1. Core significance of fatigue life of expansion joint
In piping systems, the expansion joint absorbs thermal displacement, vibration, and foundation settlement through elastic deformation of the bellows. Every time the temperature changes, every time the equipment starts and stops, the bellows have to go through a stress cycle. As the number of cycles increases, the corrugated pipe material will gradually accumulate damage, and eventually fatigue cracks appear at the crest or trough, resulting in leakage failure. The fatigue life of the expansion joint, that is, the number of cycles that the bellows can safely withstand under the action of alternating stress, is the core index to measure the reliability and economy of the expansion joint. The design life is too low, and the expansion joint fails prematurely, resulting in frequent shutdown and replacement; The blind pursuit of excessive life will lead to the increase of wall thickness, stiffness and cost of bellows, which will affect the compensation effect. Therefore, accurately understanding the influencing factors of the fatigue life of the expansion joint, mastering the calculation method and taking effective measures to prolong the fatigue life are the key to the selection design and operation and maintenance of the expansion joint. This paper will systematically expound this core topic from fatigue mechanism, design criteria, influencing factors to engineering application.
2. Basic mechanism of expansion joint fatigue
2.1 Low cycle fatigue vs. high cycle fatigue
Expansion joints are usually subjected to high cyclic stresses in the working process, and each Cycle involves plastic deformation, which belongs to the typical Low Cycle Fatigue (LCF) category. According to EJMA (American Association of Expansion Joint Manufacturers) standards, the fatigue life of expansion joints is typically between 1000-10000 full-displacement cycles, which is much lower than the 10⁶-10⁷ high-cycle fatigue life of general mechanical parts.
2.2 Generation and propagation of fatigue cracks
Bellows fatigue failure is divided into three stages:
- Crack initiation stage: In the stress concentration region of the wave crest or trough, the grain boundary slips and forms microscopic cracks
- Crack propagation stage: The crack propagates steadily along the direction of maximum principal stress, forming macroscopically visible cracks
- Fracture stage: the remaining section is insufficient to withstand the load, and the crack propagates rapidly until it leaks through
For flue systems containing corrosive media, the synergistic action of corrosion and fatigue (corrosion fatigue) can significantly reduce the fatigue life of the expansion joint, sometimes even by only 10-20% of the pure fatigue life.
2.3 Main factors affecting fatigue life
| Factors | Influence direction | Engineering implications |
|---|---|---|
| Cyclic displacement | The larger the displacement, the shorter the life | Reasonable allocation of compensation amounts in each direction |
| Working pressure | The higher the pressure, the greater the stress | It is necessary to thicken or set reinforcing rings in high pressure conditions |
| Bellows material | Material with high strength and good plasticity has long life | Inconel> 316L> 304 |
| Corrugated geometry | Longer life for those with reasonable ratio of wave height and wave pitch | Recommended Wave Height/Wave Distance =0.8-1.2 |
| Temperature | High Temperature Decreases Material Fatigue Strength | High temperature needs to be reduced |
| Medium corrosivity | Corrosion accelerated fatigue failure | Select corrosion-resistant materials according to working conditions |
3. Calculation method of fatigue life of expansion joint
3.1 EJMA Standard calculation method
The most authoritative fatigue life calculation method for expansion joints in the world is the formula in EJMA standard. The core is to calculate the maximum alternating stress amplitude of the bellows under the combined action of displacement and pressure, and then find the allowable cycle times through the strain-life curve (ε-N curve) of the material.
Simplify the calculation formula:
N = (C/σ _t) ^m
Among them:
- N: Predicted fatigue life (number of cycles)
- σ _t: Total alternating stress amplitude (MPa)
- C, m: material constant (determined by test)
For austenitic stainless steel bellows, the fatigue life roughly follows the following relationship when σ t is in the range of 200-400 MPa:
| Total alternating stress amplitude (MPa) | Predicted fatigue life (number of cycles) |
|---|---|
| 300 | About 5000-8000 |
| 400 | About 1500-2500 |
| 500 | About 500-800 |
3.2 Actual fatigue life and safety factor
Due to material discreteness, manufacturing defects and working condition fluctuations, the fatigue life of actual expansion joints tends to be lower than theoretical calculations. The EJMA standard specifies that:
- Design fatigue life = test fatigue life/safety factor
- The safety factor is usually 10-15 (for austenitic stainless steel)
- That is, if the theoretical calculation life is 10,000 times, the design value is only 700-1000 times
3.3 Fatigue correction of multiaxial displacement
When the expansion joint is simultaneously subjected to axial, transverse and angular displacements, the total stress is not simply superimposed, but the stress combination criterion should be adopted:
σ _eq = √ (σ _axial² + σ _lateral² + σ _angular²)
The combined equivalent stress is usually larger than the stress at unidirectional displacement, so multiaxial displacement can significantly reduce the fatigue life of the expansion joint.
4. Key design parameters affecting fatigue life
4.1 Bellows wall thickness
Wall thickness and fatigue life are positively correlated nonlinearly:
- Increasing wall thickness reduces stress level and prolongs fatigue life
- However, excessive wall thickness will increase stiffness, decrease compensation capacity and increase internal pressure thrust
Project recommendation: For commonly used flue expansion joints, the wall thickness of corrugated pipe should be 1.0-2.5mm, which should be determined according to the pressure grade and diameter.
4.2 Wave Number and Wave Height
- Increasing wave number: It can reduce the displacement per wave, thereby reducing single wave stress and prolonging the fatigue life of the expansion joint
- Increase wave height: improve single wave compensation capability, but increase peak stress concentration and decrease life
- Optimum wave height/pitch ratio: 0.8-1.2
4.3 Multi-layer bellows structure
The use of double or multi-layer bellows (each thinner) has the following advantages:
- Each layer deforms independently, and the stress of the inner layer and the outer layer is redistributed
- Compared with single-layer thick-wall, the fatigue life of multi-layer structure can be increased by 30-50% without increasing stiffness
- The multilayer structure also has a "failure-safe" feature: the inner layer can still be temporarily maintained when the outer layer leaks
4.4 Material selection
The fatigue strength of different materials is significantly different:
| Materials | Relative Fatigue Strength (Based on 304) | Applicable working conditions |
|---|---|---|
| 304 | 1.0 | Conventional flue gas, temperature ≤400℃ |
| 316L | 1.1-1.2 | Corrosive flue gas containing Cl⁻¹ |
| 321 | 1.1-1.15 | Temperature fluctuation condition with sensitization |
| Inconel 625 | 1.5-2.0 | High temperature (≥600℃), strong corrosion |
V. Engineering Measures to Prolong the Fatigue Life of Expansion Joints
5.1 Reasonable displacement allocation
Avoid a single expansion joint bearing excessive total displacement:
- A plurality of expansion joints are arranged in a long pipe section to absorb heat extension in sections
- Adopt double expansion joint instead of single expansion joint, increase wave number to reduce single wave stress
- Assign axial displacement and transverse displacement to different types of expansion joints (e.g. axial + hinge combination)
5.2 Optimized installation and pre-displacement
The pre-stretching or pre-compression operation during installation can make the stress distribution of the expansion joint at the working temperature more balanced, thus optimizing the fatigue life of the expansion joint:
- For cold installation, pre-displacement according to 50% of the design displacement
- The stress circulation center in the working state is close to the stress-free center, and the stress amplitude is reduced
5.3 Controlling operating conditions
- Reduce the number of starts and stops: Peak shaving units should consider the cumulative consumption of expansion joint fatigue life
- Avoid overtemperature operation: Fatigue life decreases by about 20-30% for every 50℃ increase in temperature
- Prevent water hammer and vibration: Impact loads can lead to instantaneous stress exceeding limits, accelerating fatigue
5.4 Select Low Stress Bellows Waveform
The low stress waveforms (such as unequal wave height and variable wall thickness waveforms) developed in recent years can significantly reduce the peak stress concentration coefficient, and the fatigue life of the expansion joint can be increased by 50-100% under the same compensation amount.
VI. Verification and detection of fatigue life
6.1 Type test
According to GB/T 12777 or EJMA standard, the newly designed expansion joint shall be verified by fatigue test:
- Applying alternating displacement on special fatigue testing machine
- Continuous cycle until leakage or crack occurs in bellows
- The actual test life shall not be less than 2 times the design life (considering the safety factor)
6.2 Evaluation of the remaining life of in-service expansion joints
For in-service expansion joints, the fatigue life of the remaining expansion joints can be assessed by:
- Operation ledger method: count the cumulative start-stop times and temperature cycle times, and compare the design life
- Non-destructive testing: When penetration tests detect early microcracks, the remaining life is usually less than 20%
- Strain monitoring method: On-line monitoring of corrugated pipe key point strain, combined with S-N curve to calculate the remaining life
7. Recommended value of standard for fatigue life
| Application Scenario | Recommended design fatigue life (number of cycles) | Description |
|---|---|---|
| General industrial flue | 1000 | Low start-stop frequency, ≤50 cycles per year |
| Flue of power station boiler | 1000-2000 | Peak shaving unit needs to take upper limit |
| gas turbine exhaust duct | 3000-5000 | Frequent start-stop, large temperature difference |
| Petrochemical heating furnace | 2000-3000 | Continuous operation with overhaul cycle |
| Nuclear Power/Long Cycle Operation | 5000-10000 | High reliability requirements |
VIII. Summary
The fatigue life of expansion joint is the core index of expansion joint design and operation management, and its essence is the process of accumulating damage of bellows under the combined action of alternating displacement and pressure. The key factors affecting fatigue life include cyclic displacement, working pressure, material grade, corrugation geometry parameters and temperature corrosion environment. In engineering practice, the whole life cycle management idea of "reasonable type selection, optimized design, standardized installation and monitoring operation" should be followed: in the design stage, fatigue calculation should be carried out according to EJMA standard, and 10-15 times safety factor should be taken; In material selection, priority is given to multilayer bellows and fatigue-resistant materials (such as Inconel, 316L); During the installation phase, the pre-displacement operation is performed correctly to equalize the stress distribution; In the operation and maintenance stage, a start-stop cycle ledger is established, and when the cumulative number of times reaches 80% of the design life, it is included in the replacement plan. In particular, it should be noted that corrosive media will greatly reduce the actual fatigue life, and the corrosion conditions such as desulfurization flue should be conservatively taken according to 20-30% of the pure fatigue life. By scientifically managing the fatigue life of the expansion joint, the whole life cycle cost of the equipment can be optimized under the premise of ensuring safety, and two extremes of premature failure and excessive redundancy can be avoided.