Creep of Materials

the slow, continuous plastic deformation of a solid under the action of a constant load or mechanical stress. All solids, whether crystalline or amorphous, are to some extent subject to creep.

The phenomenon of creep was noted several centuries ago; however, the systematic study of the creep of metals and alloys, rubbers, and glasses began only in the early 20th century. This study was intensified in the 1940’s as developing technology encountered the problem of creep of the disks and blades of steam and gas turbines, jet engines, and rockets, in which considerable heating is combined with mechanical stresses. Structural materials (heat-resistant alloys) were required that could withstand such loads over long periods at high temperatures. Creep was long considered to take place only at high temperatures, although it is also observed at very low temperatures. For example, significant creep is observed at – 269°C in cadmium and at – 169°C in iron.

Creep is observed upon tension, compression, torsion, and other forms of stress. Under the actual conditions of use of a heat-resistant material, creep occurs under very complex stress conditions. Creep is described by a creep curve (Figure 1), which shows the time dependence of deformation for a constant temperature and a constant applied load or stress. The curve is arbitrarily divided into three segments, or stages: AB, the region of high strain rate, or primary creep (stage I); BC, the region of constant strain rate, or secondary creep (stage II); and CD, the region of accelerated strain rate (stage III). In this diagram, E₀ is the deformation at the moment of application of the stress and the point D corresponds to the time of rupture. Both the total time to rupture and the duration of each stage depend on the temperature and the applied load. At temperatures corresponding to 0.4–0.8 of the melting point of the metal, which are of greatest practical interest, the attenuation of creep in its first stage is the result of strain hardening, or work hardening. Since the creep is taking place at high temperature, removal of the work hardening (called recovery-creep) is also possible. When the rates of work hardening and recovery-creep become equal, stage II of creep begins. The transition to stage III is associated with the accumulation in the material of defects, such as pores and microfissures, whose formation begins in stages I and II.

Figure 1. A creep curve

The creep curves described here have the same shape for a wide variety of materials—metals and alloys, ionic crystals, semiconductors, polymers, ice, and other solids. The structural mechanism of creep—that is, the basic processes leading to creep —depends both on the form of the material and the conditions under which creep occurs. The physical mechanism of creep is the same as for plasticity. The whole diversity of basic processes of plastic deformation leading to creep may be divided into processes that take place through the movement of dislocations and processes of viscous flow. The latter processes take place in amorphous solids at all temperatures and in crystalline solids, particularly metals and alloys, at temperatures close to their melting points. For constant deformations, as a result of creep, the stresses decrease over time—that is, stress relaxation takes place (Figure 2).

High resistance to creep is one of the factors that determine heat resistance. The creep strength—the pressure at which a

Figure 2. (a) Curves for the creep ∊_p of metals under various loads, (b) curves of relaxation of the stress σ for a constant deformation

given deformation is achieved in a given time—is used as a characteristic for the comparative evaluation of technological materials. In aircraft engine construction, this time is taken as 100–200 hr, whereas in the construction of stationary steam turbines it is 100,000 hr. Resistance to creep is sometimes characterized by the rate of deformation after a given time. The rate έ of a total deformation ∊ is composed of the rate of elastic deformation έ_e and the rate of creep έ_p.

Theory of creep. The theory of creep is closely related to the theory of plasticity; however, because of the great variety of mechanical properties of solids, a unified theory of creep does not exist. The flow theory is usually used for metals: έ_p = f (σ, t), where σ is stress and t is time. This theory satisfactorily explains creep at stresses that change slowly and steadily, but it gives an essentially nonlinear dependence of έ_p on σ.

A more complete description of creep is given by the strain theory: έ_p = f (σ, έ_p), which is convenient for the approximate analysis of short-term creep at high stress levels. The strain theory correctly reproduces several features of creep in the case of changing stresses, although its use involves considerable mathematical difficulties.

In polymer mechanics, the theory of structural memory is generally used:

where K (t – τ) is the “aftereffect kernel,” which characterizes the extent to which the aftereffect on the strain of a unit stress acting over a unit time interval at an earlier moment τ is observed at time t. Since the stress also acts at other moments, the total aftereffect is taken into account by an integral term. The theory of structural memory defines the entire deformation and gives a qualitative description of several more complex phenomena—for example, the backward creep effect.