Plastic deformation flow stress

Work hardening is the reason why the flow curve of metals increases in the plastic regime (see chapter 3). If the material is unloaded after plastic deformation, the stress-strain curve follows a line parallel to the elastic line. If the load is raised again, the yield strength has increased and the stress-strain curve follows the same line as on unloading. The strain until the material starts to neck or fracture is reduced the material has lost ductility. 

Another class of materials (nonmetals) is capable of extremely great elastic deformations. These are called elastomeric materials. Usually, materials exhibiting plastic deformation under stress are the more desirable for structures. Ductility is desirable so that accidental stresses beyond design values can be redistributed to safer levels by means of plastic flow. 

Bai [48] presents a linear stability analysis of plastic shear deformation. This involves the relationship between competing effects of work hardening, thermal softening, and thermal conduction. If the flow stress is given by Tq, and work hardening and thermal softening in the initial state are represented... 

In this chapter the regimes of mechanical response nonlinear elastic compression stress tensors the Hugoniot elastic limit elastic-plastic deformation hydrodynamic flow phase transformation release waves other mechanical aspects of shock propagation first-order and second-order behaviors. 

Consider the schematic stress-deformation curve of Figure 2.6. Here elastic strain e dominates until the stress reaches Y0 then, plastic deformation 8 dominates. Note that plastic flow begins as soon as a small stress is applied,... 

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 aU wrought processes, the flow of metal is caused by application of an external force or pressure that pushes or pulls a piece of metal or alloy through a metal die. The pressure required to produce plastic flow is determined primarily by the yield stress of the material (cf. Section 5.1.4.3) which, in turn, controls the load capacity of the machinery required to accomplish this desired change in shape. The pressure, P, used to overcome the yield stress and cause plastic deformation is given by... 

The Kirkendall effect alters the structure of the diffusion zone in crystalline materials. In many cases, the small supersaturation of vacancies on the side losing mass by fast diffusion causes the excess vacancies to precipitate out in the form of small voids, and the region becomes porous [11], Also, the plastic flow maintains a constant cross section in the diffusion zone because of compatibility stresses. These stresses induce dislocation multiplication and the formation of cellular dislocation structures in the diffusion zone. Similar dislocation structures are associated with high-temperature plastic deformation in the absence of diffusion [12-14]. 

In Fig. 24(a) the purely elastic deformation and the plastic elastic flow processes are plotted and hatched in a different manner. Figure 24(b) shows the dependence of stress on time. It can also be seen, that with discharge at time t0 the purely elastic residual deformation disappears at once, whereas the plastic-elastic portion does so gradually (diffusion processes). 

Plasticity can be defined as ease of deformation so that a highly plastic rubber is one that deforms or flows easily. Viscosity is the resistance to plastic deformation or flow and, hence, the inverse of plasticity. It is defined as shear stress/shear rate. Unfortunately, the terms are often used... 

Creep, yielding, and post-yielding plastic deformation (drawing) as well as flow are brought about by the stress-biased deformation and displacement (jumps) of molecular groups and chain segments. Creep is defined as the time-... 

First, let us examine the temperature dependence of the plastic flow, apf, shown in Fig. 18. As already mentioned in Sect. 2.2.2, the plastic flow requires whole chain motions like those occurring above the a transition, whatever the considered temperature. This feature is reflected in the large activation volume associated with crpf and in the independence to temperature. Consequently, one can consider the plastic flow stress as a reference behaviour in the molecular analysis of plastic deformation. 

The plastic deformation characteristics yield stress, ay, plastic flow stress, crpf, and strain softening, have been studied under uniaxial compression at a strain rate of 2 x 10-3 s-1 [53] in a temperature range from - 110 °C to typically Ta - 20 K. Indeed, for temperatures closer to Ta, the experimental results are less reliable, some creep behaviour occurring. 

As a force is applied to the item through the die, the metal first becomes elastically strained and would return to its initial shape if the force were removed at this point. As the force increases, the metal s elastic limit is exceeded and plastic flow occurs via the motion of dislocations. Many of these dislocations become entangled and trapped within the plastically deformed material thus, plastic deformation produces crystals which are less perfect and contain internal stresses. These crystals are designated as cold-worked and have physical properties which differ from those of the undeformed metal. 

The second is the absorbed hydrogen-enhanced local plasticity mechanism (HELP). This is based on the fact that the local decrease of the flow stress by hydrogen leads to highly localized failure by ductile processes, while the local macroscopic deformation remains small. Shear localization results from local hydrogen absorption, giving a macroscopically brittle fracture related to microscopic localized deformation.95... 

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