Finite Element Simulation of Tee Pipe Internal High-Pressure Forming Process

Literature Overview

The paper by Li Le, Zhou Jie, Wang Menghan, and Xia Yufeng, published in Forging Equipment and Manufacturing Technology (2004, Vol. 39, No. 6, pp. 53–55), originates from the College of Mechanical Engineering at Chongqing University. The work presents a finite element simulation of the internal high-pressure forming process for tee pipes, analyzing the influence of key process parameters—including forming force, die fillet radius, friction conditions, and material anisotropy—on the forming quality of the tee pipe. The study provides reference data and guidance for the design of internal high-pressure forming processes in actual production.

Core Technical Concepts

Internal high-pressure forming (IHPT) is a manufacturing process in which a tubular blank is placed in a die cavity and subjected to internal fluid pressure, causing the tube to expand and conform to the die shape. The process is particularly suitable for manufacturing complex cross-sectional shapes, such as tees, from seamless or welded tubes without material removal. The key advantage of IHPT is that it produces parts with near-net shape, minimal material waste, and favorable residual stress distributions.

The finite element simulation described in the paper models the entire forming process, including:

• Material deformation: The plastic deformation of the tube material under internal pressure is simulated using a nonlinear material model.
• Contact mechanics: The interaction between the tube and the die is modeled, including the effects of friction and die fillet geometry.
• Forming force: The internal pressure required to achieve the desired deformation is calculated, along with the distribution of forming forces throughout the process.
• Material anisotropy: The effect of material anisotropy, characterized by the r-value (Lankford coefficient), on the forming quality is analyzed.

Key Process Parameters and Their Influence

The forming force is the primary driver of the deformation process. Insufficient forming force results in incomplete filling of the die cavity, while excessive force leads to excessive wall thinning and potential rupture. The optimal forming force must be determined through simulation and trial forming, taking into account the material properties, tube geometry, and die design.

The die fillet radius is another critical parameter. At the intersection of the tee, the material must flow into a complex three-dimensional geometry, and the fillet radius controls the smoothness of this flow. A small fillet radius creates a sharp corner that can cause material flow stagnation and stress concentration, leading to cracking. A large fillet radius reduces the effective flow area and can cause material accumulation. The optimal fillet radius must be determined through simulation and trial forming.

Finite Element Modeling Approach

The finite element model described in the paper employs several key modeling assumptions and techniques:

1. Mesh generation: The tube blank and die are discretized using shell elements for the tube and solid elements for the die. The mesh density is refined in the region of the tee intersection, where the deformation is most complex.
2. Material model: A nonlinear material model incorporating strain hardening and strain rate effects is used to represent the tube material behavior. The material anisotropy is incorporated using the Hill yield criterion with the r-value as a material parameter.
3. Contact model: The contact between the tube and the die is modeled using a penalty-based contact algorithm, with the friction coefficient specified as a parameter.
4. Loading sequence: The internal pressure is applied incrementally, with the simulation tracking the deformation, stress, and strain distributions throughout the forming process.
5. Failure criteria: The forming limit diagram (FLD) is used to assess the risk of necking and rupture, with the simulation output compared to the FLD to identify potential failure regions.

Engineering Practice and Quality Control

The finite element simulation results provide valuable guidance for the design of the IHPT process, but they must be validated through trial forming and quality control. The key quality control measures for IHPT-produced tees include:

• Dimensional inspection: The tee geometry must be verified using coordinate measuring machines or optical comparators to ensure dimensional accuracy.
• Wall thickness measurement: The wall thickness must be measured at critical locations, particularly at the tee intersection, to verify that it meets the minimum requirements.
• Surface quality inspection: The surface finish and appearance of the formed tee must be inspected to detect any surface defects, such as scratches, dents, or material transfer from the die.
• Residual stress analysis: The residual stress distribution in the formed tee must be assessed using X-ray diffraction or hole-drilling methods to ensure that it meets the requirements for the intended service.
• Mechanical property testing: The tensile strength, yield strength, and elongation of the formed tee must be tested to verify that they meet the specified requirements.

Study Insights

The finite element simulation of the IHPT process is a powerful tool for process design and optimization. In my experience, the simulation can significantly reduce the number of trial forming cycles required to develop a production-ready process, saving both time and cost. However, the simulation results must be validated through physical trials, as the accuracy of the simulation depends on the quality of the material model, contact model, and boundary conditions.

The analysis of material anisotropy is particularly important in IHPT, as the r-value directly affects the uniformity of wall thinning and the risk of failure. In my experience, the r-value can vary significantly between different heat lots of the same steel grade, and this variation can lead to significant differences in forming quality. Therefore, it is essential to characterize the r-value for each heat lot and adjust the process parameters accordingly.

The paper also highlights the importance of the die fillet radius in controlling the material flow into the tee intersection. In my experience, the die fillet radius is often the most critical parameter in the die design, and a small change in the fillet radius can have a significant impact on the forming quality. Therefore, the die fillet radius should be carefully optimized through simulation and trial forming.

One area that the paper does not address in depth is the effect of temperature on the forming process. In production, the tube may be heated to reduce the forming force and improve formability, and the temperature distribution can significantly affect the forming quality. Future work should investigate the effect of temperature on the IHPT process and develop thermal-mechanical coupled simulations to optimize the heating strategy.

The finite element simulation approach described in the paper is directly applicable to other complex forming processes, such as hydroforming of tees, elbows, and reducers. The methodology can be extended to include the effects of tooling wear, material aging, and process variability, providing a comprehensive framework for process design and optimization.

The integration of finite element simulation with process monitoring and quality control is a key enabler of advanced manufacturing. By combining simulation with real-time process monitoring, it is possible to develop adaptive process control strategies that maintain product quality despite variations in material properties and process conditions. This is particularly important in high-volume production environments, where consistency and repeatability are essential.

In conclusion, the finite element simulation of the IHPT process is a valuable tool for process design and optimization, providing insights into the influence of key process parameters on forming quality. The study demonstrates that the forming force, die fillet radius, friction coefficient, and material anisotropy are all critical parameters that must be carefully controlled to achieve consistent product quality. The integration of simulation with trial forming and quality control is essential for developing a production-ready process, and the methodology can be extended to other complex forming processes. The continued development of finite element simulation capabilities, combined with advances in material modeling and process monitoring, will further enhance the ability to design and optimize advanced forming processes for complex pipe and fitting geometries.