# Development of a Numerical Model of the Hot Air Staking Process Based on Experimental Data
## 1 Introduction  
Due to the optimized material adaption by using multi-material-structures, the final part properties can reach maximized performance and efficiency. This fact correlates with the substitution of conventional metal applications by their plastic counterparts and is associated with the increasing demand for joining methods which enable the reliable linking of incompatible materials as well. Based on its cost-efficient processing and typically low cycle time, plastic staking is one of the most commonly used joining processes in this field. It enables the reliable joining of two or more mating parts by having a form-locked and partly force-locked connection. As chronologically shown in Figure 1, the staking process is characterized by forming an added assembly component, which is called a rivet pin. Usually, the pin is constructively associated with the thermoplastic part. The forming of the rivet pin and the subsequent formation of the rivet head lead to an undetachable undercut [1]. In literature the commonly used staking processes are classified in dependence on their heat transfer mechanism. Consequently, they have to be differentiated in heat conduction (hot forming), convection (hot air staking), intermolecular friction (ultrasonic staking), and radiation (infrared and laser staking). The fundamental forming process is basically equivalent for all staking processes and thus independent of the type of energy input. However, as shown in Figure 1, the forming tool forms the rivet pin down to the top of the upper part. The characteristic geometry of the rivet head is incorporated into the forming tool. By using single stage processes, such as hot forming, the heating and forming take place simultaneously. In a double-stage process, such as hot air staking, the shaping happens only after the sufficient plasticization of the rivet pin. In contrast to the increasing number of staking applications, regarding the dimensioning of rivet joints there is no uniform designing tool available. Consequently, the optimization of process and design is mainly based on empirical tests and expert knowledge. Nevertheless, the German guideline DVS 2216-3 [2] provides some information about preferred rivet geometries. All design recommendations in the guideline are based on the diameter of the rivet pin and the volume of the rivet head. Finally, the length of the rivet pin is a calculated parameter to reach an adapted volume of the rivet head and pin. However, the focus of the guideline is primary on the ultrasonic staking, and it summarizes the experience of industry. Detailed information regarding further rivet processes as well as reachable joint properties or emerging weld lines are not included. In respect to the relationships between process, structure, and joint properties, it has to be pointed out that the research project [3] has already investigated the relevant influencing parameters regarding a load-bearing as well as design-compatible rivet geometry for different rivet processes. Additionally, the reachable joint properties were analyzed for different kinds of plastic as well as with and without fillers. The results show that the joint properties depend on the heat transfer mechanism and the plastic material, as well as the quality of the connection area between rivet head and rivet pin. Especially for single-stage staking processes, critical defects could be detected in the connection area which lead to a weakening of the joint strength. Furthermore, the research project pointed out that the surface of the rivet head does not correlate with the internal materials structure and the joint properties. However, the research project [3] did not clearly provide close examinations of the process-dependent heating and forming behavior and its effects on the resulting material structure (e.g., crystallinity) [3; 4]. Consequently, to obtain a comprehensive understanding of the interactions between heating and forming, a numerical process simulation is used in the present paper.