Plasticity 3d Software Free Download
Adah Orhenkowski
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.[1][2] 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.[3][4][5][6] 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.
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.
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.
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.
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.[7] Shape-memory alloys such as Nitinol wire also exhibit a reversible form of plasticity which is more properly called pseudoelasticity.
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.
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.
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, 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.
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 plastic flow in both single crystals and polycrystals is defined by a critical/maximum resolved shear stress (τCRSS), 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.
During the easy glide stage 1, the work hardening rate, defined by the change in shear stress with respect to shear strain (dτ/dγ) 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 (i.e. one slip system). 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 (i.e. multiple slip systems), 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 (τflow ρ), 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.
There are several mathematical descriptions of plasticity.[12] One is deformation theory (see e.g. Hooke's law) where the Cauchy stress tensor (of order d-1 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.
In 1934, Egon Orowan, Michael Polanyi and Geoffrey Ingram Taylor, roughly simultaneously, realized that the plastic deformation of ductile materials could be explained in terms of the theory of dislocations. The 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.
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 also in widespread use.
The Tresca 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 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. On the surface, deformation is plastic. It is impossible for a material to have stress states outside its yield surface.
c80f0f1006