# Development of a Numerical Model of the Hot Air Staking Process Based on Experimental Data
## 3 Results and Discussion  
### Experimental Study to the Heating and Forming Behavior by Using the Hot Air Staking Process  
Figure 3 shows the time-dependent melt formation during heating for a heating time t\({}_{\text{E}}\) between 0 s and 8 s. The melt formation starts at the outside and continues towards the middle of the rivet pin. One advantage of PP as a material is that the plasticized and recrystallized areas are very well recognizable by the deviating materials structure in comparison to the structure after injection molding. While at short heating times a non-plasticized area remains in the middle of the rivet pin, an almost complete melting of the protruding rivet pin can be observed from a heating time t\({}_{\text{E}}\) of 8 s. As shown in Figure 4, the increase of the generated melt layer as a function of the heating time shows an almost linear or slightly progressive course, which indicates an even energy input during hot air heating. However, based on the microscopic analyses in Figure 3, a higher thickness of the melt layer could be detected on the upper side of the rivet pin than on its outside. The reason for this effect is assumed to be the area-dependent flow behavior of the hot air, the associated specific heat transfers into the material, and the heat accumulation during gas dissipation, which forms on the forming tool located in the hot air pipe. The systematic consideration of these effects is a current concern in the present project. The experimental investigations pointed out that the minimal heating time \(t_{E}\) depends primarily on the air temperature \(T_{A}\) and the air flow rate \(Q_{A}\)[10]. Simultaneously, there is a significant dependence on the selected joining force \(F_{J}\). In this context, Figure 5 shows the comparison of the melt formation as well as the formed joint for two significant different heating times \(t_{E}\). A heating time \(t_{E}\) of 3 s present a clearly deviant melt volume in comparison to the volume of the protruding rivet pin (see Figure 5a). Nevertheless, a complete forming of the rivet pin is still possible. However, a high percentage of cold forming must take place during the forming process. At the end, the joint shows four different main structural zones in the rivet head. On the one hand, there are areas (I) made of plasticized, formed, and subsequently recrystallized material, which are mainly located in the side areas of the rivet head. On the other hand, areas (II) could be detected which still have their material structure, induced by the injection molding process, and were thus subject to predominantly cold forming. Consequently, it is expected that these areas will have an increased stress state. The areas (II) extend into the lateral areas of the rivet head and lead to a structurally uneven formation of the joint. Nevertheless, no open connection or defect could be detected during the hot air staking process. Between the areas (I) and (II) there are areas (III) with increased shear stress during forming. The melt shears are generated at the structural border of the solid material during forming because of the materials flow. Finally, area (IV) shows an undefinable weld line in the rivet head. The cause of the weld line cannot be finally clarified on the basis of the experimental data. Therefore, the evolution of the individual zones during the process is subsequently analyzed with the aid of numerical process simulation. Figure 4: Melt formation characterized by the molten area \(A_{Melt}\) as a function of the heating time \(t_{E}\), the molten area is associated with Figure 3.  
Figure 3: Melt formation shown by thin sections of the rivet pin for different heating times (transmitted-light microscopy). Process parameters: material polypropylene (PP), diameter rivet pin \(d_{P}=3.0\) mm, air temperature \(T_{A}=300\)\({}^{\circ}\)C, air flow rate \(Q_{A}=75\) L/min.