Elastic deformation involves the stretching of chemical bonds. When the stress is removed, the deformation disappears. More drastic events can occur which have the effect of rearranging the atoms so that they have new neighbors after the deformation is complete. This causes an inelastic deformation that does not disappear when the stress is removed.

# Plastic Deformation of Material

Inelastic deformation that occurs almost instantaneously as the stress is applied is called plastic deformation, as distinguished from creep deformation, which occurs only after passage of time under stress.

## Plastic Deformation by Dislocation Motion

Single crystals of pure metals that are macroscopic in size and which contain only a few dislocations are observed to yield in shear at very low stresses. For example, for iron and other BCC metals, this occurs around τo = G/3000, that is, about τo = 30 MPa. For FCC and HCP metals, even lower values are obtained around τo = G/100,000, or typically τo = 0.5 MPa.

Thus, shear strengths for imperfect crystals of pure metals can be lower than the theoretical value for a perfect crystal of τb = G/10 by at least a factor of 300 and sometimes by as much as a factor of 10,000.

This large discrepancy can be explained by the fact that plastic deformation occurs by motion of dislocations under the influence of a shear stress, as illustrated in Fig. 1.

As a dislocation moves through the crystal, plastic deformation is, in effect, proceeding one atom at a time, rather than occurring simultaneously over an entire plane.

This incremental process can occur much more easily than simultaneous breaking of all the bonds, as assumed in the theoretical shear strength calculation for a perfect crystal.

The deformation resulting from dislocation motion proceeds for edge and screw dislocations, as illustrated in Fig. 2 and Fig. 3, respectively.

The plane in which the dislocation line moves is called the slip plane, and where the slip plane intersects a free surface, a slip step is formed. Since dislocations in real crystals are usually curved and thus have both edge and screw character, plastic deformation actually occurs by a combination of the two types of dislocation motion.

Plastic deformation is often concentrated in bands called slip bands. These are regions where the slip planes of numerous dislocations are concentrated; hence, they are regions of intense plastic shear deformation separated by regions of little shear. Where slip bands intersect a free surface, steps are formed as a result of the combined slip steps of numerous dislocations. (See Fig. 4.)

For a given crystal structure, such as BCC, FCC, or HCP, slip is easier on certain planes, and within these planes in certain directions. For metals, the most common planes and directions are shown in Fig. 5. The preferred planes are those on which the atoms are relatively close together, called close-packed planes, such as the basal plane for the HCP crystal.

Similarly, the preferred slip directions within a given plane are the close-packed directions in which the distances between atoms is smallest. This is the case because a dislocation can more easily move if the distance to the next atom is smaller. Also, atoms in adjacent planes project less into the spaces between atoms in the close-packed planes than in other planes, so there is less interference with slip displacement.

## Discussion of Plastic Deformation

The result of plastic deformation (yielding) is that atoms change neighbors and return to a stable configuration with new neighbors after the dislocation has passed. Note that this is a fundamentally different process than elastic deformation, which is merely the stretching of chemical bonds.

Elastic deformation occurs as an essentially independent process along with plastic deformation. When a stress that causes yielding is removed, the elastic strain is recovered just as if there had been no yielding, but the plastic strain is permanent.

Metals used in load-resisting applications have strengths considerably above the very low values observed in crystals of pure metals with some defects, but not nearly as high as the very high theoretical value for a perfect crystal. This is illustrated in Fig. 6 for irons and steels, which are composed mostly of iron.

If there are obstacles that impede dislocation motion, the strength may be increased by a factor of 10 or more above the low value for a pure metal crystal. Grain boundaries have this effect, as does a second phase of hard particles dispersed in the metal. Alloying also increases strength, as the different-sized atoms make dislocation motion more difficult.

If a large number of dislocations are present, these interfere with one another, forming dense tangles and blocking free movement. In nonmetals and compounds where the chemical bonding is covalent or partially covalent, the directional nature of the bonds makes dislocation motion difficult.

Materials in this class include the crystals of carbon, boron, and silicon, and also intermetallic compounds and compounds formed between metals and nonmetals, such as metal carbides, borides, nitrides, oxides, and other ceramics.

At ambient temperatures, these materials are hard and brittle and do not generally fail by yielding due to dislocation motion. Instead, the strength falls below the high theoretical value for a perfect crystal mainly because of the weakening effect of small cracks and pores that are present in the material. However, some dislocation motion does occur, especially for temperatures above about half of the (usually high) melting temperature, where Tm is measured relative to absolute zero.

## Creep Deformation

In addition to elastic and plastic deformation as already described, materials deform by mechanisms that result in markedly time-dependent behavior, called creep. Under constant stress, the strain varies with time, as shown in Fig. 7.

There is an initial elastic deformation εe, and following this, the strain slowly increases as long as the stress is maintained. If the stress is removed, the elastic strain is quickly recovered, and a portion of the creep strain may be recovered slowly with time; the rest remains as permanent deformation.

In crystalline materials—that is, in metals and ceramics—one important mechanism of creep is diffusional flow of vacancies. Spontaneous formation of vacancies is favored near grain boundaries that are approximately normal to the applied stress and is disfavored for parallel ones.

This results in an uneven distribution of vacancies and in vacancies diffusing, or moving, from regions of high concentration to regions of low concentration, as illustrated in Fig. 8.

As indicated, movement of a vacancy in one direction is equivalent to movement of an atom in the opposite direction. The overall effect is a change in the shape of the grain, contributing to a macroscopic creep strain.

Some other creep mechanisms that operate in crystalline materials include special dislocation motions that can circumvent obstacles in a time-dependent manner. There may also be sliding of grain boundaries and the formation of cavities along grain boundaries.

Creep behavior in crystalline materials is strongly temperature dependent, typically becoming an important engineering consideration around 0.3 to 0.6Tm, where Tm is the absolute melting temperature.

Different creep mechanisms operate in amorphous (noncrystalline) glasses and in polymers. One of these is viscous flow in the manner of a very thick liquid. This occurs in polymers at temperatures substantially above the glass transition temperature Tg and approaching Tm. The chainlike molecules simply slide past one another in a time-dependent manner. Around and below Tg, more complex behavior involving segments of chains and obstacles to chain sliding become important. In this case, much of the creep deformation may disappear slowly (recover) with time after removal of an applied stress, as illustrated in Fig. 7.

Creep is a major limitation on the engineering application of any polymer above its Tg, which is generally in the range −100 to 200C for common polymers.