# Assessment of the Durability of Threaded Joints
## 3 Experimental Results and Their Analysis
### Loosening Analysis  
The loosening of tension and bending connections is almost unexplored in scientific papers. The tightening forces of the structural members connected by threaded connections are an important factor in the reliability of an assembled unit or device. However, under cyclic loads, threaded connections loosen, which can lead to a loss of tightness of a heavily stressed vessel or to the failure of a piece of equipment. However, under cyclic loads, the threaded connections loosen, which can lead to a tightness failure of a heavily pressure vessel or to the failure of a component in the operational condition of the device. Due to the clamping of the contact surfaces between the flanges and the thread, the self-rotation of the nut, the plastic deformation in the thread and the flanges, the tension of the bolt and the tightness of the flanges may be reduced. The tensioning force must be measured for any method of tightening a threaded joint. In the experiments described in Section 3.1, it was observed that the stress of the studs decreased significantly after the threaded connections were assembled. Figure 8 shows the stress of the variation of the stud stress during the assembly of the threaded joint in the bending fixture. During the first clamping cycle, the tightening stresses were already reduced by \(\Delta\sigma\) when the stud was tensioned and the intermediate parts were compressed simultaneously (Figure 8a). The stud was repeatedly tensioned and the spacers were compressed to achieve the desired tightness. The amount of deformation of the stud was then measured by turning the nut and removing the external tension. As shown in Figure 8b, the stresses in the stud were reduced by an amount \(\Delta\sigma\). It was only after 3-4 repetitions of the tightening process that the desired stud tension and interference fit were achieved. If the tightening was limited to a single tightening, a significant (up to 16%) loosening of the threaded joint would be observed at the beginning of the cyclic bending. The loosening of threaded joints during cyclic deformation is characterised by the load (stress \(\sigma\)--strain \(\varepsilon\)) diagrams of threaded joints based on experimental  
Figure 7: (a)—one-sided fracture of the stud: 1—crack area; 2—normal propagation area of the crack; 3—accelerated propagation area of the crack; 4—brittle failure area; 5—trace of sample stoppage; (b)—two-sided fracture of the stud; (c)—the start of crack propagation in the root of the stud thread profile. data. Figure 9a-c provide a diagram of the stress variation in the bending plane of the stud edge layers. If, in the elastic phase, the maximum stresses did not exceed \(\sigma_{t}<\sigma_{y}\), then after 50 to 100 cycles the initial stress decreased to \(\sigma_{t1}\) and the bending stresses were almost unchanged \(\sigma_{b1}\approx\sigma_{b}\). As the crack spread, the tension decreased to \(\sigma_{t2}\) just before the fracture and the bending stresses to \(\sigma_{b2}\). If the stresses in the relative elasticity stage exceeded the yield stress \(\sigma_{t}>\sigma_{y}\) (Figure 9d-f), then after 50 to 100 cycles the initial stress decreased to \(\sigma_{t1}^{\prime}\)  
Figure 8: Tension stress changes (decreasing) during assembly of the threaded joint: (**a**)—initial tightening cycle; (**b**)—repeated tightening cycles. Figure 9: Loading diagrams of the threaded joints in the bending plane: when \(\sigma_{t}<\sigma_{y}\) (**a**–**c**); when \(\sigma_{t}>\sigma_{y}\) (**d**–**f**). and the bending stresses were almost unchanged at \(\sigma^{\prime}_{b1}\approx\sigma^{\prime}_{b}\). As the crack spread to the fracture, the stress decreased to \(\sigma^{\prime}_{t2}\), and the bending stresses decreased to \(\sigma^{\prime}_{b1}\). Figure 10 shows the tension reduction in the stud in a plane perpendicular to the bending (this value was continuously monitored by two sensors). After joint assembly, the stud stress was \(\sigma_{t}\).