*2.2. Metallography*

Figure 2 shows the locations of microstructure observation. C represents the cold zone and H is the hot zone. To identify and measure the content of the quenched phases, the specimens were mounted in epoxy resin, ground, and polished to a mirror finish, using 400, 1000, and 2000 grit SiC paper, followed by metallographic grinding paste. Two-stage color tint etching with 4% picral solution and 10% aqueous sodium metabisulfite solution was used to observe the quenched phases. After two-stage etching, the martensite was brown, the bainite was black, and the ferrite was white with an optical microscope. Martensite, bainite, and ferrite were manually set as green, red, and blue, respectively, by ImagePro Plus 7.0 software (Media Cybernetics, Inc., Rockville, MD, USA). The area fractions of quenched phases were quantified.

**Figure 2.** The cutting locations of specimens.

## *2.3. Springback Measurement*

The springback measurement process is shown in Figure 3. The 3D scanning of the formed component was first conducted by a PRO CMM3500 optical coordinate measuring machine (NDI International, Waterloo, ON, Canada) and the point cloud data were obtained and processed by PolyWorks software (InnovMetric Software inc, Québec, Canada). By conducting calibration and alignment between polygon data and the original model of the component, the springback angle of the formed component could be accurately measured.

**Figure 3.** Flowchart of the springback measurement process.

Figure 4 shows the scheme of springback angle measurement. The outer contour and the inner contour are the cross sections of the formed component and the original component, respectively. θ2 is the sidewall angle of the formed component and θ1 = 20◦ is the original angle. θ2 − θ1 was defined as a springback angle.

**Figure 4.** The schematic of the springback angle measurement.

#### **3. Results and Discussion**

#### *3.1. Quenched Phases Analysis*

Figure 5 displays color metallography of the formed component quenched at different tool temperatures and micrographs, calibrated by Image Pro Plus 7.0. It can be found that the quenched phases of the cold zone are almost full martensite at heating tool temperatures of 25 ◦C and 600 ◦C, which indicates that the heating tool temperature has little effect on the quenched phases of the cold zone. This may be because the cooling rate of the blank in the cold zone is greater than 100 ◦C/s, much higher than the critical speed of martensite transformation. However, the occurrence of a small amount of ferrite and bainite in the cold zone may be caused by the large plastic deformation of the U-shape component during the forming [17,18]. Martensite decreases, while ferrite and bainite increase in the hot zone with the increase of the tool temperature. When the tool temperature is higher than 200 ◦C, the area fraction of martensite drops dramatically and reaches 13% at the tool temperature of 600 ◦C. The reason may be that the start transformation temperature of martensite is 405 ◦C [19] and when the isothermal quenching temperature is higher than the start transformation temperature of martensite, bainite phase transition occurs during continuous cooling, resulting in the decrease of martensite. When quenched at the tool temperature from 300 ◦C to 600 ◦C, the area fraction of bainite increases with the increase of the tool temperature and is close to 70% at the tool temperature of 600 ◦C. The isothermal quenching for 10 s at this temperature range, which is the transition temperature range of bainite [19], results in the rapid formation and the increase of bainite. Shipway et al. [20] have also showed that bainite transition is more likely to occur than martensite transition during the isothermal quenching at this temperature range. With the increase of the tool temperature, ferrite increases slightly. George et al. [21] have demonstrated that the area fraction of ferrite is less than 10% at the tool temperature of 400 ◦C, which was close to the 9% ferrite in this paper. However, George et al. did not make research on the tool temperature higher than 400 ◦C. The studies in this paper showed that the area fraction of ferrite was 17% at the tool temperature of 600 ◦C.

**Figure 5.** Two-stage color tint etched optical micrographs and manually identified microstructure images (**a**) 25 C; (**b**) 600 C; (**c**) 200 H; (**d**) 400 H; (**e**) 500 H; (**f**) 600 H. C represents the cold zone and H is the hot zone.

### *3.2. Springback Results*

Springback angles under different heating tool temperatures are presented in Figure 6. No matter how the tool temperature changes in the hot zone, the spingback angles in the cold zone are almost unchanged. The reason is that the materials in the cold zone have almost the same temperature history and almost full martensite and, thus, the internal stress releases caused by phase transformation expansion and transformation plasticity are almost consistent [22]. The springback angle of the hot zone decreases with the increase of the tool temperature. When the tool temperature is higher than 300 ◦C, the springback angle decreases and becomes almost stable at the tool temperature higher than 550 ◦C. According to the relationship between the area fractions of phases and tool temperatures, it can be seen that martensite begins to decrease at the tool temperature higher than 300 ◦C and bainite increases dramatically. According to Åkerström and Oldenburg [23], the hardness of martensite and bainite is 510 HV and 402 HV, respectively. The decrease of the springback angle in the hot zone is due to the increase of softer bainite. When the tool temperature is higher than 550 ◦C, the area fractions of martensite and bainite are almost stable and, thus, there is no obvious change in the springback angle.

The relationship between the springback angle and the area fractions of martensite, bainite, and ferrite at different tool temperatures are shown in Figure 7. It can be seen that different quenched phases and their contents, caused by different tool temperatures, have grea<sup>t</sup> influence on the springback of the components. The springback angle shows a positive linear correlation with martensite and a negative linear correlation with bainite and ferrite. The correlation coefficient indicates that there is a noticeable linear correlation between them. With the springback angle as the dependent variable and the area fractions of martensite, bainite, and ferrite as the independent variable, a multiple linear regression analysis was carried out and the goodness of the fit, R-squared value is 0.985. The results show that there is a strong linear relationship between the springback angle and the area fractions of martensite, bainte, and ferrite. By the multi-step iterative optimization method, the relationship between the springback angle and the area fractions of quenched phases was established and is shown as Equation (1).

$$\lambda = 3.233 \times (0.0469 f\_{\rm M} + 0.0439 f\_{\rm B} + 0.0005 f\_{\rm F}) - 12.1286 \tag{1}$$

where λ is the springback angle and *f*M, *f*B, and *f*F are the area fractions of martensite, bainite, and ferrite, respectively.

**Figure 6.** Springback angles under different heating tool temperatures.

**Figure 7.** The relationship between the springback angle and area fractions of the quenched phases.

The springback angles calculated by Equation (1) at different heating tool temperatures are given in Table 2. It is found that the maximum relative error is 7.32% and the angle difference is 0.04◦, which indicates that this equation can be used to accurately predict the springback of the formed component, based on the area fractions of the quenched phases. It is worth noting that Equation (1) is the relationship between the phase content and the springback angle, and the change of the tool geometry will lead to the change of the phase content, so after the tool geometry changes, Equation (1) is still applicable. In addition, Equation (1) is obtained in the range of ferrite content less than 20% and bainite content less than 80%, and if the phase content is beyond the range, it needs to be further verified.


**Table 2.** The average springback angle under di fferent heating tool temperatures.
