# Assessment of the Durability of Threaded Joints
## 2 Research Object  
The practice of operation of heavy loaded power, chemical, transport, and mining equipment and machinery, structures shows that fatigue failure of threaded joints between the elements (the lid and body) is often caused by bending loads that are not always predicted or that have not been appropriately assessed in terms of their effect. The bending of the studs or bolts in the flanged and fastening joints occurs due to structural specifics or direction of load. Here, the nominal stress of studs reaches or exceeds 380-450 MPa, and the number of cycles to crack initiation or final failure is within the area of low-cycle failure. The joints are subjected to up to 10\({}^{3}\)-5 \(\times\) 10\({}^{3}\) load cycles during tightening and to overloads in cases of hydraulic testing, start-up, shutdown, full or partial cooling, change of efficiency and capacity, and in certain emergency and servicing of the equipment. Additional axial cyclic loading appears as a result of initialization, shutdown, change in operating mode, and lid strain. The latter also causes the bending moment. Depending on the function of the bolt and the stud joint, the tightening may reach 0.65\(\sigma_{y}\) in various units. The structure of critical threaded joints used in mineral grinding mills is shown in Figure 1.  
During drum rotation (diameter: more than 10 m; rotational speed: up to 10 rpm), the bolted and stud joints are subjected to cyclic stress and some are subjected to bending. These joints must be protected against environmental impact (production dust penetrating into the threads).  
Workmanship defects (casting pores, pits, and cracks) are unavoidable due to the geometrical form of the body parts, lids, stands, supports, and other elements of the mill. Operational strain gauges show that during mill drum rotation, the stress variation in the retaining surfaces occurs due to the negative asymmetry cycle (cycle asymmetry coefficient \(r_{a}=\sigma_{min}/\sigma_{max}=0.6\ -0.7\)). The variable tension strain state that develops in the environment of workmanship defects requires special investigation. Due to the considerable mechanical and thermal effect, the element of the structure may show low-cycle fatigue cracks, and residual strain may accumulate. In this case, the parameters of the variable nonelastic strain process limit the designed durability. If the residual strain resulting from the plastic flow at the start of loading no longer accumulates after a certain number of cycles, this means that the structure has adapted to the load.  
The experimental investigation conducted on threaded joints has shown that in certain cases, the total stress caused by the tightening and cyclic bending reaches the plastic state and penetrates to a certain depth. Further repetitive variable loading affects the strength and reliability of the joint. It has also been noticed that the cyclic plastic strain no longer accumulates, i.e., the joint shakedown has taken place as soon as a favorable field of residual stress has developed after a small number of cycles. In the event of the violation of the shakedown conditions, plastic strain of the variable sign (usually local) may occur, or single-sign strain may grow in each cycle (progressive shape change), covering the entire element of the structure or a part thereof. Theoretical articles by the authors on the topic of slack provide a review of the cyclic strength margin of threaded joints.