Deformation irreversible/permanent

The dislocations which pass through a volume element produce a deformation P, called plastic, but they do not change neither the state nor the lattice orientation oT the volume element. Therefore the plastic deformations are permanent, irreversible. 

Rubbers are exceptional in behaving reversibly, or almost reversibly, to high strains as we said, almost all materials, when strained by more than about 0.001 (0.1%), do something irreversible and most engineering materials deform plastically to change their shape permanently. If we load a piece of ductile metal (like copper), for example in tension, we get the following relationship between the load and the extension (Fig. 8.4). This can be... 

The combination of spring and dashpot in series is called the Maxwell model, and was in fact first investigated by the same Maxwell famous for his work on gases and molecular statistics. It is used to model the viscoelastic behavior of uncross-linked polymers. The spring is used to describe the recoverability of the chains that are elongated, and the dashpot the permanent deformation or creep (resulting from the uncross-linked chains irreversibly sliding by one another). 

Deformation may be of one or both of two types, irreversible deformation, called flow, and reversible deformation, called elasticity. The energy used in irreversible deformation is dissipated as heat, and the body is permanently deformed. The energy used in reversible deformation is recovered upon release of... 

If the stress is further increased, eventually a point is reached when the straight-line relationship is lost. This is termed the elastic limit. If stresses in excess of the elastic limit are applied and then removed, the spring will not return to its original length. Thus, a fraction of the change in length is permanent or irreversible, and this is termed plastic behavior. Further increase in load will result in more and more plastic deformation... 

Microindentation hardness is currently measured by static penetration of the specimen with a standard indenter at a known force. After loading with a sharp indenter a residual surface impression is left on the flat test specimen. An adequate measure of the material hardness may be computed by dividing the peak contact load, P, by the projected area of impression (Tabor, 1951). The microhardness, so defined, may be considered as an indicator of the irreversible deformation processes which characterize the material. The strain boundaries for plastic deformation below the indenter are critically dependent, as we shall show in the next chapter, on microstructural factors (crystal size and perfection, degree of crystallinity, etc.). Indentation during a microhardness test permanently deforms only a small volume element of the specimen (V 10 -10 nm ) (non-destructive test). The rest of the specimen acts as a constraint. Thus the contact stress between the indenter and the specimen is much larger than the compressive yield stress of the specimen (about a factor of 3 higher). 

Permanent irreversible deformation takes place at high temperatures as a result of mechanical stressing, e.g. above 1000 °C for fireclay. This is mostly due to the presence of a melt which at this stage has a viscosity of about 10 dPa s. The temperature of softening and permanent deformation depends on the amount and viscosity of the melt. At the same melt content, the perceptible onset of softening is shifted towards higher temperatures, the higher the melt viscosity. 

In this chapter we are concerned with the deformation of ceramics leading to a permanent shape change. This is known as plastic deformation and is both nonrecoverable and irreversible. There are several mechanisms that are responsible for plastic deformation in crystalline materials dislocation motion, vacancy motion, twinning, and phase transformation. In metals at room temperature dislocation motion is the most important of these mechanisms. In Chapter 12 we already noted that dislocations do not move easily in ceramics and this is the reason for their inherent brittleness. Nevertheless, dislocation motion is observed in ceramics under specific loading conditions. In general, plastic deformation of ceramics requires high temperatures and this is important because... 

The initial part of the curve, OA in Fig. 1, is the characteristic linear-elastic behavior of the material, i.e., the extension that occurs is fully reversible and the relationship between the force and the extension is linear. At an atomic level the bonds between the atoms of the crystal structure are just flexing. The extension in this region is however very small and can only be measured using special extensometers. This linearity ceases at point A and the material starts to behave irreversibly, i.e., permanent or plastic deformation occurs. This phenomenon is known as yielding. In this region the atoms take up new position relative to each other by the mechanism of dislocation activation. 

A permanent plastic deformation. Hardness is related to the irreversible deformation, measured from the diagonal of the residual impression, d. 

Toughness as such is measured by the area under the stress-strain curve. This area has the units of energy per unit volume and is the work expended in deforming the material (see Section 11.1). The deformation may be elastic, and recoverable, or permanent (irreversible deformation). Elastic energy is stored in the sample in terms of energy per unit volume. Because of the development of crazes within the strained material, which are microscopic voids. 

---