Chloe Zhang
Elastic perfectly plastic behavior is a property of materials that combines the characteristics of perfect elasticity and perfect plasticity. Perfect elasticity refers to a material's ability to return to its original shape after deformation, with the force required for deformation being proportional to the change in shape. On the other hand, perfect plasticity describes a material that undergoes permanent deformation without any restoring force, meaning it will not return to its original shape. In engineering, the transition from elastic behavior to plastic behavior is known as yielding, and it is often studied using stress-strain curves. These curves help engineers understand how materials behave under different levels of stress and strain, allowing them to design structures and choose appropriate materials for specific applications.
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What You'll Learn
Perfectly elastic materials suffer zero deformation under stress
Elasticity is the tendency of solid objects and materials to return to their original shape after the external forces (load) causing a deformation are removed. A perfectly elastic material is defined as a material that suffers zero deformation under any value of stress (within elastic limits). This definition is similar to that of a rigid body, which is a body that suffers no deformation under stress.
Perfectly elastic materials will break within the elastic range, and their failure is brittle without plasticity. The force required to deform perfectly elastic objects is directly proportional to the distance of deformation, regardless of how large that distance becomes. This is known as perfect elasticity, in which a given object will return to its original shape no matter how strongly it is deformed. This is an ideal concept only, as most materials that possess elasticity in practice remain purely elastic only up to very small deformations, after which plastic (permanent) deformation occurs.
The elasticity of a material is quantified by the elastic modulus, such as Young's modulus, bulk modulus, or shear modulus, which measure the amount of stress needed to achieve a unit of strain; a higher modulus indicates that the material is harder to deform. The SI unit of this modulus is the pascal (Pa). The elastic limit or yield strength is the maximum stress that can be applied before the onset of plastic deformation.
A perfectly plastic body, on the other hand, produces no restoring force for any value of stress applied. It would always suffer permanent deformation for any value of load applied, and would show plastic behaviour throughout the stress-strain curve.
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Perfectly plastic bodies produce no restoring force
Perfectly elastic and perfectly plastic materials are ideal concepts often used in engineering. A perfectly elastic material can be defined as one that suffers zero deformation under any value of stress within its elastic limit. On the other hand, a perfectly plastic body can be defined as one that produces no restoring force for any value of stress applied.
In other words, a perfectly elastic material will always return to its original shape, and the force required to deform it is proportional to the deformation. Conversely, a perfectly plastic body will always suffer permanent deformation for any value of load applied. This means that a perfectly plastic body will show plastic behaviour throughout the stress-strain curve.
The stress-strain curve for a perfectly elastic material is linear and increasing, whereas for a perfectly plastic material, it is non-linear and represented by a curve. The deformation of a perfectly plastic material is large at low stress, and the stress vs strain relationship is non-linear. This is in contrast to a perfectly elastic material, where the stress vs strain relationship is linear and the deformation is within the elastic range.
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, the mechanisms that cause plastic deformation can vary. At a crystalline scale, plasticity in metals is caused by dislocations, which are defects in the crystal structure.
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Elastic-plastic models are used to compute stress
Elastic-perfectly plastic behaviour is a concept in material science that combines the properties of elastic and plastic materials. Elastic materials return to their original shape and size when external forces causing deformation are removed. Plastic materials, on the other hand, undergo irreversible changes in shape in response to applied forces, resulting in permanent deformation.
Elastic-plastic models are mathematical tools used to compute stress based on the current value of strain and selected internal variables. These models are particularly useful for predicting the behaviour of materials under extreme conditions, such as impact loading, high pressures, and high temperatures. By understanding how materials behave under these conditions, engineers can design structures and choose appropriate materials to ensure safety and durability.
The process typically begins with a linear elastic analysis, where the material's behaviour is simulated using a linear stress-strain curve. If the stresses exceed the yield strength, a further analysis is conducted with a plastic material behaviour model. This involves employing various techniques, such as exponential hardening laws, to capture the material's response accurately.
One commonly used model is the Ramberg-Osgood formula, which simplifies the stress-strain relationship for large plastic deformations. Other models include the Johnson-Cook model, which accounts for thermal softening and strain rate hardening, and the multilinear model, which aims to replicate the material's behaviour as closely as possible. These models are applied in different scenarios, depending on the specific characteristics of the material being analysed.
The use of elastic-plastic models is essential for designing structures that can withstand significant loads without failing. By predicting the behaviour of materials under extreme conditions, engineers can make informed decisions about the suitability of different materials and optimise their designs to prevent catastrophic failures. These models are valuable tools in ensuring the safety and integrity of structures in various industries, including construction, aerospace, and automotive engineering.
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Plastic deformation is irreversible
Elasticity and plasticity are two important concepts in engineering and materials science. A perfectly elastic material is one that returns to its original shape when stress is removed, even after undergoing deformation. On the other hand, a perfectly plastic body always suffers permanent deformation for any value of load applied. This phenomenon, known as plastic deformation, is an irreversible process where the material undergoes a non-reversible change of shape in response to applied forces.
Plastic deformation is a common occurrence in metals, soils, rocks, concrete, and foams. It is a result of the breaking and reformation of atomic bonds, leading to a change in the material's microstructure. This process is facilitated by dislocation movement, where defects in the crystal lattice allow atoms to slide past each other more easily than in a perfect crystal structure. The presence of dislocations increases the likelihood of planes, and when the material is stressed, these dislocations move through the crystal lattice, enabling plastic deformation.
The transition from elastic behaviour to plastic behaviour is known as yielding. In crystalline materials, plasticity is usually a consequence of dislocations, which are relatively rare in most crystalline materials. However, some materials may have numerous dislocations as part of their crystal structure, resulting in plastic crystallinity. Additionally, elevated temperatures generally increase the mobility of dislocations, making materials more ductile and easier to deform plastically.
The amount of plastic deformation in a material can be determined by analysing its stress-strain curve. The stress at which the material departs from a linear stress-strain relationship is known as the proportional limit. By drawing a line parallel to the initial linear segment of the curve and marking the point of intersection with the horizontal axis, the horizontal distance from the origin represents the plastic strain. This value of plastic strain required to break the material defines its ductility.
Plastic deformation can be observed in various deformation processes such as rolling, forging, extrusion, and bulk drawing, where the shape of ductile workpieces is permanently changed to obtain desired microstructures and material properties. These processes require a comprehensive understanding of the mechanical and microstructural properties of the materials, external loads, and contact boundary conditions.
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Plastic deformation is caused by microcracks and sliding motions
Elastic-perfectly plastic behavior is a property of materials that undergo irreversible deformation without any increase in stresses or loads. Plastic deformation is observed in most materials, particularly metals, soils, rocks, concrete, and foams.
At high temperatures and pressures, plastic behavior can be affected by the motion of dislocations in individual grains in the microstructure. Time-independent plastic flow in both single crystals and polycrystals is defined by a critical/maximum resolved shear stress (τCRSS), which initiates dislocation migration along parallel slip planes of a single slip system. This defines the transition from elastic to plastic deformation behavior in crystalline materials.
Slip is a shear deformation that moves atoms through many interatomic distances relative to their initial positions. It is the sliding of crystal blocks over one another along various crystallographic planes referred to as slip planes. Slip happens when dislocations travel along densely packed planes and directions, where there are the most atoms per unit length.
Twinning is another mechanism of plastic deformation, which occurs along two planes due to a set of forces applied to a given metal piece. Twinning causes planes to slip more by affecting the plane’s orientation, which adds to plastic deformation.
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Frequently asked questions
Elastic behaviour is when a material returns to its original shape after deformation, and the force required to deform the material is proportional to the deformation.
Plastic behaviour is when a material undergoes permanent deformation, a non-reversible change of shape in response to applied forces.
A perfectly elastic material suffers zero deformation under any value of stress (within the elastic limit).
A perfectly plastic material produces no restoring force for any value of stress applied. Thus, a perfectly plastic body would always suffer permanent deformation for any value of load applied.
An elastic-perfectly plastic material is a term used in modelling. It is commonly used to model a material that exhibits a brittle response and a marginal difference between its ultimate stress and yield stress.
