# Influence of Lubrication Systems on the Fatigue Strength of Bolted Joints
## 3 Experimental and Numerical Investigations
### Crack Initiation and Crack Growth
The Stribeck curve subdivides for the comparison of the friction coefficient \(\mu\) with the kinematic viscosity \(\eta\) into the following ranges: solid, boundary and mixed friction up to hydrodynamic friction. The variant without lubrication and the sealing with lubricant integrated into the topcoat are in the solid-state friction range. In the case of solid-state friction, the contact partners are in direct contact. The sealant is very thin and the rigidly anchored lubricant does not form a homogeneous film on the surface. Due to the onset of wear as a result of initial assembly and relative movement, there is direct contact between the screw and nut threads. The bonded coating systems and the lubricating oil are in boundary friction, where the surfaces are covered with a molecular boundary film and come into contact with the nut thread. In the case of the variants lubricated with grease, there is a local separation of the contact partners in certain areas due to the more pronounced thickness of the lubricating film. This results in its allocation to the mixed friction range. In principle, there is a dependence on the lubricant film thickness \(d\) and the roughness [25]. The assignment of the friction states represents an explanatory approach that can attribute the different crack initiation times to the different characteristics of the lubricant. The scatter of the crack initiation numbers is significantly larger for the lubrication with bonded coatings, greases or the oil than without lubrication or for the variant with sealing. Since the application of lubrication for these variants is manual, variation in the resulting lubricant film thickness cannot be ruled out and must be further characterized. Further validation of the durability of the lubrication  
Figure 13: (**a**) Schematic Stribeck curve; (**b**) frequency drop, crack initiation, crack propagation and number of cycles to failure by fracture. properties is carried out in the form of experimental testing of the friction conditions under and after cyclic loading. Based on the different crack initiation times and the experimentally determined fracture load cycles, the length of the crack propagation period can be evaluated via the difference between these variables. A comparison of the lubricant variants investigated shows that the crack growth is slowest for oiled bolts and that the phase from the time of incipient cracking to fracture is the longest. Hypothesis II is confirmed by the fact that the mobility of the lubricant has an influence on the crack propagation behavior. The prolongation of the crack propagation time is slightly improved for the sealant with lubricant integrated in the topcoat, which is due to the low mobility of the lubricant. In contrast, for bonded coatings and greases, there is a prolonged crack propagation phase, whereby the creep ability of the lubrication is lower compared to the lubricating oil and therefore the prolongation of the crack propagation phase is correspondingly less pronounced. The theory that the creep-capable oil settles at the crack front due to the onset of capillary action with a developing crack could be proven with the methods of material analysis, such as the scanning electron microscope (SEM) (Figure 14). By means of energy dispersive X-ray analysis (EDX), an increased carbon content can be detected at the crack front and between the crack egdes. The optical discoloration and the increased C-content are evidence for the presence of the oil.