Residual stress is the stress that remains in a material after all external loads and constraints have been removed. In the context of pipe stress analysis, residual stress refers to the stress that is present in the pipe or its components due to the manufacturing process or fabrication.

During the manufacturing process of a pipe or its components, the material is often subjected to various processes such as welding, forging, rolling, or heat treatment. These processes can result in internal stresses being generated within the material, which can cause the material to deform or crack if not accounted for during pipe stress analysis.

In pipe stress analysis, it is important to consider the effect of residual stresses on the performance of the pipe system, especially if the pipe will be exposed to high temperatures or pressure. Residual stresses can affect the fatigue life of the pipe and its resistance to failure, and therefore, they must be taken into account in any comprehensive pipe stress analysis.

Why do residual stress generated in a material?

Residual stress is generated in a material due to various factors such as the manufacturing process, fabrication, or external loads applied to the material. The following are some of the common reasons for residual stress generation in materials:

• Non-uniform cooling: During the manufacturing process, if a material cools unevenly, the parts of the material that cool faster will contract more than the parts that cool slower. This difference in contraction can lead to residual stress.
• Welding: Welding is a common source of residual stress in materials. During welding, the material is subjected to high temperatures, which can result in thermal expansion and contraction. This process can create non-uniform stresses in the material, leading to residual stress.
• Forming and bending: When a material is formed or bent, the internal layers of the material are stretched and compressed. This deformation can create residual stress in the material.
• Heat treatment: Heat treatment can induce residual stress in a material if the cooling rate is not controlled properly. If the material cools too quickly or too slowly, residual stress can be generated.
• External loads: If a material is subjected to external loads during manufacturing or in-service, such as pressure or thermal loads, it can cause residual stress to develop.

In summary, residual stress is generated in materials due to the non-uniform deformation or loading conditions experienced during the manufacturing process, welding, forming or bending, heat treatment, or external loads applied to the material.

Types of residual stresses

Residual stresses can be classified into different types based on their origin, magnitude, and distribution. The following are the common types of residual stresses:

• Thermal residual stress: This type of residual stress is caused by non-uniform heating and cooling of a material, such as during welding, casting, or heat treatment. Thermal residual stresses can be tensile or compressive depending on the cooling rate and the coefficient of thermal expansion of the material.
• Mechanical residual stress: This type of residual stress is caused by the mechanical deformation of a material, such as bending, stretching, or machining. Mechanical residual stresses can be tensile or compressive depending on the type and direction of deformation.
• Transformational residual stress: This type of residual stress is caused by phase transformations in a material, such as during quenching or aging. Transformational residual stresses can be tensile or compressive depending on the type and direction of the phase transformation.
• Welding residual stress: This type of residual stress is specific to welding, and is caused by the thermal and mechanical effects of the welding process. Welding residual stresses can be tensile or compressive depending on the type of joint and the welding parameters.
• Residual stress due to shot peening: Shot peening is a surface treatment process used to induce compressive residual stress on the surface of a material, which can improve fatigue life and resistance to stress corrosion cracking.

In summary, residual stresses can be classified into different types depending on their origins, such as thermal, mechanical, or transformational, or their specific applications, such as welding or shot peening. Understanding the type and magnitude of residual stress in a material is important for designing and analyzing components that will be subjected to external loads and cyclic loading.

Measuring residual stress

There are several techniques for measuring residual stress in materials, including:

• X-ray diffraction (XRD): This method is based on the principle that the distance between the atomic planes in a crystal lattice is related to the angle of X-ray diffraction. By measuring the diffraction angles of X-rays that are scattered from the material, the residual stress can be calculated.
• Neutron diffraction: Similar to XRD, but using neutrons instead of X-rays. Neutron diffraction can penetrate deeper into the material than XRD and is therefore more suitable for measuring residual stress in thick or opaque materials.
• Ultrasonic testing: This method involves sending high-frequency sound waves through the material and analyzing the reflected waves. Residual stress can be inferred from changes in the velocity or amplitude of the sound waves.
• Hole drilling: This method involves drilling a small hole in the material and measuring the strain relief around the hole. Residual stress can be calculated by analyzing the amount of strain relief.
• Ring-core method: This method involves cutting a ring-shaped specimen from the material and measuring the amount of deformation when the ring is cut open. Residual stress can be calculated from the amount of deformation.

Each of these methods has its advantages and disadvantages, and the choice of method depends on factors such as the type of material, the size and shape of the sample, and the level of accuracy required.

Impact of Residual Stresses

Residual stresses can have significant impacts on the performance and reliability of materials and components. Some of the key impacts of residual stresses are:

• Reduced fatigue life: Residual stresses can reduce the fatigue life of a material, meaning that the material will fail at a lower number of cycles under cyclic loading than a material without residual stresses.
• Increased risk of fracture: Residual stresses can increase the risk of fracture in a material, especially if the material is exposed to high loads or harsh operating conditions.
• Deformation and distortion: Residual stresses can cause a material to deform or distort, leading to dimensional changes or surface cracking.
• Residual stress relaxation: Residual stresses can cause the material to relax over time, leading to a reduction in the material’s strength and stiffness.
• Corrosion: Residual stresses can accelerate the initiation and propagation of corrosion in a material, leading to premature failure.
• Buckling: Residual stresses can cause a material to buckle or warp under external loads, which can result in structural failure.
• Reduced bonding strength: Residual stresses can reduce the bonding strength between different layers or materials, leading to delamination or separation.

In summary, residual stresses can have a significant impact on the performance and reliability of materials and components, including reduced fatigue life, increased risk of fracture, deformation and distortion, residual stress relaxation, corrosion, buckling, and reduced bonding strength. It is therefore important to consider the effects of residual stresses in the design, manufacturing, and maintenance of materials and components.

Impact of residual stress on the fatigue life of a material

Residual stress can have a significant impact on the fatigue life of a material. Fatigue failure occurs when a material is subjected to cyclic loading that causes progressive damage and ultimately leads to failure. Residual stresses can accelerate the fatigue process and reduce the fatigue life of a material due to the following reasons:

• Residual stresses can act as additional loads on the material, which can combine with applied loads to increase the stress amplitude and reduce the fatigue life.
• Residual stresses can cause stress concentrations at critical locations, such as notches or cracks, which can initiate cracks or accelerate crack growth.
• Residual stresses can cause changes in the material microstructure, such as the formation of slip bands or the generation of dislocations, which can affect the fatigue crack growth behavior.
• Residual stresses can cause changes in the material’s elastic properties, such as Young’s modulus or Poisson’s ratio, which can affect the stress distribution and the fatigue crack initiation and propagation.

Therefore, it is important to consider the effects of residual stresses on the fatigue behavior of a material when designing and analyzing components that will be subjected to cyclic loading. This can involve performing fatigue tests on materials with and without residual stresses, and using numerical techniques such as finite element analysis to model the effects of residual stresses on the stress and strain distribution in the component.

Formula for residual stress

There is no single formula for calculating residual stress in materials, as it depends on the specific type of stress and the method of generation. However, there are different experimental and numerical techniques available to measure and estimate residual stress. Some of the common techniques for measuring residual stress include X-ray diffraction, neutron diffraction, hole drilling, and ring-core method. Numerical methods such as finite element analysis (FEA) can also be used to estimate residual stress in a material or component.

It’s important to note that residual stress is a complex and multi-axial state of stress, and its magnitude and distribution can vary depending on many factors. Therefore, the accurate measurement and estimation of residual stress require a comprehensive understanding of the material behavior and the specific loading and deformation conditions it has been subjected to.

Avoiding residual stress generation

While it is not always possible to completely eliminate residual stress in materials, there are several measures that can be taken to minimize its generation:

• Proper material selection: Choosing the right material and its quality can reduce residual stress generation. Material selection can also depend on the method of manufacture.
• Controlled cooling rates: Rapid cooling rates can result in high levels of residual stress, therefore, controlling the cooling rate during the manufacturing process can help to reduce residual stress generation.
• Stress relief heat treatment: Performing heat treatment on the material after the manufacturing process can help to relieve residual stress. This process involves heating the material to a specific temperature and then allowing it to cool slowly.
• Minimizing welds: Welding is a significant contributor to residual stress, hence, minimizing the number of welds and selecting proper welding parameters can help reduce residual stress.
• Machining: Machining operations such as turning or milling can induce residual stresses in the material, hence, controlling machining parameters can minimize residual stress generation.

By implementing these measures during the manufacturing process, the level of residual stress in the material can be significantly reduced. However, it is important to note that residual stress cannot be completely eliminated, and it is necessary to consider its impact during the design and analysis of the material or component.