# Application of Digital Twin in the Industry of Axial Hollow-Wall Pipes
## 4 Testing and Maintenance of Axial Hollow Pipe Products
### Analyze Defects and Optimize the Design  
Figure 17 displays the strain-angle characteristic curve of the socket end pipe wall, obtained from experiments and simulations. The results indicated that, in the range of 1-8 degrees of offset angle, the mechanical behavior of the pipe joint was primarily influenced by the frictional force between the pipe wall and the sealing ring, the fit between the chamfered end of the straight pipe and the diameter changed area at the end of the socket, and the structural mechanical performance of the pipe socket end. These factors collectively contributed to resisting the mechanical effects of the angular deviation on the pipe joint and ensuring sealing integrity. As the offset angle increased to the range of 9\(-\)12 degrees, the maximum stress at the pipe joint reached 49 MPa, entering the plastic deformation stage. The contact between the pipe wall and the sealing ring gradually diminished, resulting in a reduction in frictional force. Consequently, the seal integrity of the joint started to gradually diminish as well. The fit between the chamfered end of the straight pipe and the diameter changed area at the end of the socket, and the structural mechanical performance of the pipe's socket end, became the primary factors resisting deformation. During the experiments, slight leakage occurred at the pipe joint at this stage, leading to the termination of the test. In contrast, during simulations, the strain rate at the pipe joint rapidly increased at this point. Figure 18 illustrates a cloud map of the pipe joint simulation. Within the figure, the term \"S. Mises\" indicates that the stress value corresponded to the equivalent stress value calculated, based on the Mises yield criterion. The Mises yield criterion follows the fourth strength theory of material mechanics, also known as the theory of distortion energy. This theory considers distortion energy as the primary cause of material flow failure. In other  
Figure 16: Numerical simulation. Figure 17: Variation of strain at the end of the pipe. words, when the equivalent stress at a particular point within the object reaches the yield limit under specific deformation conditions, the point enters a plastic state. Furthermore, in Figure 18, the term \"PEEQ\" represents the equivalent plastic strain, which signifies the cumulative plastic strain resulting from the entire deformation process. It is computed as the sum of the absolute values of plastic strain. PEEQ provides an intuitive representation of the model's plastic strain condition after being subjected to stress. The simulated cloud map reveals that, when the straight pipe was inserted into the socket end, the stress concentration mainly occurred in the region where the sealing ring was positioned. However, the magnitude of this stress was relatively low, reaching a maximum value of only 0.246 MPa (Figure 18a). Consequently, this residual stress was unlikely to have a significant impact on the subsequent utilization of the pipeline. When the angular deviation and static water pressure were applied simultaneously, the socket end of the pipe material exhibited a quality control zone, characterized by extreme stress. This zone was observed on the offset angle side of the pipe joint (Figure 18e) and in the outer region where the pipe diameter deformed (Figure 18d). In these areas, the pipe wall underwent significant compression deformation. Importantly, this quality control zone aligned with the quality control zone identified during the pipe end-forming process test. Thus, it reaffirmed the significance of appropriate processing temperature design in ensuring the quality of the pipe material product. The sealing performance of the offset angle test was primarily influenced by the frictional force provided by the sealing ring, the deformation of the socket end of the pipe, and the fit of the socket joint. The sealing ring plays a crucial role in ensuring sealing integrity.