Alexei Volkov
Elasticity is the ability of a body to return to its original shape and size after being stretched or deformed. It is a property of materials that are solid, liquid, or gas. When an elastic material is deformed due to an external force, it experiences internal resistance and returns to its original state when the force is removed. Plasticity, on the other hand, is the quality of a body that causes it to lose its elasticity and develop a permanent deformation after the force is removed. This is also known as plastic deformation and is observed in materials such as metals, soils, rocks, concrete, and foams. The transition from elastic behaviour to plastic behaviour is known as yielding and occurs when the load exceeds the elastic limit of the material.
| Characteristics | Values |
|---|---|
| Plasticity | The ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces |
| Elasticity | The tendency of solid objects and materials to return to their original shape after the external forces (load) causing a deformation are removed |
| Plastic Deformation | Occurs when stress goes beyond the elasticity limit; the material does not return to its original size or shape and acquires a permanent deformation |
| Elastic Deformation | Occurs when stress values are lower than the proportionality limit; stress is proportional to strain |
| Non-Elastic Deformation | Occurs when stress goes beyond the proportionality limit; deformation is still elastic but nonlinear up to the elasticity limit |
| Ductile Materials | Materials that have a fair amount of plastic deformation before breaking; e.g. copper, rubber, metals |
| Brittle Materials | Materials that can't stretch or bend much without breaking; e.g. glass, concrete, ceramics |
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What You'll Learn
Plastic deformation
Plasticity, also known as plastic deformation, is a property of solid materials that undergo permanent, irreversible deformation in response to applied forces. This is distinct from elastic deformation, where materials return to their original shape and size after the removal of external forces. Plastic deformation occurs when stress is increased beyond the elastic limit, causing the material to reach a fracture point and break.
Amorphous materials, such as polymers, can also undergo plastic deformation despite lacking a well-ordered structure. When subjected to tension, these materials can exhibit crazing, forming fibrils in regions of high hydrostatic stress, resulting in a hazy appearance. This is particularly evident in open-cell foams where cell walls experience bending moments.
The transition from elastic to plastic deformation is known as yielding. In ductile materials like metals, tensile loading causes proportional increments in extension, and upon removal of the load, the material returns to its original size. However, when the load exceeds the yield strength, the extension increases more rapidly, and upon load removal, some degree of extension remains, indicating plastic deformation.
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Elastic deformation
The maximum value of stress at which a material will still remain elastic is called the elastic limit. If the stress is above the elastic limit, the material will not return to its original state and some permanent deformation sets in, a state referred to as a permanent set or plastic deformation.
Plastic deformation occurs when the stress is large enough to cause it to go beyond the elasticity limit. The material continues to be plastically deformed until the stress reaches the fracture point (breaking point).
The physical reasons for elastic behaviour vary among materials and depend on their microscopic structure. For example, the elasticity of polymers and rubbers is caused by stretching polymer chains under an applied force, whereas the elasticity of metals is caused by resizing and reshaping crystalline cells of the lattices under externally applied forces.
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Stress-strain curve
The stress-strain curve is a graphical representation of the relationship between stress and strain, which is unique to each material. It is a useful tool for understanding the elastic and plastic deformation characteristics of materials.
The curve typically consists of several stages, each indicating different mechanical properties. The first stage is the linear elastic region, where the stress is proportional to the strain, following Hooke's law, and the slope is Young's modulus. This region ends at the yield point, marking the initiation of plastic deformation. The stress at this point is called the yield strength.
The second stage is the strain hardening region, where stress continues to increase beyond the yield point, reaching a maximum at the ultimate tensile strength (UTS). During this stage, the material undergoes plastic deformation, with dislocations moving past pinning points, leading to permanent deformation.
Beyond the ultimate tensile strength, the cross-sectional area of the material begins to decrease uniformly, a process known as necking. This is characteristic of ductile materials, where geometrical instability leads to local reductions in cross-sectional area, making these regions more prone to deformation.
As deformation continues, the work-hardening rate decreases, resulting in regions with smaller areas becoming weaker. This leads to a concentration of reduction in these areas, causing the neck to become more pronounced until fracture occurs. After the neck forms, plastic deformation is focused on the neck, while the rest of the material undergoes elastic contraction due to reduced tensile force.
The stress-strain curve is a valuable tool for engineers and scientists to understand and predict the behaviour of materials under load. It helps in selecting appropriate materials for specific applications, ensuring safety and optimal performance in various structures and products.
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Plasticity in crystalline materials
The plasticity of a crystalline material is directly proportional to its ductility and malleability. In a crystal of pure metal, plasticity is caused by two modes of deformation in the crystal lattice: slip and twinning. Slip is a shear deformation that moves atoms through multiple interatomic distances relative to their initial positions. Twinning is plastic deformation that occurs along two planes due to a set of forces applied to a given metal piece. Most metals exhibit greater plasticity when heated, and some metals, like lead, exhibit plasticity at room temperature.
Crystal plasticity is a theory that studies plastic deformation in single-crystal and polycrystalline materials, taking into account the physics and geometry of deformation at the crystal or grain level. At low temperatures, plastic deformation in crystalline materials primarily occurs through slip on specific crystallographic planes in certain directions. Deformation twinning is another mode of plastic deformation that occurs on specific crystallographic planes and plays a significant role in the stress-strain response of the material and the evolution of its underlying microstructure.
The transition from elastic behaviour to plastic behaviour in crystalline materials is defined by a critical or maximum resolved shear stress (τCRSS). This initiates dislocation migration along parallel slip planes of a single slip system. The critical resolved shear stress for single crystals is given by Schmid's law: τCRSS=σy/m, where σy is the yield strength of the single crystal, and m is the Schmid factor, which depends on the angles between the slip plane and the tensile force applied.
The presence of defects within a crystal lattice can entangle dislocations or prevent them from gliding, localizing plasticity to specific regions called shear bands. Microplasticity is a local phenomenon observed in metals, where certain areas undergo plastic deformation while the metal as a whole remains in the elastic domain.
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Elastic limit
Elasticity is the ability of a solid object to return to its original shape after the removal of external forces that caused its deformation. The two parameters that determine the elasticity of a material are its elastic modulus and its elastic limit. Elastic limit, or maximum stress, is the maximum force per unit area within a solid material before the onset of permanent deformation. When the stress is removed, the material returns to its original size and shape.
The elastic limit nearly coincides with the proportional limit for some elastic materials, while for others, a region of non-proportional elasticity exists between the two. The proportional limit is the endpoint of linearly elastic behaviour. The elastic limit is the greatest stress a material can sustain without any deviation from the proportionality of stress to strain. This is also known as Hooke's law.
When the load on a material is increased, the linear behaviour ends at the linearity limit. Beyond this point, the stress-strain relation is nonlinear but still elastic. As the load increases further, the material reaches the elasticity limit, where elastic behaviour ends and plastic deformation begins. Plastic deformation is a non-reversible change of shape in response to applied forces. Once the load exceeds the elastic limit, the material becomes permanently deformed and will not return to its initial shape and size when the stress is removed.
The elastic limit is important in engineering, especially when dealing with adhesives. It is critical that the maximum stress experienced by a joint does not exceed the elastic limit, otherwise, the assembly will have a limited life.
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Frequently asked questions
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.
Plastic deformation is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces.
An object is elastic if it comes back to its original shape and size when the stress vanishes. An object has plastic behaviour when stress is larger than the elastic limit, and the object does not return to its original size or shape.
Yield strength is the threshold at which the extension increases more rapidly than in the elastic region. When the load exceeds this threshold, some degree of extension will remain when the load is removed.
Ductile materials have a larger plastic region and are able to stretch into a new shape before breaking. Examples include metals such as copper, rubber, and foams.
