Deformation tension

Droplet-deforming tensions are supplied by the continuous phase and act on the droplet interfaces. The emulsification machine itself only serves for the flow conditions required. Laminar shear flow, elongational flow, turbulent flow and cavitation-induced microturbulences are usually found in industrial emulsification machines. 

Some tests, while imdergoing deformation, are usually referred to as static, in that they are performed at slow speeds or low cycles. Examples of these tests are stretch modulus, ultimate tensile strength, and elongation to break, ie, a measure of total energy capabihties or rupture phenomena. Dynamic properties are measured by continuous cycles of varying deformation (tension, compression, or shear), at varying frequencies which can be set close to that which a component would experience in a tire. These properties are more correlative to many tire performance parameters. 

Hooke s law-relationship between engineering stress and engineering strain for elastic deformation (tension and compression)... 

The free energy is generally written as a simple linear function of the first invariant of the deformation tension. Under this assumption and taking into account the normation condition... 

A solid, by definition, is a portion of matter that is rigid and resists stress. Although the surface of a solid must, in principle, be characterized by surface free energy, it is evident that the usual methods of capillarity are not very useful since they depend on measurements of equilibrium surface properties given by Laplace s equation (Eq. II-7). Since a solid deforms in an elastic manner, its shape will be determined more by its past history than by surface tension forces. 

Force per unit area along the axis of the deformation is called the uniaxial tension or stress. We shall use the symbol a as a shorthand replacement for F/A and attach the subscript t to signify tension. The elongation, expressed as a fraction of the original length AL/Lq is called the strain. We shall use 7j as the symbol for the resulting strain (subscript t for tension). Both o... 

This result is the shear equivalent to Eq. (3.42) for tensile deformation. Note the modulus is a constant independent of strain for shear, while this is only true for a = 1 in the case of tension as shown by Eq. (3.43). 

The situation is not so simple when these various parameters are time dependent. In the latter case, the moduli, designated by E(t)and G(t), are evaluated by examining the (time dependent) value of o needed to maintain a constant strain 7o- By constrast, the time-dependent compliances D(t) and J(t)are determined by measuring the time-dependent strain associated with a constant stress Oq. Thus whether the deformation mode is tension or shear, the modulus is a measure of the stress required to produce a unit strain. Likewise, the compliance is a measure of the strain associated with a unit stress. As required by these definitions, the units of compliance are the reciprocals of the units of the moduli m in the SI system. 

An important aspect of the mechanical properties of fibers concerns their response to time dependent deformations. Fibers are frequently subjected to conditions of loading and unloading at various frequencies and strains, and it is important to know their response to these dynamic conditions. In this connection the fatigue properties of textile fibers are of particular importance, and have been studied extensively in cycHc tension (23). The results have been interpreted in terms of molecular processes. The mechanical and other properties of fibers have been reviewed extensively (20,24—27). 

A common measurement usehil in predicting threadline behavior is fiber tension, frequentiy misnamed spinline stress. It is normally measured after the crystallization point in the threadline when the steady state is reached and the threadline is no longer deformed. Fiber tension increases as take-up velocity increases (38) and molecular weight increases. Tension decreases as temperature increases (41). Crystallinity increases slightiy as fiber tension is increased (38). At low tension, the birefringence increases as tension is increased, leveling off at a spinline tension of 10 MPa (1450 psi) (38). 

Flow Past Deformable Bodies. The flow of fluids past deformable surfaces is often important, eg, contact of Hquids with gas bubbles or with drops of another Hquid. Proper description of the flow must allow for both the deformation of these bodies from their shapes in the absence of flow and for the internal circulations that may be set up within the drops or bubbles in response to the external flow. DeformabiUty is related to the interfacial tension and density difference between the phases internal circulation is related to the drop viscosity. A proper description of the flow involves not only the Reynolds number, dFp/p., but also other dimensionless groups, eg, the viscosity ratio, 1 /p En tvos number (En ), Api5 /o and the Morton number (Mo),giJ.iAp/plG (6). 

At high temperature, the behavior is different. A stmcture designed according to the principles employed for room temperature service continues to deform with time after load apphcation, even though the design data may have been based on tension tests at the temperature of interest. This deformation with time is called creep because the design stresses at which it was first recognized occurred at a relatively low rate. 

Grease Retention, Wrinkle Resistance, and Durable Press. On bending or creasing of a textile material, the external portion of each filament in the yam is placed under tension, and the internal portion is placed in compression. Thus, the wrinMe-recovery properties must be governed in part by the inherent, tensional elastic deformation and recovery properties of the fibers. In addition to the inherent fiber properties, the yam and fabric geometry must be considered. 

The emulsification process in principle consists of the break-up of large droplets into smaller ones due to shear forces (10). The simplest form of shear is experienced in lamellar flow, and the droplet break-up may be visualized according to Figure 4. The phenomenon is governed by two forces, ie, the Laplace pressure, which preserves the droplet, and the stress from the velocity gradient, which causes the deformation. The ratio between the two is called the Weber number. We, where Tj is the viscosity of the continuous phase, G the velocity gradient, r the droplet radius, and y the interfacial tension. 

In this study, the appearance and evolution sequence of planar slip bands, in addition to a dislocation cell structure with increasing e,, is identical to that observed in quasi-static studies of the effects of stress path changes on dislocation substructure development [27]. The substructure evolution in copper deformed quasi-statically is known to be influenced by changes in stress path [27]. Deforming a sample in tension at 90° orthogonal to the... 

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