Quantitative Analysis of Stress Concentration in Tees with Different Fillet Radii

Literature Overview

This paper by Li Haiyang, Guo Yanjun, Wang Lu, Xu Hui, and Li Xiaohui, published in Pressure Vessel Technology (2021, Vol. 38, No. 6, pp. 53-60), presents a finite element-based quantitative analysis of stress concentration in tee fittings with varying fillet radii at the shoulder and belly regions. Funded by the Huadian Group's key science and technology project on high-temperature high-pressure key material service damage mechanisms (CHDKJ20-01-92), the study employed image processing techniques to extract and quantify stress concentration regions from finite element analysis results. The research provides a systematic methodology for evaluating tee fitting integrity and offers manufacturing guidance for optimizing fillet geometry.

Core Technical Methodology

The study adopted a hybrid approach combining finite element analysis (FEA) with image processing techniques to quantify stress concentration characteristics:

1. Finite Element Modeling: Three-dimensional solid models of tees with different fillet radii were created and analyzed under internal pressure loading. The mesh was refined in the stress concentration regions to ensure accurate stress capture.
2. Image Processing for Stress Region Extraction: The stress distribution from FEA results was processed using image analysis techniques to isolate and quantify the stress concentration zones. This approach allowed for objective measurement of stress concentration area, volume, and spatial distribution.
3. Quantitative Parameters: The study measured local maximum equivalent stress, stress concentration coefficient (Kt), stress point distribution within the concentration zone, and geometric parameters (volume, surface area, thickness, length, width) of the stress concentration region.

Key Technical Findings

The study revealed distinct behavior at the shoulder and belly regions of the tee:

Shoulder Region Behavior

The shoulder region exhibits an optimal fillet radius beyond which further increases in radius actually worsen the stress concentration. This counterintuitive result occurs because an excessively large fillet radius alters the load transfer path, creating a new stress concentration at the transition between the fillet and the main pipe wall. The optimal radius represents a balance between smoothing the geometric discontinuity and maintaining effective load distribution.

Belly Region Behavior

The belly region (the curved area at the junction of the branch pipe and the main pipe, on the opposite side from the shoulder) shows a monotonically beneficial response to increasing fillet radius. Larger fillet radii in the belly region consistently reduce stress concentration, as they provide a more gradual transition of the load path from the branch pipe to the main pipe.

Process and Standards Analysis

The findings have direct implications for tee manufacturing processes:

• Forged Tees: The forging die design must incorporate appropriate fillet radii at both shoulder and belly regions. The shoulder radius should be optimized within a specific range rather than maximized.
• Rolled/Pressed Tees: The forming process parameters must ensure the as-formed fillet geometry meets the optimized specifications.
• Welded Tees (ASME B16.9 Type): The fillet geometry at the weld joint is determined by the weld preparation and weld profile. The study's findings suggest that weld design should aim for an optimal transition rather than simply maximizing the fillet.

For standards compliance, the study's findings are relevant to ASME B16.9 (Welded Butt Flange Fittings), ASTM A403 (Wrought Butt-Welding Fittings), and GB/T 12459 (Steel Butt-Welding Fittings). These standards specify minimum fillet radii but do not address the optimal radius for stress concentration minimization. The study provides the technical basis for potentially revising or supplementing these standards with optimized geometry recommendations.

Integration with Engineering Practice

The image processing methodology employed in this study is particularly noteworthy. Traditional FEA stress analysis provides point-wise stress values, but the image processing approach enables volumetric and areal quantification of stress concentration regions. This is valuable for:

• Fatigue Life Assessment: The volume and distribution of high-stress regions directly influence fatigue crack initiation probability and crack growth rate.
• Quality Control: The methodology can be adapted for evaluating as-manufactured tee geometry against optimized design specifications.
• Damage Tolerance Analysis: Understanding the spatial extent of stress concentration helps predict the consequences of local damage or corrosion.

Study Insights and Reflections

The most significant contribution of this paper is the identification of the non-monotonic relationship between fillet radius and stress concentration at the shoulder region. This finding challenges the conventional engineering assumption that larger fillets always reduce stress concentration. The practical implication is that tee manufacturers should not simply maximize fillet radii but should optimize them within a specific range determined by the geometry and loading conditions. For pressure vessel and piping engineers, this study provides a quantitative basis for evaluating tee fitting integrity and for making informed decisions about geometry modifications to improve fatigue performance. The methodology also demonstrates the value of combining computational analysis with image processing techniques for extracting quantitative information from complex stress fields.