Sofia Martinez
Plastic strain is a critical concept in understanding the behaviour of materials under stress. ABAQUS is a powerful tool used in engineering simulations to model and analyse the mechanical behaviour of various materials, including metals, plastics, rubbers, foams, and composites. It offers insights into the complex relationship between stress and strain, helping engineers make informed decisions about material selection and design optimisation. This topic explores how ABAQUS defines plastic strain, the methods for inputting data, and the considerations for accurate simulations, providing a deeper understanding of material behaviour beyond the yield point.
| Characteristics | Values |
|---|---|
| Plastic strain value | Changes with temperature-dependent yield stress data |
| Plastic strain calculation | epsilon_total - epsilon_elastic |
| Plastic strain calculation (more rigorous) | Integral (epsilon_plastic_point), where epsilon_plastic_point = epsilon_total_point - epsilon_elastic_point |
| Plastic strain calculation (experimental) | 0.2% |
| Plastic strain calculation (nominal) | Convert nominal stress and strain into true stress and true strain, then subtract strain from total strain |
| Plastic strain curve | Should be in ascending order |
| Plastic strain curve (truncation) | Truncate at the point of peak stress for modest amounts of plastic strain |
| Plastic strain curve (Johnson-Cook model) | Power-law relationship to describe strain rate sensitivity and an exponential relationship to describe thermal softening |
| Plastic strain curve (Abaqus) | A series of straight line segments to form a continuous, piecewise-linear plasticity curve |
| Plastic strain curve (Abaqus/Explicit) | Fits user-defined curves with curves composed of equally spaced points |
| Plastic strain curve (Abaqus/Explicit) | Attempts to use enough intervals such that the maximum error between the regularized data and the user-defined data is less than 3% |
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What You'll Learn
Plastic strain and yield stress
Plasticity refers to the nonlinear, inelastic behaviour of metals at high magnitudes of stress and strain. This behaviour is described by the material's yield point and 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 plastic behaviour of a material is described by its yield point and its post-yield hardening. The yield point is the point at which the material begins to deform permanently, and the stress at this point is called the yield stress. In most metals, the initial yield stress is between 0.05% and 0.1% of the material's elastic modulus.
Plastic strain refers to the permanent deformation of a material beyond its yield point. While elastic deformation can be recovered when the applied load is removed, plastic deformation is irreversible. Both elastic and plastic strains accumulate as the metal deforms in the post-yield region.
The *PLASTIC option in ABAQUS is used to define the post-yield behaviour for most metals. It approximates the smooth stress-strain behaviour of the material with a series of straight lines joining given data points. The data pairs on the *PLASTIC option define the true stress as a function of true plastic strain. The first data pair corresponds to the initial yield stress and must have a plastic strain value of zero.
When defining yield stress in ABAQUS, it is important to distinguish between the onset of plasticity and yield stress. While ductile materials typically do not have a clear yield point, the yield stress in ABAQUS refers to zero equivalent plastic strain, corresponding to the conventional yield stress of 0.2% residual deformation. This distinction is important for accurately modelling the material's behaviour.
In summary, plastic strain refers to the permanent deformation of a material beyond its yield point, and yield stress is the stress at which this plastic deformation begins. ABAQUS provides tools to define and analyse the post-yield behaviour of materials, allowing for a close approximation of their actual behaviour.
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Plastic strain and ductile materials
Plastic strain refers to the permanent deformation in a material after it has been loaded beyond its elastic limit. In the context of Abaqus, a software used for modelling and simulating the behaviour of materials, plastic strain is an important factor in defining the yield stress and post-yield behaviour of ductile materials.
Ductile materials, such as metals, can undergo large plastic deformations before they break. Unlike brittle materials, ductile materials do not have a clear yield point and can withstand significant strains even after they start to yield. This property of ductile materials is known as ductility, which is a measure of the degree of plastic deformation a material can sustain before fracture. Common measures of ductility include percent elongation and reduction in area.
In Abaqus, the *PLASTIC option is used to define the post-yield behaviour of ductile materials, typically metals. The first data pair entered into Abaqus must always be the yield stress associated with zero plastic strain. Subsequent data pairs can be used to fit a uniaxial curve and define how the material will respond to hardening. The stress-strain data provided to Abaqus should accurately reflect the expected strains in the simulation to ensure reliable results.
The process of converting material test data into Abaqus input involves using equations to relate true stress and strain to nominal stress and strain. This allows for the determination of plastic strains associated with each yield stress value. Abaqus then connects these stress-strain data pairs to form a continuous, piecewise-linear plasticity curve, providing a close approximation of the actual material behaviour.
It is important to note that Abaqus/Explicit may not use the exact material data defined by the user. Instead, it automatically regularizes the data for efficiency, and the response outside the defined range is assumed to be constant. Additionally, Abaqus/Explicit aims to minimise the error between the regularized data and user-defined data, typically targeting a maximum error of less than 3%.
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Plastic strain and the Johnson-Cook model
Plasticity in Abaqus can be defined by using the *PLASTIC option, which defines the post-yield behaviour for most metals. The first data pair in this option defines the initial yield stress and the corresponding initial plastic strain, which must have a value of zero.
The Johnson-Cook model, proposed by Johnson and Cook in 1983, is a plasticity model that is based on Mises plasticity with closed-form analytical equations specifying the hardening behaviour and the strain-rate dependence of the yield stress. The model integrates the effects of strain hardening, strain rate hardening, and thermal softening.
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 equation for the model includes the equivalent plastic strain, the plastic strain rate, the reference strain rate, the initial yield strength of the material at a quasi-static strain rate, and the flow stress on strain hardening behaviour at a quasi-static strain rate.
The Johnson-Cook model is a multiplicative law and is a strain, temperature-dependent viscoplastic model suited for high strain rate processes. The model takes into consideration three key factors: temperature, strain, and strain rate. By integrating these factors, the model provides a comprehensive understanding of a material's behaviour, allowing for a visualisation of the impact of different factors on strain.
The Johnson-Cook model has been widely applied in the fields of impact and structural analysis. It is commonly used for ductile metals and has a corresponding failure model that evaluates the influence of stress, strain rate, and temperature.
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Plastic strain and the stress-strain curve
Plastic strain is an important consideration when defining yield stress in Abaqus. 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.
The stress-strain curve is a graphical representation of the relationship between stress (force per unit area) and strain (proportional deformation) in a material. It is used to characterise the mechanical behaviour of materials, including metals, plastics, rubbers, foams, composites, and more. The stress-strain curve is particularly useful for understanding the elastic and plastic regions of a material's behaviour.
In Abaqus, the stress-strain curve is used to convert material test data into the appropriate input format. The equations relating true stress to nominal stress and strain, and true strain to nominal strain, are used to make this conversion. The equation relating plastic strain to total and elastic strains can then be used to determine the plastic strains associated with each yield stress value. It is important to provide the proper stress-strain data to Abaqus, especially if the strains in the simulation will be large, as there can be significant differences between nominal and true values at larger strains.
The Johnson-Cook model is a plasticity model based on Misses plasticity that is used in Abaqus to model isotropic hardening. It employs analytical equations to define the hardening behaviour and the relationship between the strain rate and yield stress. This model can be used to define classical metal plasticity, where the yield surface changes size uniformly in all directions, resulting in an increase or decrease in yield stress as plastic straining occurs.
The onset of plasticity and yield stress are important considerations when defining plastic strain in Abaqus. While ductile materials typically have a well-defined yield point, the Rp0.2-criterion was invented to address cases where the onset of yield is not a well-defined point on the stress-strain curve, such as with brittle materials. In Abaqus, a definite yield stress is entered to distinguish between elastic and plastic deformation.
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Plastic strain and the PLASTIC option
Plasticity is a property exhibited by materials that can undergo irreversible deformation after the application of a load. This is in contrast to elasticity, where deformation is reversible. Plastic strain is the measure of this permanent deformation.
In Abaqus, plastic strain can be defined in the software's material library, which offers a range of options for modelling various engineering materials, including metals, plastics, rubbers, foams, composites, and more. 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 first data pair defines the initial yield stress and the corresponding initial plastic strain, which must have a value of zero.
Abaqus connects the 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 the actual material behaviour. It is important to note that the strains provided in material test data may not be the plastic strains in the material. Therefore, the nominal stress and strain values must be converted into true stress and true strain values.
Abaqus/Explicit may not use the exact material data defined by the user, as all material data defined in tabular form are automatically regularized for efficiency. Users can adjust the error tolerance by using the RTOL parameter on the *MATERIAL option. Abaqus/Explicit also allows for the modelling of cyclic loading of a material with a constant rate of hardening, known as the Kinematic option.
The Johnson-Cook plasticity model is a specific type of Mises plasticity that can model high-strain-rate deformation of metals. This model is based on isotropic hardening and employs analytical equations to define the hardening behaviour and the relationship between the strain rate and yield stress. It is important to note that this model cannot accurately predict the unloading response of many thermoplastics.
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Frequently asked questions
Plastic strain is a feature in Abaqus that allows users to model plastic behaviour in materials such as metals, plastics, rubbers, foams, composites, and more. It is used to define the post-yield behaviour for most metals.
You can enter plastic strain data in Abaqus by using the *PLASTIC option. This option defines the true stress as a function of true plastic strain. The first data pair must define the initial yield stress and the corresponding initial plastic strain, which must be zero.
While there are only slight differences between nominal and true values at small strains, there are significant differences at larger strains. Therefore, it is important to provide the proper stress-strain data to Abaqus if the strains in the simulation will be large.
The Johnson-Cook model is a plasticity model based on Misses plasticity. It uses analytical equations to define the hardening behaviour and the relationship between the strain rate and yield stress. It is particularly suited for modelling high-strain-rate deformation of metals.
