Secondary Stress and Peak Stress in Pressure Vessels

In the design and operation of pressure vessels, stress analysis is crucial for ensuring safety and reliability. Among the various types of stress, secondary stress and peak stress significantly impact the performance, lifespan, and safety of pressure vessels. This article will explore the characteristics, sources, impacts, and design considerations related to these two types of stress.

Characteristics of Secondary Stress

Understanding secondary stress is essential for designing pressure vessels. Secondary stress arises from temperature changes, mechanical loads, or deformations of adjacent components, typically concentrating at welds and flange connections.

1. Definition and Distribution

Secondary stress refers to the additional stress inside a pressure vessel caused by factors like temperature changes, mechanical loads, or deformations of neighboring components. It usually exists at the connection points, such as welds and flanges. Changes in temperature or load can lead to secondary stress, especially in areas like fixed tube sheets in heat exchangers, where it may even extend along the entire length of pipes and shells.

2. Causes of Secondary Stress

The formation of secondary stress primarily arises from two aspects:
Balancing External Loads: Primary stress already meets the requirements for balancing external loads, meaning no additional stress is present to achieve this balance. Therefore, any extra stress must be accounted for as secondary stress.
Deformation Compatibility: Secondary stress helps ensure that the deformations of adjacent components are compatible under load, necessitating its generation to maintain deformation alignment at connections.

3. Stress Analysis Methods

In stress analysis of pressure vessels based on shell theory, deformation compatibility is crucial. The finite element method (FEM) is commonly used to analyze stress, assessing the consistency of radial displacements and angular rotations at connection points. By utilizing finite element analysis software, designers can more accurately simulate complex stress states and optimize pressure vessel designs.

Sources of Peak Stress

Peak stress refers to the high-stress state caused by stress concentration at specific locations, often found at connections and sharp corners. Although peak stress values are typically high, their distribution range is small, mainly resulting from concentrated external loads, material defects, or geometric discontinuities.

1. Factors Influencing Peak Stress

In pressure vessels, peak stress generation is influenced by:
Material Defects: Notches or irregularities at welds, flange connections, and interfaces between pipes and shells can lead to stress concentration, increasing local stress values.
Working Cycles: Frequent pressure changes and temperature fluctuations can intensify stress concentration, especially under high-temperature and high-pressure conditions, potentially affecting the material's fatigue performance.
Environmental Factors: Corrosion, wear, and other environmental issues may cause local defects in materials, leading to peak stress formation.

2. Fatigue Failure Mechanism

Fatigue failure in pressure vessels typically occurs in three stages:
Crack Initiation: Small cracks begin to form at connection points due to persistent cyclic loading in stress concentration areas.
Crack Propagation: Over time, these cracks expand, especially under high-frequency loading conditions, where the rate of crack growth may increase.
Fracture: Ultimately, when the cracks reach a critical size, the material can no longer withstand stress, resulting in equipment failure. This process often occurs without clear warning, significantly increasing the risk of accidents.

Design Considerations for Secondary and Peak Stress

In pressure vessel design, addressing both secondary and peak stress is vital for ensuring safety and reliability.

1. Design Requirements for Secondary Stress

While secondary stress may not cause immediate failure under primary loading, it can lead to instability and failure under prolonged, repeated loading. Therefore, it is essential to consider its impact during design. Particularly in high-temperature and high-pressure scenarios, designers must ensure that material selection and structural design can withstand potential secondary stress.

2. Fatigue Design for Peak Stress

Peak stress often manifests its destructive potential under frequent loading and unloading conditions. Therefore, fatigue design is necessary to ensure safety and reliability for vessels that experience regular start-stop cycles. Key design considerations include:
Material Selection: Choosing materials with good fatigue strength can reduce the risk of fatigue failure caused by peak stress.
Geometric Design: Optimizing the geometry of connection points to avoid sharp corners and sudden changes can help minimize stress concentration effects.
Welding Quality: Ensuring the quality of weld joints is crucial to prevent stress concentration arising from welding defects.

Conclusion

Overall, secondary stress and peak stress are critical factors in the design of pressure vessels. Proper stress analysis and design can effectively enhance the safety and longevity of pressure vessels. When designing and evaluating pressure vessels, it is vital to consider the characteristics of these stresses and their impacts on vessel performance. Through scientific design, careful material selection, and optimized manufacturing processes, the risks associated with secondary and peak stress can be minimized, ensuring the safe operation of pressure vessels. This approach not only improves equipment reliability but also reduces maintenance costs, extends service life, and enhances overall economic efficiency.