Omar Khalid
When defining plastic material in Abaqus, it is important to understand the differences between the regularized material curves used in the analysis and the curves specified in the input file. Material data can be functions of temperature, external fields, and internal state variables, such as plastic strain. Users must specify the appropriate plasticity model for the material, and Abaqus provides various options for modelling plasticity. The Johnson-Cook plasticity model, for example, is suitable for modelling high-strain-rate deformation of metals. The model parameters can be calibrated using experimental data or empirical relationships. To define plastic material properties, values such as density, Poisson's ratio, Young's modulus, yield strength, tangent modulus, and shear modulus are considered. When defining plasticity data, Abaqus requires true stress and true strain values to interpret the data correctly, and it connects the stress-strain data pairs with straight-line segments to form a continuous, piecewise-linear plasticity curve.
| Characteristics | Values |
|---|---|
| Plasticity model | Mises or Hill yield surfaces with associated plastic flow |
| Plasticity curve | Continuous, piecewise-linear |
| Plastic strain | Obtained by subtracting elastic strain from the value of total strain |
| Data points | Any number can be used |
| Material data | Functions of temperature, external fields, and internal state variables |
| Material curves | User-defined curves are automatically regularized by ABAQUS/Explicit |
| Hardening option | Kinematic, Johnson-Cook, User, or Combined |
| Johnson-Cook model | Suited for modelling high-strain-rate deformation of metals |
| Strain rate dependence | Entered as hardening curves at different strain rates or defined as yield stress ratios |
| Yield behavior | ABAQUS allows accurate definition of yield behavior when yield strength depends on the rate of straining |
| Plastic strain rate | Absolute value of the axial plastic strain rate in uniaxial compression |
| Predefined field variables | Temperature, equivalent plastic strain |
| Bilinear elastic-plastic material model | *MATERIAL, NAME=STEEL, *DENSITY 7800, *ELASTIC 193e+09, 0.27 *PLASTIC 207e+06, 0 UTS, UPS |
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What You'll Learn
- Use the *PLASTIC option to define post-yield behaviour for metals
- Convert nominal stress and strain to true stress and strain
- Plastic strain is obtained by subtracting elastic strain from total strain
- Use the Johnson-Cook plasticity model for high-strain-rate deformation of metals
- Defining bilinear elastic-plastic material
Use the *PLASTIC option to define post-yield behaviour for metals
The *PLASTIC option in ABAQUS is used to define the post-yield behaviour for most metals. This is done by defining 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 then connects the stress-strain data pairs with a series of straight line segments to form a continuous, piecewise-linear plasticity curve. This allows users to approximate the actual material behaviour with a high degree of accuracy. It is important to note that the strains provided in material test data used to define plastic behaviour are typically the total strains in the material, and these total strain values must be decomposed into their elastic and plastic strain components.
The Johnson-Cook plasticity model in ABAQUS is particularly useful for modelling high-strain-rate deformation of metals. This model is a type of Mises plasticity that includes analytical forms of the hardening law and rate dependence. It is commonly used in adiabatic transient dynamic analysis. The Johnson-Cook model is based on Misses plasticity and is one of several predefined models available in ABAQUS, including isotropic, kinematic, and multilinear models.
When performing an analysis, ABAQUS/Explicit may not use the exact material data defined by the user. For efficiency, all material data that are defined in tabular form are automatically regularized. This means that the regularized material curves used in the analysis may differ from the curves specified in the input file. Therefore, it is important to understand the implications of using regularized material data.
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Convert nominal stress and strain to true stress and strain
When defining plasticity data in Abaqus, you must use true stress and true strain. The relationship between true strain and nominal strain is established by expressing the nominal strain as ε = ln(1 + ε'). By adding unity to both sides of this expression and taking the natural log of both sides, we can determine the relationship between true strain and nominal strain. The relationship between true stress and nominal stress is formed by considering the incompressible nature of plastic deformation and assuming that elasticity is also incompressible, so σ = σ'/(1 + ε'). The current area is related to the original area by A = A0*(1 + ε'), and making this final substitution provides the relationship between true stress and nominal stress and strain.
Abaqus requires these values to interpret the data correctly. Often, material test data are supplied using values of nominal stress and strain. In such situations, you must convert the plastic material data from nominal stress and strain to true stress and strain. 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 strains provided in material test data used to define plastic behaviour are not likely to be the plastic strains in the material. Instead, they will probably be the total strains in the material.
While there are only slight differences between nominal and true values at small strains, there are very significant differences at larger strain values. Therefore, it is extremely important to provide the proper stress-strain data to Abaqus if the strains in the simulation will be large. The first data point must always correspond to the yield point, and the subsequent strains can be calculated from the equation provided.
To convert engineering data to true data in Abaqus, import the dataset while appointing the right fields for stress-strain information and selecting the nature of the dataset. After importing the engineering data, Abaqus plots the data points. Next, right-click on the respective dataset and select "Process". Choose "Convert" as the operation and Abaqus will create the converted dataset.
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Plastic strain is obtained by subtracting elastic strain from total strain
Plasticity in ABAQUS can be defined using the *PLASTIC option, which defines 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.
The plastic strain is obtained by subtracting the elastic strain, defined as the value of true stress divided by the Young's modulus, from the value of total strain. This is because the strains provided in material test data used to define plastic behaviour are not likely to be the plastic strains in the material. Instead, they will probably be the total strains in the material. Therefore, these total strain values must be decomposed into their elastic and plastic strain components.
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 or plastic deformation begins to occur. The strains associated with this permanent deformation are called plastic strains. Both elastic and plastic strains accumulate as the metal deforms in the post-yield region.
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Use the Johnson-Cook plasticity model for high-strain-rate deformation of metals
The Johnson-Cook plasticity model in ABAQUS is well-suited for modelling high-strain-rate deformation of metals. This model is a particular type of Mises plasticity that includes analytical forms of the hardening law and rate dependence. It is used in adiabatic transient dynamic analysis.
The Johnson-Cook model is a phenomenological material model, meaning it relies on experimental data to define a material's response. It captures the effects of strain rate, temperature, and strain hardening on the yield stress of a given material. It is particularly useful for simulating high-velocity impact, explosive loading, and other dynamic events where these factors play a crucial role.
The Johnson-Cook model consists of two sections: plasticity and damage. It is relatively simple to implement and calibrate. It accounts for the effects of strain, strain rate, and temperature. It can accurately predict the failure of materials under a wide range of loading conditions.
To use the Johnson-Cook model in ABAQUS, select Johnson-Cook from the list of Hardening options in the Edit Material dialog box. This will open the Data table, where you will need to enter specific data, including the material constant, which is independent of temperature and field variables.
The Johnson-Cook dynamic failure model is based on the value of the equivalent plastic strain at element integration points. Failure is assumed to occur when the damage parameter exceeds 1. The damage parameter is defined as the sum of an increment of the equivalent plastic strain and the strain at failure. This model is suitable for truly dynamic situations and can be used in conjunction with other failure models, such as the tensile failure model, to define tensile failure and simulate bulk metal forming or high-speed manufacturing processes.
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Defining bilinear elastic-plastic material
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 nominal stress and strain values. In such cases, you must convert the plastic material data from nominal stress and strain to true stress and strain.
The plastic strain is obtained by subtracting the elastic strain, defined as the value of true stress divided by the Young's modulus, from the value of total 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 your stress-strain data pairs with a series of straight-line segments to form a continuous, piecewise-linear plasticity curve. You can use any number of data pairs to approximate the actual material behaviour.
You can define a bilinear elastic-plastic material as follows:
> *MATERIAL, NAME=STEEL
> *ELASTIC 200.E9, 0.3
> *PLASTIC 380.E6,0.0 580.E6, 0.35
Here, the Yield stress rises from 380 MPa to 580 MPa at a plastic strain of 0.35.
Abaqus provides an anisotropic yield and creep model for materials that exhibit different yield or creep behaviour in different directions. You can define anisotropic yield or creep by specifying stress ratios that are applied in Hill's potential function.
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Frequently asked questions
The first step is to specify the appropriate plasticity model for the material.
Once the plasticity model is defined, the model parameters need to be calibrated using experimental data or empirical relationships.
The *PLASTIC option in Abaqus is 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.
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