Maya Ellison
When it comes to understanding the plastic section in Abaqus, it's important to grasp the concept of material plasticity and how it's modelled in the software. Abaqus is a powerful tool used in finite element analysis (FEA) to simulate and predict material behaviour, including plasticity. The plastic section in Abaqus deals with defining the post-yield behaviour of materials, particularly metals, and requires the use of true stress and true strain values. Users can choose from various material models, such as isotropic, kinematic, multilinear, and Johnson-Cook, or define their own custom models. This flexibility allows for accurate representations of complex material behaviours, making Abaqus a valuable resource for engineers and designers.
| Characteristics | Values |
|---|---|
| Material models | Mises plasticity, Johnson-Cook plasticity, isotropic hardening, kinematic hardening, multilinear hardening, and more |
| Material data | Functions of temperature, external fields, and internal state variables, such as plastic strain |
| Material test data | Nominal stress and strain values, which must be converted to true stress and strain values |
| Plastic strain | Determined by the equation relating plastic strain to total and elastic strains |
| Plastic option | Used to define post-yield behavior for most metals, with data pairs defining true stress as a function of true plastic strain |
| Plasticity curve | ABAQUS connects stress-strain data pairs with a series of straight line segments to form a continuous, piecewise-linear curve |
| Plastic behavior | Materials undergo both elastic and plastic deformation, with linear elastic response initially, followed by plastic deformation |
| Modeling plasticity | Various options available, including the 'Plastic' model, which uses Mises or Hill yield surfaces with associated plastic flow |
| ORNL constitutive model | Applicable to Types 304 and 316 stainless steel, with a rate-independent plasticity response and a rate-dependent creep response |
| Armstrong-Frederick model | Requires input parameters such as stress-strain history and model parameters (𝑐 and 𝑟) |
| Material properties | Density, Young modulus, and Poisson ratio |
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What You'll Learn
Defining plasticity data
When defining plasticity data in Abaqus, it is important to use true stress and true strain values. Abaqus requires these values to correctly interpret the data in the input file. However, material test data often uses nominal stress and strain values, in which case these must be converted to true stress and strain. This conversion can be done using the equations relating true stress and strain to nominal stress and strain. The relationship between true strain and nominal strain is established by expressing the nominal strain as ε = ln(1 + εtrue). The relationship between true stress and nominal stress is formed by considering the incompressible nature of plastic deformation and assuming elastic volumetric deformation is negligible, so σ = σtrue/(1 - εtrue).
The first step in defining plasticity in Abaqus is to convert nominal stress and strain to true stress and strain using the equations mentioned above. Once these values are known, the equation relating plastic strain to total and elastic strain can be used to determine the plastic strains associated with each yield stress value. The plastic strain is obtained by subtracting the elastic strain (true stress divided by Young's modulus) from the total strain.
The *PLASTIC option in Abaqus is then used to define the post-yield behaviour for most metals. The data pairs on this 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. Abaqus connects these stress-strain data pairs with straight-line segments to form a continuous, piecewise-linear plasticity curve. Users can input any number of data pairs to closely approximate actual material behaviour.
The Oak Ridge National Laboratory (ORNL) constitutive model in Abaqus applies to Types 304 and 316 stainless steel. This model is uncoupled into a rate-independent plasticity response and a rate-dependent creep response, each governed by separate constitutive laws. The Johnson-Cook plasticity model in Abaqus is particularly suited for modelling high-strain-rate deformation of metals and is a type of Mises plasticity with analytical forms of the hardening law and rate dependence.
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Converting nominal stress and strain to true stress and strain
When defining plasticity data in Abaqus, true stress and true strain values are required for the software to correctly interpret the data in the input file. However, material test data are often supplied using values of nominal stress and strain. In such cases, it is necessary to convert the plastic material data from nominal to true stress and strain.
The relationship between true and nominal stress and strain is important for accurately defining the plastic behaviour of ductile materials. Nominal stress and strain are also referred to as "engineering" values and are calculated by dividing the applied force by the original cross-sectional area of the material. In contrast, true stress considers the force divided by the current sectional area, which may decrease due to elastic and plastic deformation.
The conversion from nominal to true stress and strain can be achieved using the following equations:
- True strain = Natural log of (1 + nominal strain)
- True stress = Nominal stress x (1 + nominal strain)
These equations ensure that the true stress and strain values accurately reflect the changing dimensions of the material under deformation.
By converting nominal stress and strain to their true counterparts, Abaqus can more accurately model the plastic behaviour of materials, particularly ductile substances that exhibit significant changes in cross-sectional area during deformation. This conversion is a critical step in ensuring the reliability and accuracy of simulations involving complex loading situations.
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The ORNL constitutive model
Initially, the material is assumed to harden kinematically according to a bilinear representation of the virgin stress-strain curve. If a strain reversal occurs or the creep strain reaches 0.2%, the yield surface expands isotropically to the user-defined tenth-cycle stress-strain curve. Further hardening occurs kinematically according to a bilinear representation of the tenth-cycle stress-strain curve. You must specify the virgin yield stress and the hardening through a plasticity model definition and the elastic part of the response through a linear elasticity model definition.
The ORNL formulation can also cause the centre of the yield surface to translate during creep for use in subsequent plastic increments; this behaviour is defined through two optional user-defined parameters.
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The Johnson-Cook plasticity model
The Johnson-Cook model is based on Mises plasticity with closed-form analytical equations specifying the hardening behaviour and the strain-rate dependence of the yield stress. The yield stress is given by an equation where εp is the effective plastic strain, and A, B, n, and m are material parameters that need to be determined from experimental data. The Johnson-Cook hardening can be determined in two ways: one way is that the material yield stress is dependent on the plastic strain and temperature; the second way defines the yield stress as a function of plastic strain and temperature but also adds the strain rate as the third factor to the formulation.
The Johnson-Cook model is a function of von mises tensile flow stress, in accordance with strain hardening, strain rate hardening, and thermal softening. The model integrates the effects of strain hardening, strain rate hardening, and thermal softening, with the parameters A, B, n, C, and m denoting the yielding stress, strain hardening rate, strain hardening coefficient, strain rate hardening coefficient, and thermal softening coefficient, respectively. The Johnson-Cook model performs well in describing the coupled thermomechanical behaviours during plastic deformation, and it provides high computational efficiency and good compatibility for most engineering alloys.
When defining plasticity data in Abaqus, true stress and true strain values must be used for the software to interpret the data in the input file correctly. The PLASTIC option in Abaqus can be used to define the post-yield behaviour for most metals, with the data pairs defining the true stress as a function of true plastic strain. Abaqus connects the stress-strain data pairs with a series of straight line segments to form a continuous, piecewise-linear plasticity curve.
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$70
Modelling material plasticity
To begin modelling material plasticity in Abaqus, users must first specify the appropriate plasticity model for the material being analysed. Abaqus provides a selection of specialized plasticity models, each designed to capture the unique behaviour of different materials. For example, the clay plasticity model in Abaqus/Standard captures the non-elastic behaviour of clay materials, taking into account their high compressibility, time-dependent behaviour, and sensitivity to moisture content. On the other hand, the cast iron plasticity constitutive model simulates the elastoplastic characteristics of grey cast iron, which exhibits greater brittleness under tension compared to most metals.
After selecting the appropriate plasticity model, users must define the material's plasticity data. Abaqus requires the use of true stress and true strain values to correctly interpret the data in the input file. However, it is common for material test data to be supplied using nominal stress and strain values. In such cases, users must convert the plastic material data from nominal to true values using the equations relating the true stress and strain to their nominal counterparts.
Once the plasticity model and data have been defined, Abaqus employs advanced numerical methods to solve the governing equations and predict the plastic deformation of the material. The software connects the user-defined stress-strain data pairs with straight-line segments to form a continuous, piecewise-linear plasticity curve. This curve can be used to approximate the actual material behaviour accurately, providing valuable insights into the behaviour of materials under stress.
Additionally, Abaqus offers features such as the UHARD subroutine, which allows users to define their own hardening laws for materials. This level of customization ensures that Abaqus can accommodate a wide range of materials and loading conditions, making it a versatile tool for modelling material plasticity. By following these steps and utilizing the advanced capabilities of Abaqus, engineers and researchers can gain a deeper understanding of material behaviour and make more informed decisions in their respective fields.
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Frequently asked questions
The first step is to use the equations relating the true stress to the nominal stress and strain and the true strain to the nominal strain to convert the nominal stress and nominal strain to true stress and true strain.
Once the above values are known, the equation relating plastic strain to total and elastic strains is used to determine the plastic strains associated with each yield stress value.
The *PLASTIC option in Abaqus 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 Armstrong-Frederick model is a plasticity model in Abaqus that is typically expressed as follows: S are the equivalent stresses.
Material plasticity in Abaqus can be modelled by entering material plastic properties in the 'create material' window. These properties include material density, Young modulus and Poisson ratio.
