Alexei Volkov
Perfect plasticity is a property of materials that undergo irreversible deformation without an increase in stress or load. A perfectly plastic material always plastically (permanently) deforms under load. The elastic domain characterising the mechanical behaviour of perfectly plastic materials is always the same. The simplest mathematical expression of the yield surface for a perfectly plastic material is when the relevant stress is the total or effective stress. Putty, mud, and paraffin wax are examples of nearly perfectly plastic bodies.
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What You'll Learn
- Perfect plasticity is a property of materials to undergo irreversible deformation
- Plastic deformation is observed in most materials, particularly metals
- Plastic behaviour refers to a material that retains deformation
- Perfect plasticity is characterised by the same size and shape of the yield surface
- Perfect plasticity is assumed to have a bi-linear stress-strain curve
Perfect plasticity is a property of materials to undergo irreversible deformation
In engineering, the transition from elastic behaviour to plastic behaviour is known as yielding. Plastic deformation is observed in most materials, particularly metals, soils, rocks, concrete, and foams. However, it's important to note that there are no truly perfectly plastic materials, and the concept is used for mathematical modelling and categorisation.
When a material is in a plastic state, it follows the condition of consistency, where the yield criterion is satisfied. This ensures an appropriate description of the physical process involved in plastic deformation. The yield function is only a function of the stress state, and the elastic domain characterising the mechanical behaviour of perfectly plastic materials remains the same.
Materials that are close to being perfectly plastic include putty, mud, and paraffin wax. These materials can undergo large deformations before breaking. On the other hand, materials like clay or non-strengthening putties break relatively quickly. The plasticity of a material is directly proportional to its ductility and malleability.
In crystalline materials, plasticity is usually a result of dislocations, which are defects in the crystal structure. These dislocations can cause slip and twinning deformations, leading to irreversible changes in the material's shape.
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Plastic deformation is observed in most materials, particularly metals
The plasticity characteristics of metals can be significantly altered by various factors, such as thermal or mechanical treatments, or exposure to different environments. For example, heating a metal can increase its ductility and malleability, making it more susceptible to plastic deformation. The complex behaviour of metals during plastic deformation is described by various equations, such as the Ludwik-Hollomon and Voce equations, which take into account factors like applied stress, yield stress, plastic strain, and work hardening coefficients.
While the study of plastic deformation in metals is challenging due to the difficulty in observing internal processes, certain techniques, such as the PLX-Benchtop, can extract metal stress-strain curves, aiding in the understanding of metal behaviour. Additionally, models like the Dugdale-Barenblatt model represent the plastic zone by considering the closure stress acting on the tip of a fictitious crack.
Plastic deformation is observed in other materials besides metals, including ceramics and fiber-reinforced plastics. In ceramics, plastic deformation occurs under specific loading conditions, requiring high shear stresses due to covalent atomic bonds. On the other hand, fiber-reinforced plastics exhibit the "Felicity Effect," where AE emissions are observed at loads lower than the previous maximum, breaking the typical "Kaiser Effect" observed in other materials.
Overall, plastic deformation is a critical aspect of understanding material behaviour, particularly in engineering applications, where the ductility and plasticity characteristics of materials play a significant role in their performance and functionality.
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Plastic behaviour refers to a material that retains deformation
Plastic deformation occurs when a material is subjected to tensile, compressive, bending, or torsion stresses that exceed its yield strength. The yield strength is the load at which the material reaches its yield point, or the point at which the material fails to return to its original position. If the load exceeds the yield strength, the material will undergo plastic deformation and retain a permanent strain after the load is removed.
The plasticity of a material is directly proportional to its ductility and malleability. Ductile materials, such as metals, can undergo tensile loading and display elastic behaviour, returning to their original size when the load is removed. However, once the load exceeds the yield strength, the extension increases rapidly, and some degree of extension will remain when the load is removed. This is known as elastic-plastic deformation.
Materials exhibiting perfect plasticity are characterised by the same size and shape of the yield surface under the development of plastic deformations. The elastic domain characterising the mechanical behaviour of perfectly plastic materials remains the same. Classical examples of perfectly plastic yield criteria have been presented by Coulomb, Tresca, von Mises, Drucker and Prager, and others.
While there are no truly perfectly plastic materials, wax or putty are considered close to perfectly plastic. These materials can be used in mathematical modelling and categorisations, even though they do not exhibit the properties in reality.
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Perfect plasticity is characterised by the same size and shape of the yield surface
Perfect plasticity is a property of materials where they undergo irreversible deformation without an increase in stresses or loads. This means that the material will not return to its original configuration when the external force is removed. Materials behaving according to the theory of perfect plasticity are characterised by the same size and shape of the yield surface under the development of plastic deformations. In other words, the elastic domain characterising the mechanical behaviour of perfectly plastic materials is always the same.
The simplest mathematical expression of the yield surface for a perfectly plastic material can be expressed as: ij is the relevant stress (i.e. total or effective stress). The stress conditions characterising the reversible and irreversible response of materials with a thermoelastic (or elastic), perfectly plastic behaviour are as follows:
- Equation (4.89) expresses that elastic deformation arises as long as the stress state is inside the yield surface.
- Equation (4.90) expresses that plastic deformation arises as long as the stress state lies or travels on the yield surface.
The condition of consistency requires that a yield criterion is satisfied as long as the material is in a plastic state. This means that when loading a material characterised by plastic behaviour, the stress state must stay on the yield surface.
While no material is perfectly plastic, some materials come close, including putty, mud, and paraffin wax. These materials are soft and easily deformed, and they can be stretched a lot before breaking. They may deform under very light loads, and they will continue to deform until they break. This is in contrast to brittle materials, which have little to no deformation before rupture.
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Perfect plasticity is assumed to have a bi-linear stress-strain curve
Perfect plasticity is a property of materials that always deform plastically (permanently) under load. Perfect plasticity is assumed to have a bi-linear stress-strain curve, and the simplest mathematical expression of the yield surface for a perfectly plastic material relates to the total or effective stress.
The bi-linear stress-strain curve is a representation of the relationship between stress and strain, with the curve's first point being the yield point, or zero plastic strain and yield stress. The slope of the curve is assumed to be zero beyond the last user-defined stress-strain data point. The stress-strain curve can be used to model the behaviour of materials under load, with the curve's slope indicating the material's stiffness or softness.
The constitutive model is a mathematical tool used to compute stress based on the current value of strain and selected internal variables. The formulation of elasto-plastic constitutive models considers a one-dimensional example, where only one component of stress is computed. Stress-strain curves obtained from tensile tests are used as experimental data to develop these models.
The plastic flow rule determines the relationship between stress and plastic strain under multi-axial loading, while the elastic unloading criterion models the irreversible behaviour of solids. Plasticity theory was developed to predict the behaviour of metals under loads exceeding the plastic range, but it has since been adapted to other materials, including polymers and certain types of soil.
The yield surface is a key concept in perfect plasticity, and it refers to the condition that the stress state must remain on to ensure an appropriate description of the physical process involved in plastic deformation. The yield surface can increase in size as a result of plastic straining, and it plays a crucial role in modelling strain hardening.
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Frequently asked questions
A perfectly plastic material is one that always plastically (permanently) deforms under load.
Plasticity is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces.
Putty, mud, and paraffin wax are examples of nearly perfectly plastic materials. However, it is important to note that nothing is perfectly plastic or perfectly elastic, only the degree of elasticity or plasticity differs.
Plastic deformation is observed in most materials, particularly metals, soils, rocks, concrete, and foams. Metals show more plasticity when hot than when cold. For example, lead shows sufficient plasticity at room temperature, while cast iron does not.
Plasticity is directly proportional to the ductility and malleability of a material. Ductile materials, such as metals, can start deforming under very light loads and continue to deform until they break.
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