# Assessment of the Durability of Threaded Joints
## 3 Experimental Results and Their Analysis  
### Experimental Procedures  
The experimental investigation was carried out on M52\(\times\)4 joints made of 38 XH3 MA steel (chemical and mechanical properties according to the standard GOST 5632-2014: \(\sigma_{0.2}=800\) MPa, \(\sigma_{u}=910\) MPa, \(E=2.07\) GPa, \(\psi=59\%\), with normalization heat treatment). The stud thread root radius \(r_{c}=0.4\div 0.6\) mm.  
A special testing methodology and designed equipment were developed intended for thread joint testing, and stiff tension-bending conditions were reproduced.  
The especially self-designed fixture with the threaded joint was fitted in the TIRA test machine TIRA test 2300, max. load 100 kN (TIRA GMBH, Schalkau, Germany) and subjected to the axial load (Figure 2).  
Furthermore, the following measurement tools were used: dynamometer (in TIRA test 2300)\(-\pm\)0.5% accuracy; discontinuous deformation meter DDA 50 (50 mm base)\(-\pm\)1% accuracy; computer metering system with analog-to-digital converter SPIDER-8; data registration and processing program CATMAN--EXPRESS.  
The threaded joint consisting of the stud (1) and two nuts (2) was tightened (Figure 2a). The desired tension value and tightening of the intermediate parts were achieved by periodically tensioning the stud and turning the nut. The nuts (2) rested on the supports (3), with the intermediary parts (4) and rollers (5) between the latter. These enabled the supports (3) to turn in relation to the intermediary parts. The force _F(t)_ acting in the direction of tension (Figure 2b) generates a bending moment _M(t)_. A force acting in the compression direction produces a bending moment _M_*(_t_). The supports (3) and the nuts (2)  
Figure 1: Fragment of the mineral grinding mill: (**a**) stress concentration areas in the pressure vessel stud joints; (**b**): 1—in the stud (bolt)–nut joint; 2—in the free-threaded region; 3—in the transitional threaded region; 4—in the smooth region (due to unevenness occurring during surface processing); 5—in the stud-body joint.  
were turned over the hinge during the clamp of the upward and downward movement of the clamp of the testing machine, and the stud (1) was bent at the same time.  
Two strain gauge sensors (6) were attached to the opposite sides of the sample with their axes coincident with the plane of the neutral layer. They were used to measure the tightening stress and its change during the test. The deformation in the outer layers of the stud was measured by two other strain gauge sensors (6), and the extreme stresses \(\sigma_{max}\) and \(\sigma_{min}\) were determined.  
The displacement values \(s(t)\) and \(s^{\star}(t)\) were measured during the first cycle, when the predicted stresses \(\sigma_{max}\) and \(\sigma_{min}\) were achieved. The initiation and propagation of the crack in the stud was determined by the fluorescent magnetic particles method (ISO 9934-1:2016 Non-destructive testing. Magnetic particle testing. Part 1: General principles) and periodically stopping the test and disassembling the threaded joint.  
After the first measurements, the threaded joint was reassembled and re-tightened. Each time the position of the nuts had to be the same as during the cyclic strain process prior to disassembly of the joint. This was achieved using auxiliary nuts and pins (7) that hold the stud (1) in position relative to the nuts (2). The calculated force of the first loading cycles was determined using the tension variation cycle. Further strain was carried out according to the displacement registered during the first cycles. The testing machine was then stopped to measure the crack and register the force of the last cycle. Following measurement, the nut-stud-nut system was reassembled, and further application of the strain was resumed starting with the force registered. Then, it was moved to the fixed displacements. The maximum and minimum cycle load was measured during crack propagation.