Plastic Flow Plasticity

FIGURE 3.7 The model of plastic flow the friction element.  

These are the three simplest cases of mechanical behavior and the corresponding rheological models. By combining them as elements, one can obtain more complex models describing the rheological properties of various systems. Every such combination is typically viewed within a framework of a specific deformation regime in which one seeks to reveal the qualitatively new properties of a given model as compared to the properties of its elements. 

Physical-Chemical Mechanics of Disperse Systems and Materials 

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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. 

Major regional distribution of soft soil silt, gray, saturated, high compressibility, containing rot plants, with a depth of 10.50 to 12.30 m, thickness is 8.20-12.00 m, layer bottom elevation is from -13.92 to -8.28 m across the board widely distributed, lateral distribution of soft soil are basically the same. Clay loam—silt (sub) gray-yellow and gray, soft plastic-flow plastic state, high compression, sandy loam, silt with a depth of 16.60-23.10 m, thickness is 1.30 to 1.70 m, layer bottom elevation is from-20.92 to 14.35 meters. 

In contrast to the two previous cases, plastic flow (plasticity) is characterized by the absence of proportionality between the stress and the strain, that is, plasticity represents a case of nonlinear behavior. For plastic bodies subjected to stresses below the critical value, t < t (the so-called shear yield point), the rate of strain is zero (dy/dt = 0). Plastic flow starts at the yield stress, t = t, and does not require further increase in stress (Figure 3.6). Similar to viscous flow, plastic flow is thermodynamically and mechanically irreversible. However, in contrast to the prior case, the rate of energy dissipation in plastic flow is proportional to the rate of strain ... 

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... 

Numerous examples of polymer flow models based on generalized Newtonian behaviour are found in non-Newtonian fluid mechanics literature. Using experimental evidence the time-independent generalized Newtonian fluids are divided into three groups. These are Bingham plastics, pseudoplastic fluids and dilatant fluids. 

Bingham plastics are fluids which remain rigid under the application of shear stresses less than a yield stress, Ty, but flow like a. simple Newtonian fluid once the applied shear exceeds this value. Different constitutive models representing this type of fluids were developed by Herschel and Bulkley (1926), Oldroyd (1947) and Casson (1959). 

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

Finally, in yet another variant, the sample liquid stream and the gas flow are brought together at a shaped nozzle into which the liquid flows (parallel-path nebulizer). Again, the intersection of liquid film and gas flow leads to the formation of an aerosol. Obstruction of the sample flow by formation of deposits is not a problem, and the devices are easily constructed from plastics, making them robust and cheap. 

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). 

Resin Viscosity. The flow properties of uncured compounded plastics is affected by the particle loading, shape, and degree of dispersion. Flow decreases with increased sphericity and degree of dispersion, but increases with increased loading. Fillers with active surfaces can provide thixotropy to filled materials by forming internal network stmctures which hold the polymers at low stress. 

The processes used commercially for the manufacture of film and sheeting materials are generaUy similar in basic concept, but variations in equipment or process conditions are used to optimize output for each type of film or sheeting material. The nature of the polymer to be used, its formulation with plasticizers (qv), fillers (qv), flow modifiers, stabilizers, and other modifiers, as weU as its molecular weight and distribution are aU critical to the... 

Stabilization of the Cellular State. The increase in surface area corresponding to the formation of many ceUs in the plastic phase is accompanied by an increase in the free energy of the system hence the foamed state is inherently unstable. Methods of stabilizing this foamed state can be classified as chemical, eg, the polymerization of a fluid resin into a three-dimensional thermoset polymer, or physical, eg, the cooling of an expanded thermoplastic polymer to a temperature below its second-order transition temperature or its crystalline melting point to prevent polymer flow. 

One simple rheological model that is often used to describe the behavior of foams is that of a Bingham plastic. This appHes for flows over length scales sufficiently large that the foam can be reasonably considered as a continuous medium. The Bingham plastic model combines the properties of a yield stress like that of a soHd with the viscous flow of a Hquid. In simple Newtonian fluids, the shear stress T is proportional to the strain rate y, with the constant of proportionaHty being the fluid viscosity. In Bingham plastics, by contrast, the relation between stress and strain rate is r = where is... 

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