Flow, plastic

As two surfaces are brought together, the pressure is extremely large at the initial few points of contact, and deformation immediately occurs to allow more and more to develop. This plastic flow continues until there is a total area of contact such that the local pressure has fallen to a characteristic yield pressure of the softer material. 

Substances in this category include Krypton, sodium chloride, and diamond, as examples, and it is not surprising that differences in detail as to frictional behavior do occur. The softer solids tend to obey Amontons law with /i values in the normal range of 0.5-1.0, provided they are not too near their melting points. Ionic crystals, such as sodium chloride, tend to show irreversible surface damage, in the form of cracks, owing to their brittleness, but still tend to obey Amontons law. This suggests that the area of contact is mainly determined by plastic flow rather than by elastic deformation. 

Even if no perceptible motion occurs (see later, however), application of a force leads to microdisplacements of one surface relative to the other and, again, often a large increase in area of contact. The ratio F/W in such an experiment will be called since it does not correspond to either the usual ns or can be related semiempirically to the area change, as follows [38]. We assume that for two solids pressed against each other at rest the area of contact Aq is given by Eq. XII-1, A W/P. However, if shear as well as normal stress is present, then a more general relation for threshold plastic flow is... 

Hoover W G, Ladd A J C and Moran B 1982 High strain rate plastic flow studied via nonequilibrium molecular dynamics Phys. Rev.L 48 1818-20... 

Ladd A J C and Hoover W G 1983 Plastic-flow In close-packed crystals via non-equillbrium molecular-dynamics Phys. Rev. B 28 1756-62... 

Oldroyd, J. G., 1947. A rational formulation of the equations of plastic flow for a Bingham solid. Proc. Camb. Philos. Soc. 43, 100-105. 

Originally, vulcanization implied heating natural rubber with sulfur, but the term is now also employed for curing polymers. When sulfur is employed, sulfide and disulfide cross-links form between polymer chains. This provides sufficient rigidity to prevent plastic flow. Plastic flow is a process in which coiled polymers slip past each other under an external deforming force when the force is released, the polymer chains do not completely return to their original positions. 

Knoop developed an accepted method of measuring abrasive hardness using a diamond indenter of pyramidal shape and forcing it into the material to be evaluated with a fixed, often 100-g, load. The depth of penetration is then determined from the length and width of the indentation produced. Unlike WoodeU s method, Knoop values are static and primarily measure resistance to plastic flow and surface deformation. Variables such as load, temperature, and environment, which affect determination of hardness by the Knoop procedure, have been examined in detail (9). 

Mild steel is a satisfactory constmction material for all equipment in Ziegler chemistry processes except for hydrolysis. If sulfuric acid hydrolysis is employed, materials capable of withstanding sulfuric acid at 100°C are requited lead-lined steel, some alloys, and some plastics. Flow diagrams for the Vista and Ethyl processes are shown in Eigures 3 and 4, respectively. 

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

If it is assumed that yield and subsequent plastic flow of the material occurs in accordance with the maximum shear stress criterion, then /2 may be substituted for in the above and subsequent equations. For the shear strain energy criterion it may be assumed, as a first approximation, that the corresponding value is G j fz. Errors in this assumption have been discussed (11). 

Collapse and Bursting Pressure. If the pressure is sufficiently large to push the plastic—elastic boundary to the outer surface of the cylinder so that the fibers at that surface yield, then there is nothing to restrain the wad, and the cylinder is said to codapse. With an ideal material which does not work harden the codapse pressure, P, sometimes caded the full plastic flow pressure, the full overstrain pressure or the full thickness yield pressure, would be the bursting pressure of the cylinder. It is given by equation 10 when thus... 

Measurements of stress relaxation on tempering indicate that, in a plain carbon steel, residual stresses are significantly lowered by heating to temperatures as low as 150°C, but that temperatures of 480°C and above are required to reduce these stresses to adequately low values. The times and temperatures required for stress reUef depend on the high temperature yield strength of the steel, because stress reUef results from the localized plastic flow that occurs when the steel is heated to a temperature where its yield strength is less than the internal stress. This phenomenon may be affected markedly by composition, and particularly by alloy additions. 

Suspensions of fine sohds may have pseudoplastic or plastic-flow properties. When they are in laminar flow in a stirred vessel, motion in remote parts of the vessel where shear rates are low may become negligible or cease completely. To compensate for this behavior of slurries, large-diameter impellers or paddles are used, with (D /Df) > 0.6, where Df is the tank diameter. In some cases, for example, with some anchors, > 0.95 Df. Two or more paddles may be used in deep tanks to avoid stagnant regions in slurries. 

Metals Successful applications of metals in high-temperature process service depend on an appreciation of certain engineering factors. The important alloys for service up to I,I00°C (2,000°F) are shown in Table 28-35. Among the most important properties are creep, rupture, and short-time strengths (see Figs. 28-23 and 28-24). Creep relates initially applied stress to rate of plastic flow. Stress... 

But at the present it (Bridgman s work) increases the presumption that the discontinuity in the shock wave is to be explained by something else. The whole question of what causes such discontinuities seems to be somewhat obscure. It is apparently recognized that such a phenomena as reaching the plastic limit may explain the discontinuity at 10,(X)0 (kg/cm ) mentioned above, but the precise mechanism by which reaching the plastic flow point may induce the discontinuity seems not to have been worked out. 

An example of research in the micromechanics of shock compression of solids is the study of rate-dependent plasticity and its relationship to crystal structure, crystal orientation, and the fundamental unit of plasticity, the dislocation. The majority of data on high-rate plastic flow in shock-compressed solids is in the form of ... 

Much of what we currently understand about the micromechanics of shock-induced plastic flow comes from macroscale measurement of wave profiles (sometimes) combined with pre- and post-shock microscopic investigation. This combination obviously results in nonuniqueness of interpretation. By this we mean that more than one micromechanical model can be consistent with all observations. In spite of these shortcomings, wave profile measurements can tell us much about the underlying micromechanics, and we describe here the relationship between the mesoscale and macroscale. 

In the following development we consider a plane wave of infinite lateral extent traveling in the positive Xj direction (the wave front itself lies in the Xj, Xj plane). When discussing anisotropic materials we restrict discussion to those propagation directions which produce longitudinal particle motion only i.e., if u is the particle velocity, then Uj = Uj = 0. The <100>, <110>, and <111 > direction in cubic crystals have this property, for example. The derivations presented here are heuristic with emphasis on the essential qualitative features of plastic flow. References are provided for those interested in proper quantitative features of crystal anisotropy and nonlinear thermoelasticity. 

Wallace [15], [16] gives details on effects of nonlinear material behavior and compression-induced anisotropy in initially isotropic materials for weak shocks, and Johnson et ai. [17] give results for infinitesimal compression of initially anisotropic single crystals, but the forms of the equations are the same as for (7.10)-(7.11). From these results it is easy to see where the micromechanical effects of rate-dependent plastic flow are included in the analysis the micromechanics (through the mesoscale variables and n) is contained in the term y, as given by (7.1). 

This process of backward dislocation motion produces reverse plastic flow immediately upon reduction of longitudinal stress from the shocked state. A modification of the Orowan equation, (7.1), to the current situation is... 

What would you conclude about difficulties associated with MD simulations of plastic flow in real materials ... 

D.C. Wallace, Thermoelastic-Plastic Flow in Solids, Los Alamos Report LA-10119, 1985. 

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