Ethan Clarke
The theory of elasticity and plasticity is a branch of mechanics that deals with the calculation of stresses and strains in a body. Elasticity is the ability of a body to return to its original configuration (shape and size) once deforming forces are removed. Plasticity, on the other hand, is the quality of a body that causes it to lose its elasticity and develop a permanent distortion after the deforming force is removed. Plastic deformation occurs when the stress is increased beyond the elastic limit, causing the material to deform irreversibly. The theory of elasticity and plasticity is important in engineering and has applications in metal forming processes.
| Characteristics | Values |
|---|---|
| Elasticity | The ability of a body to return to its original configuration (shape and size) once deforming forces are removed |
| Plasticity | The quality of a body that causes it to lose its elasticity and develop a permanent distortion after the deforming force is removed |
| Elastic deformation | Deformation that subsides when the external forces that caused the change and the stress connected with it are removed |
| Plastic deformation | A persistent deformation or change in the shape of a solid body caused by a sustained force |
| Elastic deformation | Reversible |
| Plastic deformation | Irreversible |
| Elastic limit | The utmost amount to which a solid may be stretched without permanently changing size or form |
| Plastic deformation | Happens as a result of the breakdown of a few chemical bonds between the atoms that comprise the material |
| Plastic deformation | Atoms may slip past each other during plastic deformation |
| Elasticity | The tendency of solid objects and materials to return to their original shape after the external forces (load) causing a deformation are removed |
| Elasticity | An object is elastic when it comes back to its original size and shape when the load is no longer present |
| Elasticity | Physical reasons for elastic behavior vary among materials and depend on the microscopic structure of the material |
| Elasticity | The two parameters that determine the elasticity of a material are its elastic modulus and its elastic limit |
| Elastic modulus | Typical for materials that are hard to deform; in other words, materials that require a high load to achieve a significant strain |
| Elastic limit | The stress value beyond which the material no longer behaves elastically but becomes permanently deformed |
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What You'll Learn
Elasticity and plasticity definitions
Elasticity is the quality or state of being elastic. It is the ability of a strained body to recover its original size and shape after deformation. This ability is known as elastic deformation or elastic behaviour. Most solid materials exhibit elastic behaviour to some degree, but there is a limit to the magnitude of force and deformation within which elastic recovery is possible. This limit is known as the elastic limit, and stresses beyond it cause a material to yield or flow. For example, a steel bar or wire can be extended elastically only about 1% of its original length, while strips of certain rubber-like materials can be extended elastically up to 1000%.
Elastic deformation is reversible, and when deformation forces are removed, a body with elastic properties will return to its previous size and shape. The mathematical theory of elasticity and its application to engineering mechanics concern the macroscopic response of a material to stress, rather than the underlying mechanism that causes it. In simple tension tests, the elastic response of materials such as steel and bone demonstrates a linear relationship between tensile stress and the extension ratio. This relationship is expressed as Hooke's law, which applies to one-dimensional deformations but can be extended to more general deformations.
Plasticity, on the other hand, is the quality or state of being plastic, especially the capacity for being moulded or altered. In physics and materials science, plasticity is the ability of a solid material to undergo permanent deformation or a non-reversible change of shape in response to applied forces. This ability is known as plastic deformation or plastic behaviour. Plastic deformation occurs when deformation forces exceed the elastic limit of a material, and it is observed in most materials, particularly metals, soils, rocks, concrete, and foams.
Plastic deformation is irreversible, and when deformation forces are removed, a body with plastic properties will not return to its previous size and shape. In engineering, the transition from elastic behaviour to plastic behaviour is known as yielding. The plasticity of a material is directly proportional to its ductility and malleability. Perfect plasticity is a property of materials to undergo irreversible deformation without any increase in stresses or loads. Plastic deformation can be caused by various physical mechanisms, such as slip and twinning in crystalline materials, microcracks in brittle materials, and bubble or cell rearrangements in cellular materials.
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Stress and strain
The behaviour of materials under stress varies, and it depends on the type of material and its chemical composition. For instance, materials with a high elastic modulus are more resistant to deformation and require larger forces to induce deformation. Conversely, materials with a low elastic modulus are easily deformed under stress. An example is a rubber band, which has a low elastic modulus and can be stretched easily.
When a material is subjected to stress, it undergoes deformation, which can be elastic or plastic. Elastic deformation is reversible, meaning that the material returns to its original shape and size once the stress is removed. This occurs in the linear region of the stress-strain curve, where the deformation is proportional to the applied force, as described by Hooke's law. The elastic limit is the maximum amount a material can be stretched without permanent deformation. Materials such as rubber, nylon, and silicone exhibit elastic deformation.
On the other hand, plastic deformation is irreversible. The material undergoes a permanent change in shape and size even after the stress is removed. This occurs in the nonlinear region of the stress-strain curve, where the deformation exceeds the elastic limit. At this point, the material transitions from elastic to plastic deformation, known as the yield point or yield strength. Materials such as clay, mud, and wax exhibit plastic deformation.
The study of stress and strain is essential in understanding the behaviour of materials, particularly in the fields of materials science, engineering, and biomechanics. It allows for the prediction of how materials will respond to applied forces and designing structures accordingly. For example, the plastic analysis method is used by engineers to design steel structures, considering the plastic deformation and yield strength of the material.
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Elastic deformation
The concept of elastic deformation is essential in engineering, where it is studied in the context of mechanical and structural engineering. Engineers aim to understand and design structures that can withstand applied forces without permanent deformation. By analysing the stress-strain relationship and the elastic limit of materials, engineers can create structures that are stable and resilient to external forces.
In summary, elastic deformation is a temporary and reversible change in the shape or volume of a material due to applied stress. This deformation is characterised by the stretching of bonds between atoms, and it is recoverable upon removal of the force. The understanding of elastic deformation is crucial in engineering to design structures that can withstand and recover from external forces.
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Plastic deformation
In ductile materials, plastic deformation occurs when the distortion surpasses the elastic limit. For example, in metals like copper, there is an elastic zone where elastic deformation occurs. Once the material reaches its elastic limit, it will experience plastic deformation, which is a permanent distortion. On the other hand, brittle materials like rocks may not show any elastic deformation before the onset of plastic deformation. They fail very rapidly with little to no warning, and the edges at the point of rupture are typically jagged.
The physical mechanisms behind plastic deformation can be varied. In metals, plasticity is often caused by dislocations at a crystalline scale. In brittle materials like rocks, concrete, and bone, plasticity is predominantly caused by slip at microcracks. In cellular materials like liquid foams or biological tissues, plasticity is a consequence of bubble or cell rearrangements. The plasticity of a material is directly proportional to its ductility and malleability.
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Elastic limit
The elastic limit is a fundamental property of solid materials, defining the maximum stress a material can endure without undergoing permanent deformation. It is the point at which a material transitions from the elastic deformation region to the plastic deformation region. In other words, it is the threshold where elastic behaviour ends and plastic deformation begins.
Elastic deformation occurs when a material returns to its original shape and size after the removal of external forces. Within the elastic deformation region, the strain of a material is directly proportional to the applied stress, as stated by Hooke's Law.
Plastic deformation, on the other hand, is irreversible. The material does not return to its original shape and size, even when the load is removed. This is because the stress applied exceeds the elastic limit, causing the material to yield and undergo permanent structural changes.
The elastic limit is a critical parameter in mechanical design and material selection, especially in applications involving cyclic loading or precision components. It is one of the two parameters that determine the elasticity of a material, the other being the elastic modulus. A high elastic modulus is typical of materials that are hard to deform, such as steel, while a low elastic modulus is characteristic of materials that are easily deformed, such as rubber.
The elastic limit of ductile materials, such as metals, can be observed in a stress-strain diagram. As the load is gradually increased, the stress-strain relation becomes nonlinear but remains elastic until the elasticity limit is reached. Beyond this limit, the material undergoes plastic deformation until it reaches the fracture point, or breaking point.
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Frequently asked questions
Elasticity is the ability of a material to deform under an applied force and then return to its original shape once the force is removed. Elastic materials can be stretched or compressed to a certain extent without undergoing permanent deformation. Examples of elastic materials include rubber, nylon, and silicone.
Plasticity is the ability of a material to undergo permanent deformation without breaking. Plastic materials can be stretched or compressed beyond their yield point, resulting in irreversible changes in shape. Clay, mud, and wax are examples of plastic materials.
Elastic deformation is reversible, meaning the material can return to its original shape and size after the deforming force is removed. Plastic deformation, on the other hand, is irreversible. Once a plastic body is subjected to a deforming force, it does not tend to return to its previous structure.
The elasticity of a material depends on its elastic moduli, such as Young's modulus, shear modulus, and bulk modulus. Materials with higher elastic moduli are more resistant to deformation and require larger forces to induce the same amount of deformation compared to materials with lower elastic moduli.
