# Application of Digital Twin in the Industry of Axial Hollow-Wall Pipes
## 3 Establish a Digital Twin of the Pipe End-Forming Process
### Pre-Production Test
In the 50 s heating group, the pipe material's temperature increased by prolonging the heating time, which reduced the material's elastic modulus and increased the elongation at fracture; thereby, avoiding inner wall cracking. However, whitening the diameter changed area of the inner wall at the end of the socket still occurred, as depicted in Figure 8(2). Figure 6: Temperature variation. Figure 7: End-forming diagram. In the 60 s heating group, the pipe material's elastic modulus further decreased, enhancing its plastic deformation capability. The pipe body exhibited no whitening, cracks, or flanging, indicating that the material was adequately heated and reached the required temperature. The results were ideal, as illustrated in Figure 8(9). In the 70 s heating group, the pipe material's inner wall showed no whitening or cracks, but slight flanging occurred. This suggests that excessive heating of the pipe material resulted in a low elastic modulus and decreased stiffness. The sudden change in the sealing ring placement during the flaring process caused outward deformation of the pipe opening, as depicted in Figure 8(7). In the 80 s heating group, extensive flanging and cracks appeared on the outer wall, with widespread cracking on the inner wall (Figure 8(4,5)). The material lost its ability to recover elasticity after deformation, and its strength was insufficient to support the flaring process. Additionally, the weak point of the sealing ring deformed due to excessive temperature, as depicted in Figure 8(8). In the 90 s heating group, significant sagging and slight burn marks were observed on the pipe wall. Insufficient stiffness caused the pipe to sag, and partial overheating and carbonization occurred. The subsequent flaring process could not be sustained (Figure 8(3,6)). The experimental results indicated that, within the range of 15-122 \({}^{\circ}\)C, as the temperature increased, the tensile strength and stiffness of PVC pipes decreased, while elongation at fracture increased. Beyond 122 \({}^{\circ}\)C, the tensile strength and stiffness of the PVC pipes continued to decrease with increasing temperature, but the elongation at fracture decreased. This was because the thermal vibration of the PVC polymer chains increased with temperature, reducing the intermolecular forces between the chains and resulting in a decline in the overall mechanical properties of the material, but an increase in its ductility. However, when the temperature exceeded 122 \({}^{\circ}\)C, the low intermolecular forces were insufficient to resist deformation caused by external forces, leading to a decrease in the material's ductility (elongation at fracture). The peak value of 122 \({}^{\circ}\)C was not fixed and varied depending on the type and proportion of materials used in the pipe production [19; 20; 21]. Nevertheless, the tendency of the elongation at fracture of this PVC material to initially increase and then decrease with temperature has been confirmed [22; 23; 24]. The duration of end-forming heating plays a critical role in determining the tensile properties of rigid polyvinyl chloride (PVC) pipes. Based on the experimental results, it was  
Figure 4.0 Defect forms: (**1**) Small cracks on the inner wall, (**2**) Whitening on the inner wall, (**3**) Rupture of pipe end, (**4**) Small cracks on the outer wall, (**5**) Through cracks, (**6**) Sagging, (**7**) Flanging, (**8**) Sealing ring deformation, (**9**) Qualified products. found that a heating time of 60 s was most suitable for achieving the desired outcomes at the ambient temperature (15 \({}^{\circ}\)C). Additionally, the preheating temperature of the stamping equipment could be set within a range of 70-80 \({}^{\circ}\)C, which met the requirements. However, considering the importance of reducing energy consumption, a preheating temperature of 70 \({}^{\circ}\)C was deemed more appropriate.