# Clinching of High-Strength Steel Sheets with Local Preheating
## 2 Materials and Methods
### Numerical Simulation  
Mechanical clinching is an inexpensive joining process that involves cold-joining two sheets through localized hemming using a punch and die. In the traditional mechanical clinching method, the punch and die are utilized to shape the sheets and create an interlock between the lower and upper sheets. During the clinching forming process, the punch applies pressure to the upper sheet, causing it to flow onto the lower sheet. The lower sheet is supported by a rigid die. As a result, both sheets undergo plastic deformation, leading to the creation of a mechanically interlocked structure known as the clinched point [52; 53]. The typical steps of creating the clinched joint include clamping, pressing, bottom-forming, and interlock-forming (Figure 1). The pre-forming of the parts has a significant impact on the outcome of the joining process. Particularly, the pre-forming of the material on the punch side has a greater influence on the joining parameters compared to the material on the die side. Figure 2a shows the thickness of the neck (\(t_{N}\)), and the joint bottom thickness (\(X\)) and interlock (\(t_{u}\)) are the main parameters that significantly affect the load-bearing capacity of the clinched joint [27; 28; 29]. The goal of the numerical simulation was to identify the zones in the sheet metal that are moved to the area of the neck of the clinched joint. Ansys Workbench software was used for a numerical simulation of the clinching process. To simplify the task, a 2D model was employed due to the axial symmetry of the tools and the joint. Consequently, the anisotropy of the joined materials was not taken into account in the calculation. Figure 2b illustrates a schematic representation of the simulation model's input geometry, including the basic dimensions and the limiting conditions of the simulation. The nodal points of the die were removed to prevent movement during the simulation, while the nodal points of the punch elements were allowed to move only \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Thickness (mm)** & **Rp0.2 (MPa)** & **Rm (MPa)** & **A80** \\ \hline HX420 LAD+Z & 1.5 & 503 & 565 & 19.5 \\ HCT600X+Z & 1.5 & 343 & 593 & 27.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mechanical properties and thicknesses of joined materials. along the Y axis. Another boundary condition involved applying a force of 400 N on the sheet holder to secure the joined materials during the simulation of the CL joining. Once the desired path was achieved, the punch moved backward to its starting position, simultaneously releasing the force from the sheet holder. In this simulation, the punch, die, and sheet holder were considered perfectly rigid and non-deformable bodies, whereas the joined sheets were modeled as deformable bodies. A multilinear material model was employed to describe the response of the joined material to the applied load. The material model input values for the joined materials can be found in Table 3. The plastic portion of the material model followed the Holomon hardening law, with the strain hardening exponent determined experimentally based on a standardized tensile test. For the joined materials, a finite element mesh consisting of 2D quadrangular elements (PLANE 182) was used. These elements are recommended for simulating 2D  
Figure 1: Steps of the clinching process: (**a**) clamping, (**b**) pressing, (**c**) bottom-forming, (**d**) interlock-forming. Figure 2: Characteristics of clinching: (**a**) main parameters of clinched joint, (**b**) geometrical model and boundary conditions of clinching in numerical simulation. axis-symmetric problems. Each node of these elements had two degrees of freedom, representing displacements along the X and Y axes. The element size of the mesh was set to 0.1 mm. In processes like clinching, where both the sheet and the finite element mesh undergo significant deformation, it becomes necessary to remesh the elements at certain intervals [54].