## 3 Simulation and Optimization of the Joint
### Effect of the Axial Tensile Load  
Of all the loads, the axial load is an important factor affecting the strength of the joint. [PERSON] and [PERSON] [6] compared stress concentration factors values for pin and box under bending, axial and torsional loading. The results showed that stress concentration factors values of axial loading were greater than bending, while for torsion they were very small. [PERSON] et al. [27], through a series of full-scale fatigue tests, indicated that tension loads have a negative effect on the drill pipe and tool joint fatigue behavior. In actual work, the force acting on the joint is very complicated, including the pressure exerted by the rig, the weight of the joint itself, the buoyancy of the medium and the friction of the core. The force in the joints of a core barrel is generally between 100 and 150 kN. In the case of pulling out in a stuck state, the load may exceed 300 kN. To cover the actual force range, the range of axial tension during the simulation is 100-500 kN. In the simulation analysis of the equivalent stress distribution under the axial load, the constraint condition of the box joint is a fixed constraint, and the constraint condition of the pin joint is a uniform tensile load. The pin joint is subjected to a uniformly distributed tensile load. Figure 9 shows the equivalent stress distribution in the thread when the tensile load is 500 kN. Figure 9 shows that the equivalent stress concentration occurs at the relief notch because the relief notch is thinner than the threaded section. The equivalent stress in the pin and box joint assemblies decreases from the outside to the inside. For a single joint, the equivalent stress is reduced from the side closer to the inner-shoulder face to the side of the outer-shoulder face. In order to quantitatively study the stress distributions in the thread, the average equivalent stress and the maximum equivalent stress of each thread are compared. An equivalent stress path, as shown in Figure 10, is inserted into the pin joint under the tensile load. The stress path starts at point 1 along the helix to point 2. Each 360 degree rotation along the stress path is counted as one turn. Then, the sum of the stress values at the nodes is calculated for each turn. These nodes fall on the stress path when meshing. The sum of stress is then divided by the number of nodes to obtain the average equivalent stress on each thread, the results of which are is shown in Figure 11a. The maximum equivalent stress of each circle is shown in Figure 11b. The ordinate represents the average equivalent stress for each turn of the thread, and the number of threads is shown in Figure 6. Figure 11 shows that the distribution characteristics of the average equivalent stress in the thread under different axial tensile loads are as follows: the stress is high at the two ends and low in the middle, and the stress is highest near the inner-shoulder surface. A comparison of the curves shows that when the axial tensile load is low, the stress in each thread is relatively uniform. However, as the tensile load increases, the distribution of the thread stress becomes more uneven. The maximum equivalent stress of the thread has a similar distribution pattern as the equivalent stress, but the fluctuation is significantly larger than  
Figure 9: Stress distributions in the (**a**) pin joint and (**b**) box joint. the average stress. Both the average stress distribution and the maximum stress distribution indicate that the surface near the first thread is a dangerous section. When analyzing the stress distribution in the joint under the axial load, the friction between the thread surfaces can be ignored, and the contact surface is considered to have only normal stress. The results shown in Figure 12 were obtained under a tensile force of 500 kN. The compressive stress distribution in the contact surface is shown in Figure 12a. Similarly, the normal stress on the contact surface is also reduced from the inner-shoulder face side to the outer-shoulder side.