Plastic deformation dislocation processes

As in time-independent plastic deformation, dislocations play an important role in the time-dependent plastic deformation of metals. At the onset of creep deformation, the number of dislocations in the material usually increases, causing hardening that can be experimentally observed by the reduction in the creep rate at constant stress. However, the dislocation density cannot increase arbitrarily since recovery occurs simultaneously (see section 6.2.8), with dislocations annihilating by climb. This process becomes the easier, the closer the dislocations are. Accordingly, after some transition time, an equilibrium between the generation of additional dislocation segments by plasticity and the annihilation of dislocations by recovery will be found. This equilibrium causes the creep rate to become constant in the secondary stage. 

Once the precipitates grow beyond a critical size they lose coherency and then, in order for deformation to continue, dislocations must avoid the particles by a process known as Orowan bowing(23). This mechanism appHes also to alloys strengthened by inert dispersoids. In this case a dislocation bends between adjacent particles until the loop becomes unstable, at which point it is released for further plastic deformation, leaving a portion behind, looped around the particles. The smaller the interparticle spacing, the greater the strengthening. 

The plastic deformation patterns can be revealed by etch-pit and/or X-ray scattering studies of indentations in crystals. These show that the deformation around indentations (in crystals) consists of heterogeneous rosettes which are qualitatively different from the homogeneous deformation fields expected from the deformation of a continuum (Chaudhri, 2004). This is, of course, because plastic deformation itself is (a) an atomically heterogeneous process mediated by the motion of dislocations and (b) mesoscopically heterogeneous because dislocation motion occurs in bands of plastic shear (Figure 2.2). In other words, plastic deformation is discontinuous at not one, but two, levels of the states of aggregation in solids. It is by no means continuous. And, it is by no means time independent it is a flow process. 

In textbooks, plastic deformation is often described as a two-dimensional process. However, it is intrinsically three-dimensional, and cannot be adequately described in terms of two-dimensions. Hardness indentation is a case in point. For many years this process was described in terms of two-dimensional slip-line fields (Tabor, 1951). This approach, developed by Hill (1950) and others, indicated that the hardness number should be about three times the yield stress. Various shortcomings of this theory were discussed by Shaw (1973). He showed that the experimental flow pattern under a spherical indenter bears little resemblance to the prediction of slip-line theory. He attributes this discrepancy to the neglect of elastic strains in slip-line theory. However, the cause of the discrepancy has a different source as will be discussed here. Slip-lines arise from deformation-softening which is related to the principal mechanism of dislocation multiplication a three-dimensional process. The plastic zone determined by Shaw, and his colleagues is determined by strain-hardening. This is a good example of the confusion that results from inadequate understanding of the physics of a process such as plasticity. 

In general terms, as has already been mentioned, plastic deformation is a transport process analogous with electrical and thermal conductivity. These involve an entity to be transported, a carrier that does the transporting, and a rate of transport. In the case of electrical conductivity, charge is the transport entity, electrons (or holes) are the carriers, and the electron net velocities determine the rate. In the case of plastic deformation, displacement, b (cm) is the transport entity, dislocations are the carriers, N ( /cm2), and their velocities, v (cm/sec) determine the shear deformation rate, d8/dt. In two dimensions, the latter is given by the Orowan Equation ... 

Plastic deformation, unlike elastic deformation, is not accurately predicted from atomic or molecular properties. Rather, plastic deformation is determined by the presence of crystal defects such as dislocations and grain boundaries. While it is not the purpose of this chapter to discuss this in detail, it is important to realize that dislocations and grain boundaries are influenced by things such as the rate of crystallization, particle size, the presence of impurities, and the type of recrystallization solvent used. Processes that influence these can be expected to influence the plastic deformation properties of materials, and hence the processing properties. 

Dislocations are commonly present in two regions. A layer with high mismatch may relax so that interface dislocations are created to accommodate the strain. A network at the interface is thns observed. Shp dislocations may be generated by local plastic deformation due to thermal or mechanical strain and propagate elsewhere in the layer. Dislocations in the layer itself may also be generated during the growth process, dne, for example, to the presence of inclusions. 

Annealing in metals can first lead to stress relaxation in which stored internal strain energy due to plastic deformation is relieved by thermally activated dislocation motion (see Figure 5.18). Because there is enhanced atomic mobility at elevated temperatures, dislocation density can decrease during the recovery process. At still higher temperatures, a process known as recrystallization is possible, in which a new set of... 

Despite the similarities in brittle and ductile behavior to ceramics and metals, respectively, the elastic and permanent deformation mechanisms in polymers are quite different, owing to the difference in structure and size scale of the entities undergoing movement. Whereas plastic deformation (or lack thereof) could be described in terms of dislocations and slip planes in metals and ceramics, the polymer chains that must be deformed are of a much larger size scale. Before discussing polymer mechanical properties in this context, however, we must first describe a phenomenon that is somewhat unique to polymers—one that imparts some astounding properties to these materials. That property is viscoelasticity, and it can be described in terms of fundamental processes that we have already introduced. 

Dislocations multiply in a facile manner during a plastic deformation process, and several mechanisms for this have been observed by electron miscroscopy. Dislocations are destroyed by the processes of recovery and recrystallization during annealing after plastic deformation. Since dislocations cause low-yield stresses in metals and other solids, solid strengthening is accomplished either by eliminating dislocations or by immobilizing them. 

By necessity, the treatment of solid state kinetics has to be selective in view of the myriad processes which can occur in the solid state. This multitude is mainly due to three facts 1) correlation lengths in crystals are often much larger than in fluids and may comprise the whole crystal, 2) a structure element is characterized by three parameters instead of only by two in a liquid (chemical species, electrical charge, type of crystallographic site), and 3) a crystal can be elastically stressed. The stress state is normally inhomogeneous. If the yield strength is exceeded, then plastic deformation and the formation of dislocations will change the structural state of a crystal. What we aim at in this book is a strict treatment of concepts and basic situations in a quantitative way, so far as it is possible. In contrast, the often extremely complex kinetic situations in solid state chemistry and materials science will be analyzed in a rather qualitative manner, but with clearcut thermodynamic and kinetic concepts. 

This chapter is concerned with the influence of mechanical stress upon the chemical processes in solids. The most important properties to consider are elasticity and plasticity. We wish, for example, to understand how reaction kinetics and transport in crystalline systems respond to homogeneous or inhomogeneous elastic and plastic deformations [A.P. Chupakhin, et al. (1987)]. An example of such a process influenced by stress is the photoisomerization of a [Co(NH3)5N02]C12 crystal set under a (uniaxial) chemical load [E.V. Boldyreva, A. A. Sidelnikov (1987)]. The kinetics of the isomerization of the N02 group is noticeably different when the crystal is not stressed. An example of the influence of an inhomogeneous stress field on transport is the redistribution of solute atoms or point defects around dislocations created by plastic deformation. 

This is the process by which a crystal undergoes plastic deformation, as a result of which one atomic plane moves over another. Slip is believed to occur through the movement of dislocations. The total deformation of a given crystal is the sum of many small lateral displacements in parallel crystallographic planes of a given family. Moreover, each slip plane becomes more resistanl to further deformation than the remaining potential slip planes. 

Microcrystalline cellulose is one of the most commonly used filler-binders in direct compression formulations because it provides good binding properties as a dry binder, excellent compactibility, and a high dilution potential. It also contributes good disintegration and lubrication characteristics to direct compression formulas. When compressed, microcrystalline cellulose undergoes plastic deformation. The acid hydrolysis portion of the production process introduces slip planes and dislocations into the material. Slip planes, dislocations, and the small size of the individual crystals aid in the plastic flow that takes place. The spray-dried particle itself, which has a higher porosity compared with the absolute porosity of cellulose, also deforms... 

Movement of dislocations is a primary mechanism for plastic deformation. A dislocation s motion is impeded when they encounter obstacles, causing the stress required to continue the deformation process to increase. Grain boundaries are one of the obstacles that can impede dislocation glide, so the number of grain boundaries along a slip direction can be expected to influence the strength of a material. In the early 1950s, two researchers, Hall (1951) and Petch (1953),... 

It has been shown that several polymers exhibit instabilities in their plastic deformation process. It should finally be mentioned that instabilities may also occur during the plastic deformation of metals This phenomenon which is called the Portevin-Le Chatelier effect, is generally interpreted in terms of different modes of dislocation movement depending on whether or not dislocations move by dragging along their atmosphere of impurities behind them. 

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