## 2 Methods
### Methodology for Evaluating Joint Quality  
Various scientific studies have shown that the mechanic joining strength of two powder metallurgically produced components is largely determined by the quality of the joining zone. Defects within the joining zone such as pores strongly reduce the strength [18; 33]. German [34] found that for sintered steel, an increase in density from 90% to 100% nearly doubles the tensile strength. Surface roughness leads to an increase in the distance between the joining surfaces and thus makes the joining process more difficult, so the surfaces should be as smooth as possible [21; 25].  
Evaluating the joint quality can be very challenging and is usually carried out on the basis of mechanical properties by means of tensile tests [16; 21]. However, for this study, a new methodological approach is developed to investigate the contact ratio of the sintered joint. The basis for this is the metallographic preparation of the specimen shown in Figure 4.  
Figure 4: Size of the selected flat cylinder to determine the contact area after sintering (**left**) and stacked green parts before sintering (**right**) (scale in centimeters).  
Figure 3: Nabertherm VHT40/16 cold wall retort furnace used to sinter the parts presented in this study.  
This method provides a closer insight into the joint itself and facilitates the analysis of the contact ratio of the joint. The contact ratio is described as the ratio of the area of both components in contact to the unconnected area, based on the total sample length. To experimentally investigate this ratio, the manufactured and sintered specimens are cut in half orthogonally to the joint plane and both sides are metallographically prepared so that the cutting cross-section is visible. Then, after grinding and polishing, a panoramic image of the contact zone is taken with a Keyence VHX-5000 microscope, which is a standard method in metallography. Using an automated color-contrast algorithm of the Keyence software, the remaining gap between the parts of the joining zone is colored green (compare Figure 5). The resulting image is fed into a developed Matlab script, which For this, the vertical pixel rows of the images are evaluated pixel-by-pixel for the occurrence of the coloring. If the script identifies green pixels, this area is classified as not connected, and vice versa. The ratio of connected to unconnected areas is then determined along the length of the contact area to be measured. The procedure is visualized in Figure 5. This methodology also allows for a determination of the average gap height by automatically counting the number of green pixels per vertical pixel row and calculating the average value over the entire sample length. This can then be converted into a micrometer measurement based on the magnification.  
This procedure yields the contact ratio across the entire cross-section, but it only represents a one-dimensional example measurement of the entire contact area. In addition, it can only be applied to sintered parts, as green parts can not be metallographically analysed by this method since they would simply fall apart. All specimens are roughly cut in the middle, and due to the cylindrical specimen shape, it is not expected that significant deviation occurs over other cross-sections of the contact area. To transfer these experimental data from the sintered part to the green part contact and from the two-dimensional analysis of sections to the full contact zone, a simulation model is used (see Section 2.6).