# Study on L-Bending Springback of 45 Steel Leather Cutting Tool Coupled with Local Induction Heating
## 2 Materials and Methods
### Numerical Simulation  
The L-bending process of 45 steel sheets was simulated via the finite element model (FEM) in the ANSYS workbench 2022 R2 software to explain the springback mechanism and predict the springback rate. The induction heating process was realized based on the sequential coupling technique, and local heating was realized by importing the results of the transient thermal analysis into the stress analysis [26]. The transient thermal analysis of the sheet is first performed by applying a temperature field of 800 \({}^{\circ}\)C. The bending simulation process is then divided into several time steps with corresponding temperature cooling values to ensure the accuracy of the simulation. The VOCE model is a nonlinear function that fits a plastic strengthening curve of a material based on its properties. The accuracy of the simulation can be improved by VOCE modeling. The nonlinear isotropic hardening model based on the VOCE function was used in the ANSYS software, as shown in Equation (1):  
\[\sigma=\sigma_{0}+R_{0}\epsilon_{p}+R_{\infty}(1-e^{-\hbar\epsilon_{p}}) \tag{1}\]  
where \(\epsilon_{p}\) is the plastic true strain, and \(\sigma_{0}\), \(R_{0}\), \(R_{\infty}\), and \(b\) are the four material constants of, the initial yield point, linear coefficient, exponential coefficient, and exponential saturation coefficient, respectively. The hardening model is based on the isotropic hardening law, which has the largest springback in comparison to other hardening laws and has high prediction accuracy. The [PERSON] isotropic yield criterion was used since the anisotropic effect played a minimal role in the bending process and was negligible [27]. The stress-strain relationship of 45 steel at room temperature and 800 \({}^{\circ}\)C was obtained in a tensile experiment [23; 28]. The parameters of the VOCE model were obtained by fitting the stress-strain curve, as shown in Table 3. The stress-strain curve obtained by fitting is shown in Figure 4. The VOCE hardening model accurately predicted the behavior of 45 steel between the yield and tensile strength regions. The forming mold and sheet were regarded as flexible bodies in the FEM, and due to the complexity of the sheet model, the tetrahedral mesh with a smoother transition  
Figure 3: Temperature change curve of the heating process. was selected. The non-contact and non-heating areas of the mold had a mesh size of 4 mm, which accelerated the speed of the solution. In order to ensure the accuracy of the simulation results, the mesh size of the induction heating area and the contact area were set to 1 mm, and the thickness direction of the sheet was set to at least 3 layers of mesh. The total number of meshes in the model was 55,026, and there were 97,060 nodes. The two stages of the simulated machining process were loading and unloading. The loading phase refers to controlling the angle required for outer tool rotation. The unloading phase refers to the outer tool returning to its original position. The springback was generated after unloading. The bending angle and springback were obtained by solving the element Euler's angle. The thermal conductivity, specific heat, and other thermophysical characteristics of 45 steel were considered in the finite element model [29]. The friction coefficient in the simulation was set to a fixed value of 0.1 because the bending experiment did not employ lubricating oil, which was similar to the friction coefficient study of many earlier bending investigations. This study would not go into detail about the tiny temperature change that occurs inside the mold during the local heating phase. The VOCE model employed in this study solely took into account the impacts of plastic strain and temperature because the influence of the strain rate was minimal at low mold velocities [27]. The link between the rotation angle of the outer mold and the bending angle of the sheet was established experimentally because the bending mechanism regulated the bending angle of the sheet through the rotation of the outer mold.