# Assessment of the Durability of Threaded Joints
## 3 Experimental Results and Their Analysis
### Loosening Analysis
After 50 to 100 cycles of stress-controlled cyclic bending, the stud t decreased by the amount \(\Delta\sigma_{t}=\sigma_{t}-\sigma_{t1}\). For a certain number of cycles before the crack occurs, the tension was almost constant. As the crack spread, the strain decreased, and the difference just before the fracture compared to a stable process was \(\sigma^{\prime}_{t}=\sigma_{t1}-\sigma_{t2}\). No self-turning of the nut was observed in the tested connections. All threaded joints of the appropriate diameter were tested with the same device, so the deformation of the contact surfaces of the intermediate parts is almost irrelevant to the results obtained. The variation in stud stress during the loading with a controlled strain (\(\epsilon=\text{const. }\)) cyclic bending process is related to the crimping of the contact surfaces of the stud and the nut, the shear of the first turns, the bearing surface of the crimping of the bearing surface of the nut, and the deformation in the gap environment. The latter factor must be distinguished from the others as it has the greatest influence. From the experimental data obtained, it can be concluded that, if the assembly has been carried out by multiple turns of the nut, the stress on the stud at the beginning of the load is reduced by a maximum of 5% for \(\sigma_{t}>\sigma_{y}\) and by about 3% for \(\sigma_{t}<\sigma_{y}\). In the general case, the relaxation of the nut-stud-nut system is made up of several components:  
\[\Delta\sigma_{t}=\Delta\sigma_{tb}+\Delta\sigma_{tn}+\Delta\sigma_{td}+\Delta \sigma_{t}^{>} \tag{3}\]  
Based on the experimental data obtained by the authors, a relationship between the stud tension stress and the size of the crack, expressed as \(h_{cr}/d\) (\(h_{cr}\) is the depth of the crack, \(d\) is the diameter of the stud shank), was established, as shown in Figure 11.  
Figure 11: Tension stress dependence of crack parameters. Figure 10: Loading diagrams of threaded joints in the plane perpendicular to bending: (**a**)—initial tightening cycle; (**b**)—at the start of cyclic loading; (**c**)—before fracture. In the relatively elastic stage, the stresses due to tension and bending at the beginning of the deformation are represented by dashed lines 1 and 2. After the first few cycles, the stress decreased from \(0.8\sigma_{y}\) to \(0.76\sigma_{y}\) and remained stable for a long time. The stress magnitude as the crack started and spread is shown in curve 3. If the initial stress was \(0.7\sigma_{y}\), the magnitude of the stress varied with the crack according to curve 4. This chapter presents a study on the tension stress in threaded joints during the different phases of cyclic loading, starting from the assembly. By tightening the stud and multiple turns of the nut, it is possible to avoid torsional stresses (which significantly reduce the strength of the stud) and stabilize the tension already in the tightening process. The following failure process parameters were obtained and used in the next section to analyse the shakedown of the threaded joints: the geometry of the crack, its propagation patterns, and the magnitude of the stress.