# Influence of Lubrication Systems on the Fatigue Strength of Bolted Joints
## 3 Experimental and Numerical Investigations
### Crack Initiation and Crack Growth  
The crack growth phase is defined by the difference between the number of cycles to failure and the number of cycles to crack initiation. For this purpose, a methodology was derived which, based on the change in frequency of the test system, allows direct assignment of the damage that has already occurred over the crack area. As an example, five individual frequency curves are shown for the variant without lubrication for the load amplitude F\({}_{\text{A}}\) = 5 kN (Figure 10). In addition, a master curve is derived as the mean value of the individual tests, and the beginning of the continuous frequency drop for this curve is shown as an example. The central issue describes the definition of the onset of damage, described as crack initiation. For example, the beginning of the continuous frequency drop (N(f\({}_{\text{max}}\))) or a critical frequency change rate (df/dN) can be defined as the crack initiation criterion. As the crack progresses, the frequency drops faster until an unstable behavior concludes with the failure by fracture. To define a crack initiation criterion, tests were stopped at different frequency drops to mark the already damaged area by heat-t  
Figure 10: Frequency–load cycle curves derived from the fatigue test for the samples without exemplary lubrication exemplary. By subsequently measuring the fracture surface, this procedure can be used to directly assign damage to the frequency drop. The greater the frequency drop, the larger the crack area marked by the heat tint. A correlation between crack depth and crack area with frequency behavior can be derived from a large number of tests. It can be seen that for a defined frequency drop, different maximum crack depths are produced, which can be attributed to the large number of different crack locations and the local loading there in each case. The systematic analysis of the frequency change df/dN shows that for a defined frequency change rate, a reproducible size of the crack area can be assigned. The load-dependent crack criterion chosen here is defined by the frequency change df/dN = \(-2\cdot 10^{-6}\) Hz/cycle (Figure 12). Considering this methodology, the comparison of the number of cycles for the beginning of the continuous frequency drop, the crack initiation, the crack propagation and to failure via fracture for the investigated lubricant variants is presented in Figure 13.  
Figure 11: Exemplary illustration of heat-tinted fracture surfaces stopped at different drops in frequency. (**a**) Example 1, frequency drop of \(-0.003\) Hz; (**b**) example 2, frequency drop of \(-0.004\) Hz. Figure 12: Definition of crack initiation criterion by a critical frequency–load cycle ratio. By lubricating the thread, it can be deduced, regardless of the type of lubricant, that not only is the time of fracture shifted to a higher number of cycles, but also the time of the crack initiation occurs later than without lubrication. Consideration of the thread friction coefficients determined in the torque/preload test does not allow the conclusion that the lowest thread friction coefficient leads to the latest crack initiation time. The relative movement resulting from the cyclic loading requires a more differentiated consideration of hypothesis I and of the experimental determination of the coefficient of friction. The simplified alternating sliding between the screw and nut thread due to a lower thread friction coefficient requires a characterization of the resistance of the friction conditions. Compared to the one-time tightening of the bolted joint in the standard test according to DIN EN ISO 16047, the repeated installation test or oscillating friction wear test represent approaches to characterize the friction conditions for cyclic loading. One way of classifying the friction conditions is given by the Stribeck curve [29] (Figure 13).