Omar Khalid
Accumulated plastic strain is an important concept in engineering, particularly when dealing with materials such as pipe steel. It refers to the sum of plastic strain increments, irrespective of their sign and direction, and it occurs when the yield limit of a material is exceeded. This can lead to reduced ductility and toughness of the material, and it may also increase the hardness of the material, making it more susceptible to stress corrosion cracking. To calculate accumulated plastic strain, one must start from the strain tensor, which can be reported as a matrix, and consider the components of the plastic strain tensor and the Kronecker delta. This calculation is essential to ensure that the material properties do not become substandard, especially in terms of fracture toughness. Various models and equations, such as the Barcelona Basic Model (BBM) and the cyclic stress-strain curve, are used to understand and quantify accumulated plastic strain in different materials.
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What You'll Learn
- The plastic strain increments are calculated from the point where the material stress-strain curve deviates from a linear relationship
- Accumulated plastic strain is limited to ensure that the material properties of the pipe do not become substandard
- The yield limit is stored as a positive value, as there is no need to keep track of its sign
- The plastic strain increments must be integrated or added together along the loading path to give the total plastic strains
- Accumulated plastic strain is commonly used in the determination of the effect of reeling
The plastic strain increments are calculated from the point where the material stress-strain curve deviates from a linear relationship
Plastic strain increments are calculated from the point where the material stress-strain curve deviates from a linear relationship. This is done to ensure that the material properties of the pipe do not become substandard, especially in terms of fracture toughness. Accumulated plastic strain can increase the hardness of the material and its susceptibility to stress corrosion cracking, particularly in the presence of H2S.
The plastic strain increment is the additional deformation that occurs when the material is stressed beyond its elastic limit. In other words, it is the permanent deformation that occurs when the material is stretched or compressed beyond its elastic range. This is important in engineering applications to understand and predict the behaviour of materials under load.
The calculation of plastic strain increments is based on the stress-strain curve of the material, which plots the stress applied to the material against the resulting strain. The curve typically starts as a linear relationship in the elastic region, where the material returns to its original shape when the load is removed. However, when the material is stressed beyond its elastic limit, the curve deviates from linearity and enters the plastic region, where permanent deformation occurs.
The plastic strain increments are calculated by integrating or adding together the incremental deformations along the loading path. This can be related to the stress-strain curve through established equations such as the Prantl-Reuss equation or more complex models like the Barcelona Basic Model (BBM) or Barcelona Expansive Model (BExM). Additionally, computational methods, such as the fully implicit return mapping algorithm, can be employed to compute the plastic strain increments.
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Accumulated plastic strain is limited to ensure that the material properties of the pipe do not become substandard
Accumulated plastic strain is defined as the sum of plastic strain increments, irrespective of sign and direction. When the yield limit is exceeded, the pipe steel will accumulate plastic strain. This can reduce the ductility and toughness of the pipe material. It may also increase the hardness of the material, making it more susceptible to stress corrosion cracking in the presence of H2S.
To avoid this, special strain aging and toughness testing must be carried out. Accumulated plastic strain is limited to ensure that the material properties of the pipe do not become substandard. This is especially relevant for the fracture toughness of the pipe.
The general requirement of the accumulated plastic strain is that it should be based on strain aging and toughness testing of the pipe material. A permanent/plastic strain of up to 2% is allowable without testing. This is also valid in the operational case. If the pipeline is to be exposed to more than 2% accumulated plastic strain, the material should be strain-aged tested.
DNV OS-F101 requires that the pipe material meet additional quality requirements if it is to be used for accumulated plastic strains of 2% or more. This includes increased pipe inspection and restricted maximum differences between pipe-end thicknesses and local wall thickness variation. Recent testing of modern pipeline steel has shown that plastic strain up to 5% or even 10% can be acceptable, although a safety margin is desirable.
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The yield limit is stored as a positive value, as there is no need to keep track of its sign
Accumulated plastic strain is a critical concept in engineering and materials science, referring to the sum of plastic strain increments that occur when a material deviates from its linear stress-strain relationship. This phenomenon is particularly relevant in ensuring that the material properties of pipes do not deteriorate, compromising their ductility, toughness, and susceptibility to stress corrosion cracking.
To delve into the specifics of yield limit, we must understand its role in characterising the behaviour of materials under stress. The yield point, as defined in engineering, signifies the juncture where elastic behaviour culminates and plastic behaviour commences. Below this yield point, materials exhibit elastic deformation, reverting to their original shape upon stress removal. Conversely, surpassing the yield point results in irreversible plastic deformation, where a fraction of the deformation becomes permanent.
The yield limit is a pivotal parameter in determining the maximum allowable load that a mechanical component can endure without succumbing to permanent deformation. Consequently, it is imperative to accurately calculate and monitor the yield limit.
In the context of the discussion, the yield limit is stored as a positive value. This is attributed to the adopted model's distinction between compression and tensile values, rendering the sign of the yield limit inconsequential. Equation 5.29, which is employed to ascertain stress values, further substantiates this approach by exclusively yielding real number results for positive ε, rendering negative strain values incompatible with the proposed equation.
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The plastic strain increments must be integrated or added together along the loading path to give the total plastic strains
Plastic strain is a phenomenon that occurs when a material's yield limit is exceeded. It is characterised by permanent deformation, reduced ductility and toughness, and an increase in the material's hardness. This can have significant implications for the material's performance and susceptibility to stress corrosion cracking.
Accumulated plastic strain is defined as the sum of plastic strain increments, irrespective of their sign and direction. It is calculated from the point where the material stress-strain curve deviates from a linear relationship and is tracked from the time of fabrication to the end of the material's lifetime. The plastic strain increments are integral in determining the total accumulated plastic strain.
The calculation of accumulated plastic strain is crucial for ensuring that the material's properties remain within acceptable standards. One method to determine the plastic strain increment is the traditional Newton method. However, other methods, such as the Barcelona Basic Model (BBM) or the Barcelona Expansive Model (BExM), can also be employed. The choice of method depends on the specific material and experimental conditions.
The plastic strain increments must be integrated or added together along the loading path to determine the total plastic strain. This process involves considering the stresses and the uniaxial stress-strain curve, which can be related through the Prantl-Reuss equation. By summing up these plastic strain increments, the total accumulated plastic strain can be calculated. This calculation is essential for understanding the behaviour and performance of materials under loading conditions.
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Accumulated plastic strain is commonly used in the determination of the effect of reeling
Accumulated plastic strain is defined as the sum of plastic strain increments, irrespective of sign and direction. It is calculated from the point where the material stress-strain curve deviates from a linear relationship and is computed from the time of fabrication to the end of the lifetime of the material. It is a critical parameter to monitor as it can increase the yield stress of a material and also increase the yield/ultimate stress ratio.
Recent testing of modern pipeline steel has shown that plastic strains up to 5% or even 10% can be acceptable. To ensure an extra safety margin, a certain ratio between the yield stress and the ultimate tensile stress is also desirable. An allowable accumulated plastic strain level of 2% is recommended for umbilical design. Accumulated plastic strain needs to be maintained within certain limits to avoid unstable fracture or plastic collapse for a given tube material and weld procedure.
Overall, accumulated plastic strain is an important parameter to monitor during the reeling process to ensure the pipeline's integrity and safety.
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Frequently asked questions
Accumulated plastic strain is defined as the sum of plastic strain increments irrespective of sign and direction. It is calculated from the point where the material stress-strain curve deviates from a linear relationship.
The general requirement of the accumulated plastic strain is that it should be based on strain aging and toughness testing of the pipe material.
An allowable accumulated plastic strain level of 2% is recommended for umbilical design. However, recent testing of modern pipeline steel has shown that plastic strain up to 5% or even 10% can be acceptable.
If the strain is elastic, the sample returns exactly to its initial shape when unloaded. If plastic strain occurs, there is permanent deformation.
The critical equivalent plastic strain is the maximum equivalent strain that can be borne to ensure perforation stability. If the equivalent plastic strain exceeds the critical value, the perforation will be unstable.
