Finite Element Analysis of Elastoplastic Stress Distribution in Extruded Tees

Literature Overview

The paper by Xuan Fuzhen and Li Peining, published in 2002 in the journal Chemical Equipment and Piping (Volume 39, Issue 5, pages 43-45), presents a systematic finite element analysis (FEA) of the elastoplastic stress distribution in extruded tees. The authors investigated the influence of two key geometric parameters—the nominal diameter-to-wall thickness ratio (D/T) and the shoulder radius-to-nominal diameter ratio (r/D)—on the stress distribution in the transition region between the run and branch of the tee. The study was conducted at the Chemical Machinery Research Institute of East China University of Science and Technology. The results indicate that increasing the shoulder transition radius reduces the maximum stress in the main and branch transition areas but simultaneously expands the high-stress zone, while increasing the wall thickness effectively reduces the stress levels in the intersection and belly regions without altering the fundamental stress distribution pattern.

Core Technical Methodology

Extruded tees are manufactured by the hot extrusion of a solid steel billet through a shaped die, resulting in a seamless fitting with complex geometry. The stress distribution in extruded tees is governed by the interaction of internal pressure, external loads, and the geometric discontinuities at the run-branch intersection. The elastoplastic FEA approach used in this study accounts for both elastic and plastic deformation, which is essential for accurately predicting the stress state under conditions where yielding occurs.

The FEA model typically employs axisymmetric or three-dimensional elements depending on the complexity of the tee geometry. For a standard equal tee, the geometry can be simplified to an axisymmetric model if the branch is aligned with the axis of symmetry. However, for unequal tees or tees with eccentric branches, a full three-dimensional model is required.

The elastoplastic analysis is particularly important for extruded tees because the extrusion process itself introduces residual stresses and plastic deformation in the material. The combination of process-induced residual stresses and service loads can lead to premature failure if not properly accounted for in the design.

Analysis of Geometric Parameters

Influence of Shoulder Radius (r/D)

The shoulder radius is the fillet radius at the intersection of the run and branch of the tee. The authors found that increasing the shoulder radius has two competing effects:

1. Stress reduction: A larger shoulder radius reduces the geometric stress concentration at the intersection, thereby lowering the maximum stress in the transition region. This is because the stress concentration factor is inversely related to the fillet radius, and a smoother transition allows the load to be distributed over a larger area.
2. High-stress zone expansion: While the peak stress is reduced, the region over which the stress exceeds a certain threshold (e.g., the yield strength) is expanded. This means that although the maximum stress is lower, a larger volume of material is subjected to elevated stress, which may have implications for fatigue and creep resistance.

Influence of Wall Thickness (D/T)

The wall thickness ratio D/T is a fundamental geometric parameter that governs the stress state in pressure-containing components. The authors found that:

1. Stress reduction: Increasing the wall thickness (i.e., decreasing D/T) effectively reduces the stress levels in both the intersection and belly regions. This is consistent with the basic membrane stress formula, where the hoop stress is inversely proportional to the wall thickness.
2. Stress distribution invariance: The fundamental stress distribution pattern is not altered by changes in wall thickness. This means that the relative stress concentrations at the intersection and belly remain unchanged, and the location of the maximum stress is preserved.

Comparison with Engineering Standards

The findings of this study are directly relevant to the design and qualification of extruded tees according to international standards. The following table compares the geometric parameters investigated in the study with the requirements of key standards:

The stress concentration factors derived from FEA can be used to supplement or refine the empirical factors provided in piping codes. For example, ASME B31.3 provides stress intensification factors for tees based on empirical data and simplified analytical models. The FEA results from this study can be used to validate these factors for specific geometric configurations and to identify cases where the code factors may be unconservative.

Integration with Manufacturing Practice

The extrusion process for tees involves the hot deformation of a solid steel billet through a shaped die. The process parameters, including the extrusion temperature, reduction ratio, and die geometry, directly influence the final geometry and residual stress state of the tee. The findings of this study have the following implications for manufacturing practice:

• Die design: The shoulder radius in the die must be designed to produce the desired r/D ratio in the final product. A larger die radius produces a larger shoulder radius in the tee, which reduces the peak stress but may increase the extrusion force and energy consumption.
• Post-extrusion heat treatment: The extrusion process introduces significant plastic deformation and residual stresses. Post-extrusion annealing or normalizing is typically required to relieve these stresses and restore the material properties. The FEA results can be used to predict the residual stress state before and after heat treatment.
• Quality control: The geometric parameters (D/T and r/D) must be verified through dimensional inspection and non-destructive testing to ensure compliance with the specified requirements. The FEA results can be used to define the acceptance criteria for these parameters.

Key Questions and Reflections

The study raises several important questions for engineers involved in the design and qualification of extruded tees:

• How does the stress distribution in extruded tees compare with that of forged tees? Forged tees are produced by the hot forging of a steel billet, which results in a different grain flow pattern and residual stress state. The FEA results for extruded tees may not be directly applicable to forged tees, and separate analyses are required.
• What is the effect of the extrusion process on the material properties? The hot extrusion process can alter the grain structure, texture, and mechanical properties of the steel. The FEA model must use material properties that accurately represent the post-extrusion condition, which may differ from the as-received condition of the steel billet.
• How can the FEA results be used to optimize the design of extruded tees? The study provides a framework for investigating the influence of geometric parameters on the stress distribution. This framework can be extended to include additional parameters, such as the branch angle, eccentricity, and wall thickness variation, to develop a comprehensive design optimization methodology.

Study Insights and Implications

This paper provides valuable insights into the elastoplastic stress behavior of extruded tees under internal pressure and external loads. The key finding is that the shoulder radius and wall thickness are the two most influential geometric parameters, and their optimization is essential for ensuring the structural integrity of the tee. The study also highlights the importance of considering both the peak stress and the high-stress zone volume when evaluating the structural performance of a tee. For engineering practice, the FEA methodology described in this paper can be used to validate and refine the stress concentration factors provided in piping codes, and to support the design and qualification of extruded tees for specific applications. The findings are particularly relevant for high-pressure and high-temperature applications where the margin between the design stress and the material yield strength is small.

Reference Value and Outlook

The finite element analysis methodology presented in this paper has been widely adopted in the industry for the design and qualification of pipe fittings. Modern FEA software, such as Abaqus, ANSYS, and ABAQUS, provides advanced elastoplastic material models, adaptive meshing, and contact analysis capabilities that enable more accurate and efficient simulations. The study also paved the way for the development of design charts and lookup tables that allow engineers to quickly estimate the stress concentration factors for a wide range of geometric configurations. Future research in this area may focus on the integration of FEA with process simulation to predict the residual stress state introduced by the extrusion process and to optimize the post-extrusion heat treatment to minimize the impact of these stresses on the structural performance of the tee.