Chloe Zhang
Plastic strain is a key consideration when defining yield stress in Abaqus, a software suite for computer-aided engineering analysis. Abaqus allows users to define a material's yield behaviour accurately when the yield strength depends on the rate of straining and the anticipated strain rates are significant. The plastic strain value is typically expected to be zero at all values of yield stress, and the first point of tabular data in Abaqus should represent the yield stress associated with zero plastic strain. However, there are exceptions, such as when the yield point on the stress-strain curve is not well-defined, as in the case of brittle materials.
| Characteristics | Values |
|---|---|
| Plastic strain value | Changes with temperature-dependent yield stress data |
| First point of tabular data | Yield stress associated with zero plastic strain |
| Plastic deformation | Isotropic uniaxial hardening law |
| Total strain | 0.2% |
| Yield stress | Referred to 0 equivalent plastic strain |
| Plastic strain equation | plastic_strain = epsilon_total - epsilon_elastic |
| Plastic strain equation (more rigorous) | plastic_strain = Integrale (epsilon_plastic_point) where epsilon_plastic_point = epsilon_total_point - epsilon_elastic_point |
| Plastic strain in Abaqus | True stress as a function of true plastic strain |
| Plastic strain calculation | Subtracting elastic strain (value of true stress/Young's modulus) from total strain |
| Plasticity curve | Continuous, piecewise-linear |
| Plasticity model | Isotropic, kinematic, Johnson-Cook, User |
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What You'll Learn
Plastic strain and yield stress
Plastic strain refers to permanent deformation that remains after the removal of stress. It is generally time- and rate-dependent. In the context of Abaqus, a software used for simulation and modelling, plastic strain is a critical factor in defining the post-yield behaviour of metals.
When defining plastic behaviour in Abaqus, it is essential to provide the proper stress-strain data, especially for large strains. The *PLASTIC option in Abaqus allows users to define the post-yield behaviour for most metals by specifying the true stress as a function of true plastic strain. The first data pair defines the initial yield stress, with the corresponding initial plastic strain being zero. Abaqus then connects these data pairs with straight-line segments to form a continuous, piecewise-linear plasticity curve.
The onset of yield stress in Abaqus is not always clear, especially for ductile materials, except in the case of carbon steels with lower and upper yield limits. The Rp0.2-criterion was invented to address this issue, as the onset of yield is not a distinct point on the stress-strain curve.
Plastic strain is also crucial in determining the effect of reeling in pipelines, where cyclic bending plastic strain occurs during the reeling-unreeling cycles. Accumulated plastic strain can impact the material properties, toughness, and susceptibility to stress corrosion cracking. To ensure the material's performance, it is recommended to limit the accumulated plastic strain and perform strain aging and toughness testing.
In summary, plastic strain and yield stress are closely related concepts, with plastic strain being the permanent deformation that occurs after the removal of stress, and yield stress being the point at which a material yields and deforms plastically. Abaqus provides tools to define and analyse these behaviours, particularly in metals, to ensure accurate simulations and informed engineering decisions.
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Plastic strain and total strain
Plastic strain is a permanent deformation that remains even after the removal of stresses. It is generally time- and rate-dependent. In Abaqus, the *PLASTIC option is used to define the post-yield behaviour for most metals. The data pairs on the PLASTIC option define the true stress as a function of true plastic strain. The first data pair defines the initial yield stress and the corresponding initial plastic strain, which must have a value of zero.
Total strain, on the other hand, reaches a maximum value and returns to zero. In Abaqus, the total strain values must be decomposed into elastic and plastic strain components. The plastic strain is obtained by subtracting the elastic strain, defined as the value of true stress divided by Young's modulus, from the value of total strain.
It is important to note that the relationship between plastic and total strain is not always straightforward. While it is generally assumed that greater total strain leads to greater plastic strain, this statement is specific to the results of uniaxial tensile tests and may not apply to crash simulations or other complex scenarios.
In conclusion, understanding the distinction between plastic strain and total strain is crucial when using Abaqus to model and analyse the behaviour of materials under various conditions. By correctly interpreting the results and considering the unique characteristics of each type of strain, engineers can make more informed decisions and predictions about the performance and limitations of different materials.
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Plastic strain and true stress
Plastic strain refers to the permanent deformation of a material when subjected to stress. Unlike elastic deformation, where a material returns to its original shape after the stress is removed, plastic deformation results in a lasting change. This distinction is crucial in engineering applications, as materials that exhibit significant plastic deformation may not be suitable for certain structural roles.
True stress, on the other hand, is a measure of the actual stress experienced by a material, taking into account the reduction in cross-sectional area due to deformation. As a material is stretched or compressed, its cross-sectional area changes, which affects the stress distribution within the material. True stress accounts for these changes, providing a more accurate representation of the stress state than engineering stress, which assumes a constant original cross-sectional area.
In Abaqus, a popular engineering simulation software, the relationship between true stress and plastic strain is essential for accurately modelling material behaviour. Abaqus allows users to define the post-yield behaviour of metals using the *PLASTIC option. By inputting data pairs of true stress and true plastic strain, Abaqus can construct a piecewise-linear plasticity curve that closely approximates the actual behaviour of the material. This curve is fundamental in predicting how a material will respond under various loading conditions.
The process of defining plasticity in Abaqus involves several steps. Firstly, the user must convert nominal stress and strain values into true stress and true strain values using appropriate equations. Then, the plastic strain can be determined by relating it to the total and elastic strains. Finally, the true stress-true plastic strain data pairs are input into Abaqus, allowing the software to generate the plasticity curve. It is important to note that the input data must accurately represent the material's behaviour, especially when simulating large strains, to ensure reliable simulation results.
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Plastic strain and nominal stress
Plasticity is a material behaviour that is caused by the geometry of the test specimen, the nature of the test itself, and the stress and strain measures used. The plastic behaviour of a material is described by its yield point and its post-yield hardening. The shift from elastic to plastic behaviour occurs at a certain point, known as the elastic limit or yield point, on a material's stress-strain curve. The stress at the yield point is called the yield stress. In most metals, the initial yield stress is 0.05 to 0.1% of the material's elastic modulus. The deformation of the metal before reaching the yield point creates only elastic strains, which are fully recovered if the applied load is removed. However, once the stress in the metal exceeds the yield stress, permanent (plastic) deformation begins to occur.
The plastic strain is obtained by subtracting the elastic strain, defined as the value of true stress divided by Young's modulus, from the value of total strain. The plastic strain value is not always zero at all values of yield stress, as it changes with temperature. The first point of tabular data in ABAQUS must always be the yield stress associated with zero plastic strain.
When defining plasticity data in ABAQUS, you must use true stress and true strain. ABAQUS requires these values to interpret the data in the input file correctly. However, material test data are often supplied using values of nominal stress and strain. In such cases, the plastic material data must be converted from nominal to true stress and strain. The relationship between true strain and nominal strain is established by expressing the nominal strain as ε = ln(1 + ε'). The relationship between true stress and nominal stress is formed by considering the incompressible nature of plastic deformation and assuming that elastic volumetric deformation is negligible: σ = E ε.
The flow curve, or the true stress versus true plastic strain diagram, is the basis for understanding and predicting the plastic deformation behaviour of materials. The tensile test is a classical way of extracting the true stresses and true plastic strains from the nominal stress-strain curve. The true stress is calculated from the nominal stress and nominal strain, assuming constant volume. The true stress is typically calculated assuming constant volume and ignoring elastic volume changes. This is a good approximation for materials with comparatively low strength and high bulk modulus, such as plain low carbon steels.
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Plastic strain and elastic strain
Plasticity in ABAQUS is defined by the relationship between true stress and nominal stress and strain. The PLASTIC option in ABAQUS defines the post-yield behaviour for most metals, with the first data pair defining the initial yield stress and the corresponding initial plastic strain, which must be zero. The plastic strain is obtained by subtracting the elastic strain from the total strain value.
Elastic strain and plastic strain refer to the different types of deformation that occur in engineering applications. Deformation is the change in size or shape of an object, and it can be elastic or plastic. Elastic deformation occurs when applied stress does not surpass the energy required to break molecular bonds, allowing the material to deform reversibly and return to its original shape once the stress is removed. This is known as Young's modulus. The relationship between stress and strain is generally linear and reversible up until the yield point, and the deformation is elastic.
Plastic deformation occurs when the stress surpasses the elasticity limit, causing the material to deform irreversibly and not return to its original shape and size, even when the load is removed. This is the plastic region, and plastic behaviour ends at the breaking point. Ductile materials, such as metals, show a gradual decrease in stress with increasing strain, meaning they become easier to deform as stress-strain values approach the breaking point.
In ABAQUS, the user must enter a definite yield stress that allows the program to clearly distinguish between elastic and plastic deformation. This is important for accurately modelling the behaviour of materials.
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Frequently asked questions
Plastic strain is the strain obtained by subtracting the elastic strain (value of true stress/Young's modulus) from the value of total strain.
To calculate plastic strain, you must first convert nominal stress and strain into true stress and true strain. Once these values are known, you can use the equation relating plastic strain to total and elastic strain to determine the plastic strain associated with each yield stress value.
The initial yield stress at zero plastic strain is 380 MPa.
You can define plasticity in Abaqus by using the *PLASTIC option, which defines the post-yield behaviour for most metals. The first data pair defines the initial yield stress and the corresponding initial plastic strain, which must be zero.
