increase in the temperature. During the forming stage, the temperature at the interior of the sheet is significantly higher than the temperature at the exterior. During the cooling stage following the process of forming, the sheet shrinks and curves inwards. This is driven by the release of thermal stress induced by the sharp thermal gradient along the thickness. This aggravates the bulge at the sidewall. Therefore, although the springback angle decreases with a rise in the temperature, the bulging problem becomes more serious.
UV significantly influences the bulge of the sidewall (ρ) during the process of warm incremental forming (Fig 11(b) and Table 3). The rate of reduction of bulging increases with an increase in the amplitude at all tested temperatures. The maximum reduction rate of ρ is 9.2%, 10.8% and 9.8% for the parts at 150 °C, 200 °C, and 250 °C, respectively when the applied frequency was 11.2 µm. The effect of UV on the value of the springback angle θ1 is relatively weak during the forming process. The maximum fluctuation is less than 0.7°.
Table 3 Spring-back angle and sidewall curl (the target value of θ1: 145°)
Temperature (°C)
|
150
|
200
|
250
|
Amplitude(µm)
|
0
|
3.8
|
7.8
|
11.2
|
0
|
3.8
|
7.8
|
11.2
|
0
|
3.8
|
7.8
|
11.2
|
ρ (mm)
|
246.3
|
250.7
|
265.7
|
269.0
|
217.2
|
215.9
|
224.5
|
240.8
|
207.8
|
209.9
|
221.1
|
228.2
|
θ1 (°)
|
148.9
|
148.9
|
149.2
|
148.6
|
147.2
|
147.6
|
147.5
|
147.9
|
146.8
|
146.8
|
147.4
|
146.8
|
Deviation of θ1 (°)
|
3.9
|
3.9
|
4.2
|
3.6
|
2.2
|
2.6
|
2.5
|
2.9
|
1.8
|
1.8
|
2.4
|
1.8
|
3.4 Simulation results
3.4.1 Temperature distribution
The simulation results were compared. The temperature distribution of the sheet measured by the thermal imager is shown in Fig. 13. The temperature values at points P1 to P6 in Figs. 13(a) and (c) are compared in Fig. 14. Before forming, the temperature gradually decreases from the center to the edge, and the temperature at point P1 is the maximum. With the progress of the forming process, the maximum temperature position gradually shifts from P1 to P3, which is on the sidewall of the part. This is because the shape of the sheet changes with the progress of the forming process. This results in distance variation between the sheet and the electric pipes. The increase in thermal radiation results in a high temperature of the sidewall. Figure 15 also compares the temperature evolution of P3 during the forming process (determined through simulation and experiments). The results reveal that the temperature of P3 fluctuates at different stages of the forming process (see the local schematic diagram in Fig. 15). The trend is well predicted by simulation techniques. According to Figs. 13-15, the simulation well reflects the characteristics of the sheet temperature distribution. The difference between the simulated and experimentally obtained temperatures at all points from P1 to P6 was within 4 °C, and the simulated temperature error was less than 1.6%.
3.4.2 Stress and strain analysis
Figure 16 compares the equivalent stress of the deformed part under conditions of varying amplitudes. Significant stress concentration is observed in part not subjected to ultrasonic vibration (especially the corner area). The stress concentration can result in rupture during the forming of the part. It is obvious that the stress distribution of the part is improved when UV is applied (Figs. 16(b)-(d)). The overall stress distribution is more uniform in this part when compared to the part not subjected to UV. The number of stress concentration zones in the corner area of the part reduces.
To further investigate the effect of UV on the degree of stress reduction, the stress values at points P1-P5 in Fig. 16(a) are presented in Fig. 17. It is obvious that the overall stress values at each point under conditions of UV are significantly lower than the values recorded in the absence of UV. UV with amplitudes of 3.8 µm, 7.8 µm, and 11.2 µm was applied. The decrease in the average value of stress at each point was 14.2%, 11.2%, and 19%, respectively. These results indicate that UV helps reduce the flow stress and alleviate the stress concentration during the process of warm incremental forming.
Figure 18 shows the equivalent plastic strain distribution of the part under conditions of the warm SPIF process. The points P1-P5 in Fig. 18 (a) are selected, and the equivalent plastic strain magnitudes of each point are shown in Fig. 18 (b). During the incremental forming process, the forming tool is processed from the periphery to the center of the part. As the points P1 to P4 are located at the top of the part, they were fully deformed by the forming tool. The equivalent plastic strain values at each point were >0.6. It is obvious that the overall equivalent plastic strain value at each point under conditions of UV is larger than the values recorded in the absence of UV, especially for the points P1 and P3 at the straight wall. It indicates that under conditions of a high frequency of intermittent pressing, the equivalent plastic strain increases during the process of warm incremental forming. This makes the deformation of the material easier and reduces the extent of material stacking during the deformation process. This might also be one reason that the formability of the sheet is improved when UV is applied at appropriate temperatures.
3.4.3 Comparison of shape accuracy
After forming, the section contour of the part is measured and compared with that generated from simulation studies, as shown in Fig. 19. The blank holder area of the sheet is almost straight and selected as the reference. For comparison, a simulation using the conventional method is also carried out in which the temperature distribution of the sheet is assumed to be homogeneous, and evolution is not taken into account. Figure 19 shows that obvious deviation occurs at the sidewall and the bottom for the simulations. The maximum deviation in the vertical direction is 3.2 mm when simulation following the conventional method. The deviation is 2.1 mm when the fully thermal–mechanical coupling method is adopted. The average deviations are also calculated for the two simulations, which indicate that a reduction of 35.2% is achieved following the fully thermal-mechanical coupling method.
During the experiment, it was observed that the center of the sheet sinks downward during the heating stage (before forming). Pre-expansion attributable to the increased temperature is also observed, as shown in Fig. 20 (a).
The simulation conducted following the fully thermal-mechanical coupling method can reflect the pre-expansion process, as can be seen in Fig. 20 (b). The maximum height achieved during the pre-expansion process under conditions of heating reaches approximately 8 mm. This deformation is remarkable and has a significant influence on the deformation of the sidewall. The conventional method assumes that the temperature of the sheet is constant and does not take into account the thermal deformation occurring using the actual forming process. Therefore, the prediction accuracy of the fully thermal-mechanical coupling method is better than that of the conventional method.