Plasticity

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plasticity

[plas′tis·əd·ē]
(mechanics)
The property of a solid body whereby it undergoes a permanent change in shape or size when subjected to a stress exceeding a particular value, called the yield value.

Plasticity

 

in art, a quality belonging to sculpture; the artistic rendering of three-dimensional form. The term “plasticity” refers to the emotionality, artistic wholeness, and visual persuasiveness of the modeling of three-dimensional forms in sculpture. It is also used to express the harmony between the expressiveness of the modeling and the weightiness and inner fullness of the form.

The word “plasticity” also has a broader meaning, referring to the expressiveness of three-dimensional form in all of the plastic arts: architecture, painting, engraving, and the decorative and applied arts. Thus, plasticity is associated both with the representation of three-dimensionality on a planar surface and with the creation of an actual three-dimensional volume.

In the broadest sense, plasticity refers to a palpable manifestation of beauty and to the sculptural quality, clarity, and harmonious unity of a given image. The term is used in this sense in discussions of poetry, music, and literary narratives. In movement and dance, plasticity refers to an elegance and fluidity of line analogous to sculpture.

The term “plasticity” is also used in the physical sense to denote a material’s ability to retain a shape imparted by pressure deformation. Thus, we speak of the plasticity of soft materials used in sculpture, such as clay, wax, and Plasticine, and the plasticity of paints, as seen in the texture of oil paints.

REFERENCES

Kantor, A. “Plastichnost;.” Tvorchestvo, 1973, NO. 9.
Hetzer, T. “Vom Plastischen in der Malerei.” In his book Aufsätze und Vorträge [vol.] 2, Leipzig [1957]. Pages 131–69.

A. M. KANTOR


Plasticity

 

(in physiology), the ability of cells and organs in animals and plants to change their properties, within known limits, in response to the conditions under which the cells and organs function. Thus, the plasticity of, for example, the central nervous system is reflected in the capacity for functional restoration when a certain part of the brain is destroyed. Synapses are another example of a structure that exhibits plasticity.


Plasticity

 

a property of solids whereby the solids irreversibly change their dimensions and shape—that is, are plastically deformed—under the action of mechanical loads. The plasticity of crystalline solids or materials is connected with the action of various microscopic mechanisms of plastic deformation; the relative role of each mechanism is determined by external conditions, such as temperature, load, and rate of deformation. These mechanisms are considered below in the order of increasing numbers of atoms that take part in the elementary act of plastic deformation.

Self-diffusional and diffusional plasticity. The action of compressive forces causes a displacement of atomic layers of a crystal from the regions of its surface on which the forces act to regions where tensile forces act. Mass transfer can occur through self-diffusion along the surface or through the volume of the crystal. If the crystal is not very small—that is, if its specific surface (the ratio of surface to volume) is not too large—volume self-diffusion is the most effective mechanism. It occurs through the “dissolving,” that is, the penetration, of the surface-layer atoms into the interior of the crystal in the form of interstitial atoms in the regions of compression and through the “deposition” of these atoms in the regions subjected to the action of the tensile forces. A flow of vacancies occurs simultaneously in the opposite direction. These vacancies are generated in the region of action of the tensile forces and are annihilated in the places of compression. In the majority of cases, self-diffusional deformation is connected primarily with directed fluxes of vacancies, which are formed more readily than interstitial atoms (Figure 1).

Figure 1. Self-diffusional plasticity: (I) crystal with vacancies at the initial moment of action of the stresses σ (the small arrows indicate the directions of the displacements of the atoms), (II) deformation arising from the flow of vacancies under the action of the stresses, (III) final deformation of the crystal

A crystal consisting of atoms of various types exhibits in a homogeneous stress field an orientational ordering with respect to the positions of the atoms (Figure 2,a). As a result, the crystal acquires a certain deformation that is dependent on the degree of ordering. The ordered state may become disadvantageous after the removal of the stresses but is preserved for some time, since the return to the disordered state occurs with the speed of the diffusion jumps of the atoms. If an inhomogeneous stress field is generated in the crystal, the impurity atoms with large radii and the interstitial atoms (Figure 2,b) tend to move into the extended regions of the lattice, and the atoms with small radii tend to move into the compressed regions. There appears an inhomogeneous distribution of concentrations, which stabilizes the initial inhomogeneous deformation. The maximum deformation that can result from orientational ordering or concentrational inhomogeneity is limited by the composition of the crystal. Thus, self-diffusional and diffusional deformations are determined by the fluxes of point defects—vacancies, interstitial atoms, and impurity atoms. Under real conditions, the migration of defects results from thermal fluctuations, whose frequency decreases rapidly with decreasing temperature. These plasticity mechanisms therefore act only at sufficiently high temperatures (no lower than 0.5 of the absolute melting temperature).

Figure 2. Diffusional plasticity: (a) orientational ordering of impurity atoms (solid circles) in a homogeneous stress field, (b) redistribution of impurity atoms in an inhomogeneous stress field; (I) initial crystal, (II) crystal with impurity atoms under the action of stresses, (III) final deformation of crystal

Crowdion plasticity. Crowdion plasticity is due to the formation and movement of crowdions, which are atomic clusters formed along the close-packed rows of atoms in a crystal. When a point is pressed into the surface of the crystal (Figure 3), material is removed from the indentation zone by crowdions “running away” from under the point. As a result, an increased concentration of interstitial atoms is generated some distance away from the place of indentation.

Dislocation plasticity. A typical form of plastic deformation is the slip, or glide, along crystallographic planes. Slip occurs most easily along close-packed planes in the close-packed directions. Slip along a system of parallel planes produces a macroscopic displacement, and the combination of displacements corresponding to slip along different systems constitutes the

Figure 3. Crowdion plasticity: (I) crystal before indentation, (II) formation of crowdions upon penetration by the point, (III) final changed shape. Interstitial atoms were formed in the crystal.

principal part of the plastic deformation of crystals. Slip occurs nonuniformly. At first it embraces a certain region of the slip plane (Figure 4), and then the boundaries of this region are extended over the entire plane. The boundary of propagation of the slip is called a dislocation or dislocation line. The development of slip may therefore be regarded as the formation and movement of dislocations. The rate of deformation is proportional to the density (the total length of dislocations per unit volume) and to the rate of movement of the dislocations. Dislocations always arise in real crystals in the process of formation of the crystals. Under the action of stress, these dislocations are capable of enlarging their extent (multiplication of dislocations). For this reason, the stage of formation of new dislocations limits slip only in exceptional cases—for example, the beginning of deformation in dislocation-free microcrystals. In the remaining cases, slip development is determined by the movement of dislocations.

Figure 4. Elementary slip as a result of the movement of a dislocation

Since the atoms in the vicinity of dislocations have been displaced from their equilibrium positions, their movement into new equilibrium positions, which correspond to a shearing of the crystal along the slip plane by a single interatomic distance, requires considerably smaller expenditures of energy than for atoms in an undistorted crystal. The larger the zone of distortion surrounding the dislocation, the lower the energy barrier for the displacement. All materials are divided into two groups according to dislocation mobility. The order of magnitude of this barrier in covalent crystals approaches the energy of interatomic bonds and can be overcome only by thermal activation (thermal fluctuations). For this reason, the mobility of dislocations becomes noticeable only at sufficiently high temperatures; at moderate temperatures, covalent crystals are nonplastic. In metallic and ionic crystals, the binding energy is 103—104 times greater than the barrier for the movement of dislocations, and the barrier vanishes at stresses of 10–3G to 10–4G, where G is the shear modulus. The motion of dislocations at such stresses does not require thermal activation, and the mobility of the dislocations exhibits a weak dependence upon the temperature. The resistance to the motion of dislocations in a perfect crystal lattice is negligibly low, which produces the high plasticity of ionic and metallic crystals.

Real crystals contain various defects, such as point defects, impurity atoms, dislocations, and particles of other phases. The slip resistance depends on the interaction of moving dislocations with these defects. The interaction between dislocations is the principal interaction in plastic crystals without impurities. A part of the slip resistance is connected with the direct collision of dislocations and can be decreased by thermal activation. The predominant part, however, is caused by the long-range interaction between dislocations through the stress fields that the dislocations generate around themselves. This part is almost independent of the temperature. As a result of their interaction with each other, the dislocations are slowed and come to a stop. For this reason, if the deformation is to proceed with constant speed, uninterrupted generation of new dislocations is required. There results in the crystal a continuous increase of the dislocation density, which can reach 1011-1012 cm–2. The mutual slip resistance of the dislocations increases correspondingly; work hardening of the crystal occurs.

The development of interactions between dislocations is reflected in the stress-strain curve (Figure 5). In typical cases, the curve displays three characteristic parts, which correspond to the three basic stages of the evolution of a dislocation structure.

Figure 5. Stress-strain curve for a zinc single crystal

In stage I, slip is easy. The dislocation density is relatively low. Each dislocation has time to traverse a distance comparable with the size of the crystal before stopping, and an appreciable part of the dislocations emerges on the surface of the crystal. The slip resistance is due to the interaction between the individual dislocations, the density of which increases with the deformation relatively slowly. The coefficient of work hardening is therefore small in this case (~10–3G).

With an increasing degree of deformation and a growing dislocation density, the distribution of the dislocations becomes essentially inhomogeneous. The dislocations form compact pileups in the slip planes (Stage II). The stress fields from these pileups are, in turn, the cause of supplemental plastic deformation. This local deformation is randomly directed and may not be reflected in the overall change of the crystal’s shape, but it increases the dislocation density as a result of the appearance of dislocations in the secondary slip systems. The interaction between the dislocations of the primary and secondary systems leads to the formation of dislocation clusters and a dislocation cell structure (Figure 6). The character of the dislocation structure is preserved throughout Stage II and only the size of the cells decreases. The coefficient of work hardening is approximately equal to 10–2G.

Figure 6. Schematic representation of the distribution of dislocations during Stage II of plastic deformation

A further increase in the dislocation density leads to “extrusion” of a part of the dislocations from the slip planes in which the dislocations were located. In the process, dislocations of opposite signs meet and are annihilated. A lessening of the dislocation density occurs with an accompanying decrease in the coefficient of work hardening (Stage III). Continuity violation processes (the formation of microcracks) begin at the same time. These processes ultimately lead to the crystal’s destruction, which determines the maximum attainable magnitude of plastic deformation.

At high temperatures, the dislocation mechanisms is combined with the diffusion and self-diffusion mechanisms. In crystals with impurities, stress relaxation at the sites of dislocations or of dislocation pileups may occur as a result of redistribution of the impurity atoms. Impurity “atmospheres” are formed around the dislocations, and the dislocation plasticity decreases (deformation aging). The removal of impurities, therefore, usually increases the plasticity. On the other hand, dislocations are effective sinks and sources of vacancies and interstitial atoms. The generation or annihilation of these defects leads to the completion or to the reduction of the incomplete atomic planes, which terminate at dislocations, and, consequently, to the climb of the dislocations out of the slip plane. Fluxes of point defects between dislocations of different signs lead to plastic deformation of the self-diffusion type; the dislocation climb resulting from the fluxes permits the dislocations to bypass obstacles located in the slip plane. The slip path traversed by each dislocation under the conditions of high-temperature deformation increases—as compared to ordinary temperatures, at which the diffusion mobility is low. The processes of lessening of the dislocation density owing to the mutual annihilation of the dislocations proceed more intensively, the work hardening decreases, and the deformation develops under a constant load (creep).

Twinning. The twinning mechanism involves a deformation of a unit cell of a crystal with a resulting orientation change of part of the crystal relative to the acting forces. The reoriented part of the crystal undergoes relative to the initial crystal a twinning shear, whose magnitude is determined by the symmetry of the crystal lattice. Under real conditions, the development of the deformation proceeds through the generation and propagation of the lamellae of the twin component in the initial crystal. If a twin lamella terminates within the crystal, stress fields appear at its ends, and the interaction between the twins results in work hardening. In some crystals, for example, calcite, twinning is the basic mechanism of plastic deformation. Usually, however, twinning develops primarily at low temperatures, when slip is difficult and conditions are generated for the local concentration of stresses that is required for the generation of twins.

Plasticity resulting from phase transformation. An irreversible change of shape can result from the formation under load of a new phase having a crystal lattice different from that of the initial crystal. The initial phase must be metastable with respect to the phase being formed, at least under the action of mechanical stresses. Since the relative stability depends also on the temperature, the plasticity in this case depends essentially on the temperature of deformation relative to the temperature of the phase equilibrium. In certain cases, by decreasing through a change in temperature the stability of the phase forming under load, the deformation, produced during the transformation can be destroyed. The crystal returns to its initial shape (memory effect).

Polycrystals. In polycrystals the action of the above plastic deformation mechanisms in the interior of the grains is complicated by the interaction between grains. The deformation of a polycrystal is the overall result of deformation in many grains that are oriented differently with respect to the loads and are subjected to different conditions. The development of the deformation therefore does not have the clearly defined stages exhibited by the deformation of single crystals (Figure 5). The intergranular boundaries impede the propagation of dislocations and, as a rule, strengthen crystalline solids at low temperatures. On the other hand, at high temperatures the presence of the boundaries, which are sources or sinks for defects, increases the plasticity. The combination of dislocation and self-diffusional deformation in the boundary regions leads to high plasticity in these regions and, as a result, a specific mechanism for the high-temperature deformation of polycrystals, namely, slip along grain boundaries. The displacement of the grains relative to each other occurs in a manner similar to the movement of the particles in friable materials and in some cases makes possible a deformation of up to 1,000 percent (superplasticity). High plasticity can also be achieved if recrystallization can occur in the course of deformation—recrystallization results in the removal of the most distorted and consequently least plastic grains, which are absorbed by the growing grains with a more perfect structure. The constant restoration of plasticity owing to recrystallization is made wide use of in the hot working of metals.

The plasticity of simple amorphous solids is connected with the diffusional rearrangements of atoms and molecules. The plasticity of a number of materials is due to the movement of non-deforming solid particles with respect to each other in some viscous medium. Phenomena of this type include the plasticity of such materials as clays and friable solids that have been moistened with water.

The study of plasticity is of great practical interest. Such research permits the efficient selection of materials in industry, where the materials’ plasticities must usually conform to a large number of requirements posed by the processing and subsequent use of the materials under various conditions. Research on the various aspects of plasticity is carried on by a number of branches of applied and theoretical mathematics and physics. Solid-state physics (in particular, the theory of dislocations) studies the microscopic mechanisms of plasticity. Continuum mechanics (theories of plasticity and creep) examines the plasticity of solids by abstracting from the solids’ atomic and crystal structure; other concerns of continuum mechanics include the strength of materials.

REFERENCES

Friedel, J. Dislokatsii. Moscow, 1967. (Translated from English.)
Fizika deformatsionnogo uprochneniia monokristallov. Kiev, 1972. Nabarro, F. R., Z. S. Bazinski, and D. B. Holt.
Plastichnost’ monokristallov. Moscow, 1967. (Translated from English.)
Honeycombe, R. Plasticheskaia deformatsiia metallov. Moscow, 1972. (Translated from English.)

A. L. ROITBURD

plasticity

1. That property of freshly mixed cement paste, concrete, mortar, or soil which determines its resistance to deformation or its ease of molding.
2. The ability of a plaster or lime putty to hold or retain water, so that it can be troweled easily.

plasticity

The ability of a material to be deformed to a new permanent shape when stressed. Plastic deformation is terminated either by removal or reduction of the imposed forces or by fracture of the metal. See plastic range.