Rigid-Plastic Finite Element Analysis of Radial Extrusion of Tee Pipe Fitting

Literature Overview

This paper published in the Journal of Huazhong University of Science and Technology (1991, Vol. 19, No. A3, pp. 55-62) by Xia Juchun, Ding Yongxiang, Li Zan, and Hu Guoan from the Department of Mechanical Engineering, Huazhong University of Science and Technology, presents a rigid-plastic finite element analysis of the radial extrusion process of tee pipe fittings. The study uses the Lee-Kobayashi rigid-plastic finite element method to simulate the metal flow during radial extrusion and to calculate the strain rate field and stress field distributions. The research is significant because it provides a theoretical and computational framework for understanding and optimizing the radial extrusion process of tee pipe fittings, which are critical components in piping systems.

Theoretical Framework and Mathematical Model

The study begins by establishing the theoretical basis for the rigid-plastic finite element analysis of radial extrusion. The Lee-Kobayashi method is a rigid-plastic finite element method that assumes the material behaves as a rigid-plastic solid, meaning that elastic deformation is neglected and the material yields immediately upon loading. This assumption is valid for metal forming processes where the plastic deformation is much larger than the elastic deformation.

The mathematical model of the rigid-plastic finite element method involves several key equations. The equilibrium equations express the balance of forces in the deformed body. The constitutive equations relate the stress to the strain rate through the flow stress function of the material. The kinematic equations express the strain rate in terms of the velocity gradient. The boundary conditions include the velocity boundary conditions at the die and the stress boundary conditions at the free surface.

The study verifies that the metal flow during radial extrusion of a tee pipe fitting can be treated as a plane strain problem. This simplification is valid because the deformation is primarily in the plane of the tee fitting, and the out-of-plane deformation is negligible. The plane strain assumption reduces the three-dimensional problem to a two-dimensional problem, which significantly reduces the computational effort while maintaining good accuracy.

Simulation Results and Metal Flow Analysis

The finite element simulation of the radial extrusion process of a tee pipe fitting produces detailed information about the metal flow, strain rate field, and stress field. The metal flow pattern shows how the material deforms as it is extruded radially to form the branch of the tee fitting. The strain rate field shows the distribution of the strain rate throughout the deformed region, which is critical for understanding the material deformation and the risk of forming defects such as cracks or folds.

The stress field shows the distribution of the stress throughout the deformed region, which is critical for understanding the forming forces and the risk of forming defects such as excessive thinning or buckling. The simulation results reveal that the metal flow during radial extrusion of a tee pipe fitting is complex, with significant variations in the strain rate and stress fields. The branch root of the tee fitting is a region of high strain rate and high stress, which is a critical area for the quality of the final product.

The simulation results also reveal the effect of process parameters on the metal flow and the stress field. The extrusion speed, the die geometry, and the material properties all have a significant effect on the forming process. The extrusion speed affects the strain rate field and the forming forces. The die geometry affects the metal flow pattern and the strain rate distribution. The material properties affect the flow stress and the risk of forming defects.

Engineering Application and Process Optimization

The rigid-plastic finite element analysis of radial extrusion provides a powerful tool for process optimization and defect prevention. By simulating the forming process under different conditions, the engineer can identify the optimal process parameters and die geometry that produce the highest quality tee pipe fitting with the lowest forming forces and the lowest risk of defects.

The analysis can also be used to predict the forming defects that may occur during the radial extrusion process. For example, the analysis can predict the risk of cracks at the branch root of the tee fitting, which is a common defect in the radial extrusion of tee pipe fittings. By identifying the critical regions and the critical process parameters, the engineer can take measures to prevent the formation of defects.

The analysis can also be used to optimize the die design. The die geometry has a significant effect on the metal flow and the stress field, and the optimal die geometry can be determined by minimizing the forming forces and the risk of defects. The analysis can also be used to predict the effect of die wear on the forming process and to determine the optimal die replacement interval.

Study Insights and Implications

This study provides a rigorous theoretical and computational framework for the analysis of the radial extrusion process of tee pipe fittings. The key insight is that the rigid-plastic finite element method is a powerful tool for understanding and optimizing the metal forming process. The study demonstrates that the plane strain assumption is valid for the radial extrusion of tee pipe fittings, which significantly simplifies the analysis while maintaining good accuracy. The study also demonstrates the importance of the strain rate field and the stress field in understanding the metal flow and the risk of forming defects. Engineers involved in the design and optimization of metal forming processes should adopt the rigid-plastic finite element method as a standard tool for process analysis and optimization. The lessons learned from this study can be applied to other metal forming processes, such as the extrusion of other pipe fittings, the forging of shafts, and the rolling of plates. The rigorous approach taken in this study serves as a model for the application of finite element analysis to metal forming processes, and the results provide valuable guidance for the design and optimization of the radial extrusion process of tee pipe fittings.