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{{Short description|Non-reversible deformation of a solid material in response to applied forces}}{{redirect|Plastic material|the material used in manufacturing|Plastic}}{{Metal yield.svg |290px}}{{Stress v strain A36 2.svg |290px}}{{Continuum mechanics|solid}}In physics and materials science, plasticity (also known as plastic deformation) is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces.BOOK, Jacob, Lubliner, 2008, Plasticity theory, Dover, 978-0-486-46290-5, BOOK, Bigoni, Davide, Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability, Cambridge University Press, 2012, 978-1-107-02541-7, 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.BOOK, Milan, Jirásek, ZdenÄ›k P., Bažant, ZdenÄ›k P. Bažant, 2002, Inelastic analysis of structures, John Wiley and Sons, 0-471-98716-6, BOOK, Wai-Fah, Chen, 2008, Limit Analysis and Soil Plasticity, J. Ross Publishing, 978-1-932159-73-8, BOOK, Mao-Hong, Yu, Yu Mao-Hong, Guo-Wei, Ma, Hong-Fu, Qiang, Yong-Qiang, Zhang, 2006, Generalized Plasticity, Springer, 3-540-25127-8, BOOK, Wai-Fah, Chen, 2007, Plasticity in Reinforced Concrete, J. Ross Publishing, 978-1-932159-74-5, 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 â€“ 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

(File:PlasticityIn111Copper.jpg|thumb|alt=A large sphere on a flat plane of very small spheres with multiple sets of very small spheres contiguously extending below the plane (all with a black background)|Plasticity under a spherical nanoindenter in (111) copper. All particles in ideal lattice positions are omitted and the color code refers to the von Mises stress field.)

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.Ziegenhain, Gerolf; and Urbassek, Herbert M.; "Reversible Plasticity in fcc metals" in Philosophical Magazine Letters, 89(11):717-723, 2009 DOI 10.1080/09500830903272900 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.JOURNAL, Maaß, Robert, Derlet, Peter M., Micro-plasticity and recent insights from intermittent and small-scale plasticity, Acta Materialia, January 2018, 143, 338–363, 10.1016/j.actamat.2017.06.023, 1704.07297, 2018AcMat.143..338M, 119387816,

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 materialsBOOK, last1Courtney, first1Thomas, titleMechanical Behavior of Materials, date2005, publisherWaveland Press, Inc, locationLong Grove, Illinois, isbn978-1-57766-425-3, editionSecond,

Time-independent plastic flow in both single crystals and polycrystals is defined by a critical/maximum resolved shear stress (Ï„CRSS), 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

(File:Critical Resolved Shear Stress Versus Temperature.png|thumb|The three characteristic regions of the critical resolved shear stress as a function of temperature)There are three characteristic regions of the critical resolved shear stress as a function of temperature. In the low temperature region 1 (T ≤ 0.25Tm), the strain rate must be high to achieve high Ï„CRSS which is required to initiate dislocation glide and equivalently plastic flow. In region 1, the critical resolved shear stress has two components: athermal (Ï„a) and thermal (Ï„*) 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 (0.25Tm