Plasticity (physics)
In physics and materials science, plasticity is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is known as yielding.
Plastic deformation is observed in most materials, particularly metals, soils, rocks, concrete, and foams. However, the physical mechanisms that cause plastic deformation can vary widely. At a crystalline scale, plasticity in metals is usually a consequence of dislocations. Such defects are relatively rare in most crystalline materials, but are numerous in some and part of their crystal structure; in such cases, plastic crystallinity can result. In brittle materials such as rock, concrete and bone, plasticity is caused predominantly by slip at microcracks. In cellular materials such as liquid foams or biological tissues, plasticity is mainly a consequence of bubble or cell rearrangements, notably T1 processes.
For many ductile metals, tensile loading applied to a sample will cause it to behave in an elastic manner. Each increment of load is accompanied by a proportional increment in extension. When the load is removed, the piece returns to its original size. However, once the load exceeds a threshold – the yield strength – the extension increases more rapidly than in the elastic region; now when the load is removed, some degree of extension will remain.
Elastic deformation, however, is an approximation and its quality depends on the time frame considered and loading speed. If, as indicated in the graph opposite, the deformation includes elastic deformation, it is also often referred to as "elasto-plastic deformation" or "elastic-plastic deformation".
Perfect plasticity is a property of materials to undergo irreversible deformation without any increase in stresses or loads. Plastic materials that have been hardened by prior deformation, such as cold forming, may need increasingly higher stresses to deform further. Generally, plastic deformation is also dependent on the deformation speed, i.e. higher stresses usually have to be applied to increase the rate of deformation. Such materials are said to deform visco-plastically.
Contributing properties
The plasticity of a material is directly proportional to the ductility and malleability of the material.Physical mechanisms
In metals
Plasticity in a crystal of pure metal is primarily caused by two modes of deformation in the crystal lattice: slip and twinning. Slip is a shear deformation which moves the atoms through many interatomic distances relative to their initial positions. Twinning is the plastic deformation which takes place along two planes due to a set of forces applied to a given metal piece.Most metals show more plasticity when hot than when cold. Lead shows sufficient plasticity at room temperature, while cast iron does not possess sufficient plasticity for any forging operation even when hot. This property is of importance in forming, shaping and extruding operations on metals. Most metals are rendered plastic by heating and hence shaped hot.
Slip systems
Crystalline materials contain uniform planes of atoms organized with long-range order. Planes may slip past each other along their close-packed directions, as is shown on the slip systems page. The result is a permanent change of shape within the crystal and plastic deformation. The presence of dislocations increases the likelihood of planes.Reversible plasticity
On the nanoscale the primary plastic deformation in simple face-centered cubic metals is reversible, as long as there is no material transport in form of cross-slip. Shape-memory alloys such as Nitinol wire also exhibit a reversible form of plasticity which is more properly called pseudoelasticity.Shear banding
The presence of other defects within a crystal may entangle dislocations or otherwise prevent them from gliding. When this happens, plasticity is localized to particular regions in the material. For crystals, these regions of localized plasticity are called shear bands.Microplasticity
Microplasticity is a local phenomenon in metals. It occurs for stress values where the metal is globally in the elastic domain while some local areas are in the plastic domain.Amorphous materials
Crazing
In amorphous materials, the discussion of "dislocations" is inapplicable, since the entire material lacks long range order. These materials can still undergo plastic deformation. Since amorphous materials, like polymers, are not well-ordered, they contain a large amount of free volume, or wasted space. Pulling these materials in tension opens up these regions and can give materials a hazy appearance. This haziness is the result of crazing, where fibrils are formed within the material in regions of high hydrostatic stress. The material may go from an ordered appearance to a "crazy" pattern of strain and stretch marks.Cellular materials
These materials plastically deform when the bending moment exceeds the fully plastic moment. This applies to open cell foams where the bending moment is exerted on the cell walls. The foams can be made of any material with a plastic yield point which includes rigid polymers and metals. This method of modeling the foam as beams is only valid if the ratio of the density of the foam to the density of the matter is less than 0.3. This is because beams yield axially instead of bending. In closed cell foams, the yield strength is increased if the material is under tension because of the membrane that spans the face of the cells.Soils and sand
Soils, particularly clays, display a significant amount of inelasticity under load. The causes of plasticity in soils can be quite complex and are strongly dependent on the microstructure, chemical composition, and water content. Plastic behavior in soils is caused primarily by the rearrangement of clusters of adjacent grains.Rocks and concrete
Inelastic deformations of rocks and concrete are primarily caused by the formation of microcracks and sliding motions relative to these cracks. At high temperatures and pressures, plastic behavior can also be affected by the motion of dislocations in individual grains in the microstructure.Time-independent yielding and plastic flow in crystalline materials
Time-independent plastic flow in both single crystals and polycrystals is defined by a critical/maximum resolved shear stress, initiating dislocation migration along parallel slip planes of a single slip system, thereby defining the transition from elastic to plastic deformation behavior in crystalline materials.Time-independent yielding and plastic flow in single crystals
The critical resolved shear stress for single crystals is defined by Schmid’s law τCRSS=σy/m, where σy is the yield strength of the single crystal and m is the Schmid factor. The Schmid factor comprises two variables λ and φ, defining the angle between the slip plane direction and the tensile force applied, and the angle between the slip plane normal and the tensile force applied, respectively. Notably, because m > 1, σy > τCRSS.Critical resolved shear stress dependence on temperature, strain rate, and point defects
There are three characteristic regions of the critical resolved shear stress as a function of temperature. In the low temperature region 1, the strain rate must be high to achieve high τCRSS which is required to initiate dislocation glide and equivalently plastic flow. In region 1, the critical resolved shear stress has two components: athermal and thermal shear stresses, arising from the stress required to move dislocations in the presence of other dislocations, and the resistance of point defect obstacles to dislocation migration, respectively. At T = T*, the moderate temperature region 2 is defined, where the thermal shear stress component τ* → 0, representing the elimination of point defect impedance to dislocation migration. Thus the temperature-independent critical resolved shear stress τCRSS = τa remains so until region 3 is defined. Notably, in region 2 moderate temperature time-dependent plastic deformation mechanisms such as solute-drag should be considered. Furthermore, in the high temperature region 3 έ can be low, contributing to low τCRSS, however plastic flow will still occur due to thermally activated high temperature time-dependent plastic deformation mechanisms such as Nabarro–Herring and Coble diffusional flow through the lattice and along the single crystal surfaces, respectively, as well as dislocation climb-glide creep.Stages of time-independent plastic flow, post yielding
During the easy glide stage 1, the work hardening rate, defined by the change in shear stress with respect to shear strain is low, representative of a small amount of applied shear stress necessary to induce a large amount of shear strain. Facile dislocation glide and corresponding flow is attributed to dislocation migration along parallel slip planes only. Moderate impedance to dislocation migration along parallel slip planes is exhibited according to the weak stress field interactions between these dislocations, which heightens with smaller interplanar spacing. Overall, these migrating dislocations within a single slip system act as weak obstacles to flow, and a modest rise in stress is observed in comparison to the yield stress. During the linear hardening stage 2 of flow, the work hardening rate becomes high as considerable stress is required to overcome the stress field interactions of dislocations migrating on non-parallel slip planes, acting as strong obstacles to flow. Much stress is required to drive continual dislocation migration for small strains. The shear flow stress is directly proportional to the square root of the dislocation density, irrespective of the evolution of dislocation configurations, displaying the reliance of hardening on the number of dislocations present. Regarding this evolution of dislocation configurations, at small strains the dislocation arrangement is a random 3D array of intersecting lines. Moderate strains correspond to cellular dislocation structures of heterogeneous dislocation distribution with large dislocation density at the cell boundaries, and small dislocation density within the cell interior. At even larger strains the cellular dislocation structure reduces in size until a minimum size is achieved. Finally, the work hardening rate becomes low again in the exhaustion/saturation of hardening stage 3 of plastic flow, as small shear stresses produce large shear strains. Notably, instances when multiple slip systems are oriented favorably with respect to the applied stress, the τCRSS for these systems may be similar and yielding may occur according to dislocation migration along multiple slip systems with non-parallel slip planes, displaying a stage 1 work-hardening rate typically characteristic of stage 2. Lastly, distinction between time-independent plastic deformation in body-centered cubic transition metals and face centered cubic metals is summarized below.| Body-centered cubic transition metals | Face-centered cubic metals |
| Critical resolved shear stress = high & strongly temperature-dependent | Critical resolved shear stress = low & weakly temperature-dependent |
| Work hardening rate = temperature-independent | Work hardening rate = temperature-dependent |
| Necking strain increases with temperature | Necking strain decreases with temperature |