Rheology elastic deformation

Rheology is the science of the deformation and flow of matter. It is concerned with the response of materials to appHed stress. That response may be irreversible viscous flow, reversible elastic deformation, or a combination of the two. Control of rheology is essential for the manufacture and handling of numerous materials and products, eg, foods, cosmetics, mbber, plastics, paints, inks, and drilling muds. Before control can be achieved, there must be an understanding of rheology and an ability to measure rheological properties. 

Rheology is the science that deals with the deformation and flow of matter under various conditions. The rheology of plastics, particularly of TPs, is complex but understandable and manageable. These materials exhibit properties that combine those of an ideal viscous liquid (with pure shear deformations) with those of an ideal elastic solid (with pure elastic deformation). Thus, plastics are said to be viscoelastic. 

The rheology of lubricated polytetrafluoroethylene compositions was studied by Lewis and Winchester. The mechanism appeared to be a combination of permanent and elastic deformations in the region just before the orifice of the die in the extruder. As a result of permanent deformation, the polymer particles are partially transformed into long fibers. The relative amounts of permanent and recoverable deformation were related to the rate and temperature of extrusion and the geometry of the extruder. Plastic deformation is favored by extruding at temperatures above the 19 and 30° transitions (Snelling and Lontz). 

AFM can also be used to probe local mechanical properties of thin films of food biopolymers, which are difficult to measure using traditional rheological methods. Several mechanical models have been developed to analyze the Young s modulus of food systems. One of the simplest models, the Hertz model, assumes that only the elastic deformation exists in a surface with spherical contacts, and the adhesion force can be neglected (Hugel and Seitz 2001). Equation (8.2) describes the relationship between the loading force, F and the penetration depth, d, where a is the radius of contact area, R the curvature of the tip radius, Vi and the Poisson s ratios of the two contact materials that have Young s modulus, Ei and E2. ... 

When attempting to describe more accurately the rheological behaviour of ceramic plastic mixes, one should also take into account the elastic behaviour above the yield point. If a plastic body is abruptly stressed by a constant load, there first occurs rapid clastic deformation followed by delayed elastic deformation and irreversible flow. Similarly, instant as well as delayed relaxation take place after stress relief. If a formed product has only a limited possibility to relax, it retains some interna stress w hich may be the cause of drying defects. 

There are three main rheological properties of materials viscous flow, plastic flow, and elastic deformation. The stress deformation behavior of elastic materials is represented by a straight line through the origin. However, in this case, the... 

The viscosities of polymer melts, calculated from the storage modulus and the loss modulus, have to be within a range to resist the applied forces, which act against the rheological forces. But they should not be as large as to prevent the necessary deformation before the start of sodification. The elastic part of deformation has to be small since an elastic deformation happens more rapidly than a viscous one. Therefore, a considerable elastic deformation can lead to a cohesive fracture of the fiber in the molten state. The ratio of the viscous to the elastic energy of the polymer melt may be seen as one of the most important factors for the spinnability of polymers. For the usual commercially used spinnable polymers, such as, for example, poly(ethylene terephthalate), the ratio is about G"/G >10... 

As is known, a highly elastic deformation is accompanied by redistribution of internal stresses and is always associated with viscous deformation. Because of this, for full deformation of a viscous polymer we will have a rheological model (Figure 2.42c), which is governed by the equation ... 

Yield Stress Measurement. The foundations of the rheological treatment to fluids exhibiting a yield stress are due to Bingham (5). Under steady flow conditions, it is common to neglect the contribution from elastic deformation and to use the term Bingham fluid response. Normally, the Herschel-Bulkley equation 9 is used to characterize the flow. 

Ektar Performance Plastic s trade name for its family of copolyester thermoplastic elastomer, elastic constant See modulus of elasticity, elastic deformation See deformation, elastic en-ergy, plastic work rheology, elastic fracture See melt fracture, elastic hysteresis See hysteresis, elastic, elasticity A property that causes plastic to return to its original size and shape after removal of a force causing deformation. See coefficient of elasticity deformation and toughness extruder-web stretching and... 

Generalizations of the Newton s flow law [7.2.3] for polymeric liquids are aimed to describe in more or less details the features of their rheological behavior. The most important among these features is the ability to accumulate elastic deformation during flow and thus to exhibit the memory effects. At first we restrict ourselves to the case of small deformation rates to discuss the basic principles of the general linear theory of viscoelasticity... 

If the shear rates are constants, the non-Newtonian fluids can also be classified according to their viscosity dependence on time. This classification has been widely applied to describe the rheological characteristics of coatings. For the development of deformation, the time evolution corresponds to the effect of the increase of shear rate. Three typical cases occur with the time evolution the thixotropic fluids exhibit the decrease of viscosity, corresponding to pseudo-plastic fluids the rheopectic fluids exhibit the increase of viscosity, corresponding to dilatant fluids while the viscoelastic fluids exhibit partial recovery of the deformation of pseudo-plastic fluids after the removal of the stress. Since polymers can perform a large scale of elastic deformation, this character appears extremely significant. 

Rheology is the study of the deformation of materials. This includes the elastic deformation of solids such as metals as well as the viscous behavior of fluids such as water or oil. There is a wide range of materials that exhibit both a viscous and an elastic response to an applied force, and polymers fall into this group. One of the best ways to determine the viscous nature of these materials is with a capillary rheometer. 

The viscous behaviour of material could be rather complex. As aforementioned, it may be described with time-dependant functions. Time-dependant deformations can be both reversible and/or irreversible but in either case dissipation of energy is involved. This point will be clarified in section 3. According to material rheology, a reversible mechanism means that the deformations would be recovered once the material is unloaded. For example, the elastic deformation is fully reversible and instantaneous. On the other hand, an irreversible mechanism means that the deformations will not be recovered once the material is unloaded. However, emphasis will be put on a reversible mechanism such as the creep/ relaxation phenomenon. 

Figures 4.12 and 4.13 show some results obtained with the torsion pendulum instrument by Izmaylova et al. [35-37]. These figures show the typical rheological and deformation curves of the 2D interfacial layers formed at the interface between an aqueous gelatin solution and benzene. The deformation curves show the force as a function of time at a constant rate of deformation, and the rheological curves show the steady-state rate of the deformation as a function of the shear stress. These experimental data allow one to obtain direct quantitative characteristics of the elasticity in the slow and fast regions and, most importantly, the critical stress values that correspond to strength (by extrapolation to the x-axis. Figure 4.13).

Figure 6.2 High-temperature tensile creep testing apparatus. (Reproduced from Leaderman, H. (1962) Large longitudinal retarded elastic deformation of rubberlike network polymers. Trans. Soc. RheoL, 6, 361. Copyright (1962) Society of Rheology.)...

The first component of the angmented Hybrid Model relates to the elastic behavior of UHMWPE, which is captured by the elastic spring (E) in the rheological representation and the elastic deformation gradient F. The polar decomposition [26] of F involves a left stretch tensor, V , and a rotation tensor, R . Using V , the logarithmic tme strain (E )... 

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