Plasticity (Physics) Information @ CountyPool.com

In physics Physics is a natural science that involves the study of matter and its motion through space-time, as well as all applicable concepts, such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves and materials science Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. This science investigates the relationship between the structure of materials at atomic or molecular scales and their macroscopic properties. It includes elements of applied physics and chemistry, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces^[1]. For example, a solid piece of metal or plastic 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 called yield The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the.

Plastic deformation is observed in most materials including metals, soils, rocks, concrete, foams, bone and skin.^[2]^[3]^[4]^[5]^[6]^[7] However, the physical mechanisms that cause plastic deformation can vary widely. At the crystal scale, plasticity in metals is usually a consequence of dislocations In materials science, a dislocation is a crystallographic defect or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials. The theory was originally developed by Vito Volterra in 1905. Some types of dislocations can be visualized as being caused by the termination of a plane. In most crystalline materials such defects are relatively rare. But there are also materials where defects are numerous and are part of the very 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.

For many ductile Ductility is a mechanical property that describes the extent in which solid materials can be plastically deformed without fracture metals A metal is a chemical element that is a good conductor of both electricity and heat and forms cations and ionic bonds with non-metals. In chemistry, a metal is an element, compound, or alloy characterized by high electrical conductivity. In a metal, atoms readily lose electrons to form positive ions (cations). Those ions are surrounded by, tensile loading applied to a sample will cause it to behave in an elastic In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform is removed. The relative amount of deformation is called the strain manner. Each increment of load is accompanied by a proportional increment in extension, and when the load is removed, the piece returns exactly to its original size. However, once the load exceeds some threshold (the yield strength The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the), the extension increases more rapidly than in the elastic region, and when the load is removed, some amount of the extension remains.

It must be noted however that elastic In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform is removed. The relative amount of deformation is called the strain deformation is an approximation and its quality depends on the considered time frame and loading speed. If the deformation behavior includes elastic deformation as indicated in the adjacent graph it is also often referred to as elastic-plastic or elasto-plastic deformation.

Perfect plasticity is a property of materials to undergo irreversible deformation without any increase in stresses or loads. Plastic materials with hardening necessitate increasingly higher stresses to result in further plastic deformation. Generally plastic deformation is also dependent on the deformation speed, i.e. usually higher stresses have to be applied to increase the rate of deformation and such materials are said to deform visco-plastically.

1 Physical mechanisms
2 Mathematical descriptions of plasticity
- 2.1 Deformation theory
- 2.2 Flow plasticity theory
3 Yield criteria
- 3.1 Tresca criterion
- 3.2 Von Mises criterion
4 References
5 Further reading
6 See also

Physical mechanisms

Main article: Plastic deformation in solids Plastic deformation in solids is a term used in metallurgy, materials science and solid state physics, and refers to an irreversible change in the internal molecular structure of an object. This change may be due to either (or both) of the following factors: 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.

Plasticity in metals

Slip systems

Main article: Slip (materials science)#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 wiki page. The result is a permanent change of shape within the crystal and plastic deformation. The presence of dislocations increases the likelihood of planes slipping.

Reversible plasticity

On the nano scale the primary plastic deformation in simple fcc metals is reversible, as long as there is no material transport in form of cross-glide. ^[8]

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.

Plasticity in 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 Cytoplasmic fibrils are observed on the protoplasmic cylinders found in most spirochetal species, although no function of the cytoplasmic fibrils has been ascribed 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.

Plasticity in martensitic materials

Some materials, especially those prone to Martensitic Martensite, named after the German metallurgist Adolf Martens , most commonly refers to a very hard form of steel crystalline structure, but it can also refer to any crystal structure that is formed by displacive transformation. It includes a class of hard minerals occurring as lath- or plate-shaped crystal grains. When viewed in cross-section, transformations, deform in ways that are not well described by the classic theories of plasticity and elasticity. One of the best-known examples of this is nitinol Nickel titanium, also known as nitinol, is a metal alloy of nickel and titanium, where the two elements are present in roughly equal amounts, which exhibits pseudoelasticity: deformations which are reversible in the context of mechanical design, but irreversible Non-equilibrium thermodynamics is a branch of thermodynamics concerned with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are not isolated from their environment and are therefore continuously sharing matter and energy with other systems. This sharing of matter and in terms of thermodynamics In science, thermodynamics is the study of energy conversion between heat and mechanical work, and subsequently the macroscopic variables such as temperature, volume and pressure. The first to give a concise definition of the subject was Scottish physicist William Thomson who in 1854 stated that:.

Plasticity in 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.

Mathematical descriptions of plasticity

Deformation theory

An idealized uniaxial stress-stress curve showing elastic and plastic deformation regimes for the deformation theory of plasticity.

There are several mathematical descriptions of plasticity^[9]. One is deformation theory (see e.g. Hooke's law In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit. Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials. Hooke's) where the stress tensor (of order d in d dimensions) is a function of the strain tensor. Although this description is accurate when a small part of matter is subjected to increasing loading (such as strain loading), this theory cannot account for irreversibility.

Ductile Ductility is a mechanical property that describes the extent in which solid materials can be plastically deformed without fracture materials can sustain large plastic deformations without fracture The word fracture is often applied to bones of living creatures, or to crystals or crystalline materials, such as gemstones or metal. Sometimes, in crystalline materials, individual crystals fracture without the body actually separating into two or more pieces. Depending on the substance which is fractured, a fracture reduces strength or inhibits. However, even ductile metals will fracture when the strain In continuum mechanics, deformation or strain is the change in the metric properties of a continuous body B in the displacement from an initial placement κ0 to a final placement κ(B). A change in the metric properties means that a curve drawn in the initial body placement changes its length when displaced to a curve in the final placement. If becomes large enough - this is as a result of work-hardening of the material, which causes it to become brittle A material is brittle if it is liable to fracture when subjected to stress. That is, it has little tendency to deform before fracture. This fracture absorbs relatively little energy, even in materials of high strength, and usually makes a snapping sound. Heat treatment Heat treatment is a method used to alter the physical, and sometimes chemical properties of a material. The most common application is metallurgical. Heat treatments are also used in the manufacture of many other materials, such as glass. Heat treatment involves the use of heating or chilling, normally to extreme temperatures, to achieve a desired such as annealing Annealing, in metallurgy and materials science, is a heat treatment wherein a material is altered, causing changes in its properties such as strength and hardness. It is a process that produces conditions by heating to above the re-crystallization temperature and maintaining a suitable temperature, and then cooling. Annealing is used to induce can restore the ductility Ductility is a mechanical property used to describe the extent to which materials can be deformed plastically without fracture of a worked piece, so that shaping can continue.

Flow plasticity theory

In 1934, Egon Orowan, Michael Polanyi Michael Polanyi, FRS (March 11, 1891, Budapest – February 22, 1976, Northampton, England) was a Hungarian–British polymath whose thought and work extended across physical chemistry, economics, and philosophy. He was a Fellow of the Royal Society and a Fellow of Merton College, Oxford and Geoffrey Ingram Taylor, roughly simultaneously, realized that the plastic deformation of ductile materials could be explained in terms of the theory of dislocations In materials science, a dislocation is a crystallographic defect or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials. The theory was originally developed by Vito Volterra in 1905. Some types of dislocations can be visualized as being caused by the termination of a plane. The more correct mathematical theory of plasticity, flow plasticity theory, uses a set of non-linear, non-integrable equations to describe the set of changes on strain and stress with respect to a previous state and a small increase of deformation.

Yield criteria

Comparison of Tresca criterion to Von Mises criterion. Main article: Yield (engineering) The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the

If the stress exceeds a critical value, as was mentioned above, the material will undergo plastic, or irreversible, deformation. This critical stress can be tensile or compressive. The Tresca and the von Mises criteria are commonly used to determine whether a material has yielded. However, these criteria have proved inadequate for a large range of materials and several other yield criteria are in widespread use.

Tresca criterion

This criterion is based on the notion that when a material fails, it does so in shear, which is a relatively good assumption when considering metals. Given the principal stress state, we can use Mohr’s circle In continuum mechanics, the concept of stress, introduced by Cauchy around 1822, is a measure of the average amount of force exerted per unit area of a surface within a deformable body on which internal forces act . In other words, it is a measure of the intensity or internal distribution of the total internal forces acting within a deformable to solve for the maximum shear stresses our material will experience and conclude that the material will fail if:

Where σ₁ is the maximum normal stress, σ₃ is the minimum normal stress, and σ₀ is the stress under which the material fails in uniaxial loading. A yield surface may be constructed, which provides a visual representation of this concept. Inside of the yield surface, deformation is elastic. Outside of the surface, deformation is plastic.

Von Mises criterion

The von Mises yield surfaces in principal stress coordinates circumscribes a cylinder around the hydrostatic axis. Also shown is Tresca's hexagonal yield surface. Main article: Von Mises yield criterion

This criterion^[10] is based on the Tresca criterion but takes into account the assumption that hydrostatic stresses do not contribute to material failure. Von Mises solves for an effective stress Karl von Terzaghi first proposed the relationship for effective stress in 1936. For him, the term ‘effective’ meant the calculated stress that was effective in moving soil, or causing displacements. It represents the average stress carried by the soil skeleton under uniaxial loading, subtracting out hydrostatic stresses, and claims that all effective stresses greater than that which causes material failure in uniaxial loading will result in plastic deformation.

Again, a visual representation of the yield surface may be constructed using the above equation, which takes the shape of an ellipse. Inside the surface, materials undergo elastic deformation. Outside of the surface they undergo plastic deformation.

References

^ J. Lubliner, 2008, Plasticity theory, Dover, ISBN 0486462900, 9780486462905.
^ M. Jirasek and Z. P. Bazant, 2002, Inelastic analysis of structures, John Wiley and Sons.
^ W-F. Chen, 2008, Limit Analysis and Soil Plasticity, J. Ross Publishing
^ M-H. Yu, G-W. Ma, H-F. Qiang, Y-Q. Zhang, 2006, Generalized Plasticity, Springer.
^ W-F. Chen, 2007, Plasticity in Reinforced Concrete, J. Ross Publishing
^ J. A. Ogden, 2000, Skeletal Injury in the Child, Springer.
^ J-L. Leveque and P. Agache, ed., 1993, Aging skin:Properties and Functional Changes, Marcel Dekker.
^ Gerolf Ziegenhain and Herbert M. Urbassek: Reversible Plasticity in fcc metals. In: Philosophical Magazine Letters. 89(11):717-723, 2009 DOI
^ R. Hill, 1998, The Mathematical Theory of Plasticity, Oxford University Press.
^ von Mises, R. (1913). Mechanik der Festen Korper im plastisch deformablen Zustand. Göttin. Nachr. Math. Phys., vol. 1, pp. 582–592.

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