The specifications of the casing head and casing coupling used in the experiment are 13–3/8 in. The diameter of the casing head is 339.7 mm, and the wall thickness is 9.7 mm. The diameter of the casing coupling is 339.7 mm, and the wall thickness is 10 mm. The casing head and casing coupling are shown in Figure 1. The threads of the casing head and casing coupling are trapezoidal threads with a thread tooth height of 0.062 in, a pitch of 0.2 in, and a taper of 1/16.

The material of the casing head is J55 steel, with a yield strength of 380 MPa and a tensile strength of 518 MPa. The material of the casing coupling is 30CrMo steel, with a yield strength of 758 MPa and a tensile strength of 862 MPa. The chemical compositions of casing heads and casing couplings are shown in Table 1.

Three working conditions were designed in the experiment to test the tripping tensile load of the casing head and casing coupling. The working conditions were as follows: loosening the casing head and casing coupling by half a buckle, loosening one buckle, and loosening three buckles. The experiment first uses a machine to completely tighten the casing head and casing coupling, then inverts the casing coupling the relevant number of turns according to the number of buckles to be loosened, and then the casing head and coupling were installed in the composite loading experimental system (maximum tensile load is 2,500 t) as shown in Figure 2A for the experiment. The schematic diagram of the experimental process is shown in Figure 2B. The composite loading experimental system provides tensile load on the casing head and casing coupling. After the experiment starts, stretch the casing head and coupling until they are tripped. After the test, the casing head and casing coupling were cut to observe the damage results at the thread, and samples were taken for scanning electron microscopy to analyze the thread damage mode. The model of the scanning electron microscope is TESCAN MIRA LMS + Quantax 200 XFlash 6|60.

The tensile test results are shown in Figure 3. It can be seen that more threads are exposed at the connection position between the casing head and the casing coupling. The tensile loading during the experiment is shown in Figure 4. The tensile force of the composite loading system was loaded at a constant speed. When the casing head and casing collar were pulled apart, the tensile force of the composite loading system would also decrease rapidly. During the loading process, the loading rate of the tension was 120 kips/min, which was 533.76 kN/min.

The tensile test results are shown in Table 2. The relationship between the minimum tensile load for tripping and the number of loose buckles in the experiment is shown in Figure 5. It can be seen that with the increase in the number of loosenesses of the casing head and casing coupling, the minimum load required for the two to trip continuously decreases. When the number of loose buckles increases from half a buckle to one buckle, the minimum load required for tripping decreases from 5,933 kN to 5,434 kN, a decrease of 8.4%. When the number of loose buckles increases from one to three, the minimum load required for tripping decreases from 5,434 kN to 3,876 kN, a decrease of 28.7%. The main reason for this phenomenon is that the number of threads connecting the casing head and the casing coupling decreases as the number of loose threads increases (Wang et al., 2020). At the same time, due to the existence of the taper, the contact area between threads will also decrease as the number of loose threads increases.

The experimental results of the casing head and casing coupling are shown in Figure 6. It can be seen that there are many broken filaments of different lengths at the casing head, and there are also many broken filaments on the casing coupling. The broken filaments can be inferred that the threads were broken during the tripping process of the casing head and the casing coupling. At the same time, it can be concluded from the different lengths of the filaments that the thread breaks are partial breaks and not complete breaks. The black substance on the thread surface is the lubricating oil used in threaded connections.

In order to further observe the damage of the trapezoidal threads of the casing head and casing coupling, wire cutting was performed on the threaded part. The cut entities are shown in Figures 7, 8. Figure 7 shows the damage results and cross-section of the casing head. From Figure 7A, it can be seen that the overall damage to the thread is small. At the same time, because the tooth height and pitch of the thread are small, the damage is almost invisible to the naked eye. In Figure 7B, it can be seen that the damage results in the thread. First, there are unbroken filaments at the thread, and second, the top of the thread is deformed. It can be seen that there is plastic deformation and partial fracture at the top of the thread of the casing head.

Figure 8 shows the damage results and cross-section of the casing coupling. It can be seen from Figure 8A that the thread is relatively complete as a whole, and no signs of damage are found. From Figure 8B, we can see that the cross section of the thread is very intact, and no deformation can be seen.

It can be seen from the above results that during the tripping process of the casing head and casing coupling, the damage was mainly concentrated on the casing head part, and almost no damage was found on the casing coupling. The main reason for this phenomenon is that the strength of the casing head is lower than that of the casing coupling. During the tension tripping process, the thread belonging to the casing head will first undergo plastic deformation, and at the same time, local threads will break to form filaments. The main reason for the different lengths of the filaments is that during the experiment, the casing was placed horizontally, which was affected by gravity. Subsequently, the fit between the threads will produce a small amount of offset due to the gap existing in the loosening.

In order to determine the damage mode of the thread at the casing head, the damaged part of the casing head was sampled and observed using a scanning electron microscope. The SEM observation position is shown in Figures 9A, B, and the SEM results are shown in Figure 9C. The observation scales for this position are 10 μm, 5 μm and 1 μm. It can be seen that the microstructures at different scales are dominated by dimples, so it can be inferred that the wire drawing formation method of thread damage is ductile fracture.

Based on the above analysis, the whole process of tripping the casing head and casing coupling under tensile load can be obtained. Under the action of tensile load, the threads of the casing head and casing coupling begin to interact. The threads of the low-strength casing head subsequently undergo plastic deformation. As the tensile load continues to increase, ductile fracture occurs in the plastic deformation area of ​​the thread, eventually causing the casing head and casing coupling to trip.

The setting of the numerical model should be consistent with the actual object. Considering that there are too many threads on the casing head and casing coupling, and the thread tooth height is small relative to the wall thickness of the casing head (1.5:10), it is not conducive to meshing. At the same time, the structure of the casing head and the casing coupling is symmetrical to the axis position. Finally, considering the practices of other scholars (Wang et al., 2020), the numerical model is established as the cross-section part of the solid model. The specific numerical model is shown in Figure 10. The number of threads in the model is 21. The parameters of the threads are the same as in Section 2 of this article. As shown in the figure, the red part is the casing head model, and the blue part is the casing coupling model. Hexahedral mesh is used in the modeling process, the mesh type is C3D8R. The boundary conditions of the model are set to make the entire model symmetrical about the z-axis, and the edge position of the casing head is fixed. The stretching position is arranged above the casing coupling.

The commercial software Abaqus was used to perform numerical model calculations. Considering that there is a large deformation process, such as thread destruction, in the model calculation, the simulation algorithm adopts the explicit dynamics algorithm. The contact between the casing head and the casing coupling is set to ‘General contact (explicit),’ the friction formula is ‘Penalty’, and the friction coefficient is 0.3 (Swissi et al., 2019). The material model of the casing head and casing coupling is an elastic-plastic material model, and the specific parameters are shown in Table 3.

Through comparative analysis with experimental results, the appropriate mesh size can be obtained, thereby ensuring the accuracy of numerical simulation and improving calculation efficiency. The experimental results when the casing head and casing coupling were loosened by one buckle were selected as a reference to verify the mesh size. The mesh has six sizes to choose from 0.05 mm, 1 mm, 2 mm, 3 mm, 4 mm, and 5 mm. The comparison of the minimum tensile load required for tripping simulated by meshes of different sizes and the experimental results is shown in Figure 11. It can be seen that as the mesh size decreases, the simulation results of the minimum tensile load required for the casing head and casing coupling to trip have decreased. When the mesh size is 1 mm, the simulation results are already close to the experimental results. The results of 0.5 mm are close to the results of 1 mm, but the time required for simulation will increase significantly. In order to perform numerical simulation more accurately and efficiently, the grid size is selected to be 1 mm.

After the mesh size of the numerical model is determined, the accuracy of the model needs to be verified by comparison with experimental results. The accuracy verification is mainly carried out from two aspects, namely, the minimum load required for model tripping and the damage result of the model mesh.

The comparison between the numerical simulation results and the experimental results of the minimum tensile load required for model tripping is shown in Table 4. It can be seen that when the number of loose buckles is half, the numerical simulation results are larger than the experimental results first, while when the number of loose buckles is one and three buckles, the numerical simulation results are relatively smaller. From the perspective of errors, the errors in the three working conditions are 167 kN, 234 kN, and 176 kN, respectively. The error ranges are all within 5%, which is an acceptable error. The model damage results are shown in Figure 12. It can be seen that the threads of the casing head are broken, but the threads of the casing coupling are intact, which is consistent with the experimental results. Through comparison of these two aspects, it can be considered that the error of the numerical simulation results is acceptable.

By analyzing the stress distribution diagram, it can be obtained that the stress distribution of the casing head and casing coupling during the stretching process, and then understand the vulnerable locations of the casing head and casing coupling. Figures 13, 14 show the stress distribution diagrams in different states when the casing head and casing coupling are loosened by 1 and 7 buckles, respectively. It can be seen from the figure that the stress of the threaded part is larger than that of other parts, that is, the areas with the highest stress are concentrated in the threaded part. It can be seen from Figures 13A, B that the maximum stress area is concentrated in the thread root area. Figures 14A, B show that the maximum stress area is concentrated at the contact position between the casing head and the casing coupling thread, and there is also a maximum stress area at the thread root. Comparing Figures 13, 14, it can be seen that during the tension tripping process of the casing head and casing coupling, the maximum stress area is mainly the thread contact head position and the thread root. It can be seen from Figure 13C and Figure 14C that the thread fracture occurs in the area with the greatest stress, which is also the head position where the thread contacts.

From the above analysis, it can be inferred that during the stretching process of the casing head and casing coupling, the stress is mainly concentrated on the thread part. The stress in the thread part is mainly concentrated at the thread root and the head position where the threads contact. When the thread strength is less than the tensile strength, the thread will be damaged, and the damage location will be at the head position where the thread contacts.

The simulation results of the tripping of the casing head and casing coupling under different working conditions are shown in Figure 15. It can be seen that both the casing head and the casing coupling can be fully tripped. The minimum tensile load required for tripping is shown in Table 5, and the line graph shown in Figure 16 can be obtained by processing it. It can be seen that as the number of loosening of the casing head and casing coupling increases, the minimum tensile load required for tripping continues to decrease.

By fitting the experimental and numerical simulation results in Figure 16, the relationship between the minimum tensile load F m required for tripping and the number of loose buckles n d can be obtained, as shown in Eq. 1. F m = 4753.65 e − n d 2.6 + 2141.21 (1)

In previous research (Sacquepey and Spenlé, 1993), the minimum tensile load required for bolt tripping can be calculated using Eq. 2. F m = 0.757 τ m π d L e (2) in the formula, τ m is the ultimate shear strength, ⅆ is the basic major diameter, L e is the thread engagement length.

When the research object is bolted, the L e parameter in formula (2) changes regularly. For the trapezoidal thread of the casing head and casing coupling, as the number of loose buckles increases, the thread engagement length decreases. At the same time, the contact length between threads will also be reduced (see Figures 13, 14). Therefore, this study combines formula (1) and formula (2) and obtains formula (3) as follows. F m = A τ m π d e B n d + C (3)

In formula (3) A, B, and C are constants. Substituting the parameters of the casing head and casing coupling studied in this study into formula (3), the calculation formula of this study can be obtained, as shown in formula (4). F m = 0.011 τ m π d e − n d 2.6 + 2141.21 (4)

For different types of trapezoidal threaded casing, the minimum tensile load required for the casing head and casing coupling to trip can be obtained through experimental results and combined with Eq. 3. For the same trapezoidal threaded casing in this study, the minimum tensile load required can be calculated using Eq. 4.