# Development of a Numerical Model of the Hot Air Staking Process Based on Experimental Data
## 1 Introduction
The basic challenge in the numerical simulation of a staking process is the change of the plastic material from solid to molten state and back during staking. Additionally, the thermal condition has a primary influence on the resulting material structure and must be considered with sufficient accuracy. Thus, the simulation model has to consider the elastic-plastic material behavior in the solid state as well as the viscous flow behavior of the plastic melt. Regarding the numerical analysis of the manufacturing process, in which solids interact with fluids, various calculation approaches exist. On the one hand, polymer injection forming (PIF) was simulated in [5] by means of a coupled fluid structure calculation. In this case, the sheet metal was linked with the plastic part, by using the Euler-formulation and  
Figure 1: Main principle of a staking process, (**a**) before staking, (**b**) end position of the forming tool, (**c**) return of the forming tool after staking. [PERSON]'s description. Regarding the simulation of the staking process, this approach could not apply, because of the continuously changing material state during forming. On the other hand, processes, in which solids interact with fluids, were calculated with pure structure code. In [6] and [7] the viscous flow behavior of adhesives during a clinching process was simulated in numerical simulation by using the rate-power-law. Nevertheless, even with this process simulation, the definition of the melt range was carried out in advance. Additionally, the literature provides some information about the numerical simulation of infrared staking [8; 9]. In this regard, the viscous flow behavior of the plastic melt was neglected. Furthermore, the elastic-plastic material behavior was only considered in the temperature range of 25 \({}^{\circ}\)C to 100 \({}^{\circ}\)C.  
In summary, the current literature confirms that the numerical process simulation, in which solids interact with fluids, is basically possible. Nevertheless, the current work has the limitation to assign the local material state (viscous or elastic-plastic material behavior) in advance. The current literature also shows, that the numerical simulation of staking processes investigates in fact the heating and cooling behavior in the influence to the tensile strength [8; 9]. Nevertheless, all simulations were carried out without the consideration of the viscous material behavior of the melt. Beyond that, no work is known on process simulation which provides information about macroscopic errors, such as weld lines or cavities due to shrinkage. However, based on the state of the art, the following scientific approach can be defined. In comparison between simulation and experiment, the influence of design, material, and process should be analyzed regarding the double-stage process hot air staking. In this regard, the heating and forming behavior for this process should be investigated. The aim is to create a simulation model, based on experimental data, close to reality, to predict the melt formation during heating as well as the materials structure after forming. The simulation should give some information about the minimal heating time of the rivet pin to form the rivet head and should predict the potentially weak points of the joint. Additionally, the numerical simulation should already increase the process transparency for future investigations in regard to the linking between the joint properties and the physical values, such as materials stress and strain.