Limit Pressure of Equal-Diameter Welded Ttees with Circumferential Cracks Engineering Estimation Method

Literature Overview

This second paper by Xuan Fuzhen, Liu Changjun, and Li Peining from East China University of Science and Technology, published in Petrochemical Equipment (2001, Vol. 30, No. 5), extends the limit analysis framework to tees containing circumferential cracks. Funded under the National "95" Science and Technology Key Project (96-918-02-03), this study specifically addresses the belly-center crack configuration common in petrochemical industry applications, where tees are subjected to cyclic loading and potential crack initiation at stress concentration zones.

Technical Methodology

The authors apply the lower bound theorem of limit analysis, which provides a rigorous lower bound estimate of the limit load for a given assumed stress field. The key simplification involves modeling the crack as a geometric discontinuity that reduces the effective load-bearing cross-section at the belly (the curved region connecting the main and branch pipes). The resulting estimation formula is both concise and accurate, as validated by both experimental data and finite element numerical solutions.

Validation Method	Agreement with Formula	Reliability
Experimental data	Good agreement	High confidence
Finite element numerical solution	Good agreement	High confidence
Theoretical lower bound theorem	Rigorous lower bound	Mathematically guaranteed

The simplicity of the derived formula is a major advantage for engineering application, as it can be readily implemented in hand calculations or incorporated into computer-based fitness-for-service assessment software.

Crack Configuration and Stress Analysis

The belly-center crack is a particularly critical defect configuration because the belly region experiences complex multiaxial stress states under internal pressure. The circumferential crack orientation means that the crack faces are subjected to hoop stress, which is typically the dominant stress component in pressure vessels. The lower bound theorem approach ensures that the estimated limit pressure is always less than or equal to the true limit pressure, providing a conservative (safe-side) estimate.

Crack Parameter	Effect on Limit Pressure	Sensitivity
Crack length	Reduces limit pressure proportionally	High
Crack depth	Reduces limit pressure significantly	Very high
Crack position (belly center)	Maximum stress concentration	Critical location

Engineering Practice Application

For fitness-for-service assessment of in-service tees containing detected circumferential cracks, this estimation formula provides a practical tool for determining the remaining load-carrying capacity. In petrochemical facilities, where tees are frequently inspected using ultrasonic testing or magnetic particle testing, the detection of circumferential cracks is not uncommon. The formula enables rapid assessment of whether the cracked tee can continue to operate at design pressure or requires repair or replacement.

Study Insights and Limitations

The strength of this work lies in its practical engineering orientation: the formula is simple enough for field use yet rigorous enough to provide reliable estimates. However, the study is limited to the belly-center crack configuration. Engineers should note that cracks at other locations (such as the intersection line or near the weld seam) may exhibit different limit pressure behavior. For comprehensive assessment, engineers should consider multiple crack configurations and select the most critical one for evaluation. The lower bound nature of the estimate means that the true capacity may be higher, but the conservative approach is appropriate for safety-critical applications.