Stress extensional

The average extensional stress is obtained by integrating across the element so... 

So from the deflnition of swelling ratio and using the subscript, E, to denote extensional stresses then... 

Any deformation of the matrix material in the x-direction is ignored. Thus, the change in strain energy is presumed to be dominated by the energy of transverse (extensional) stresses. Thus, for the matrix. 

Any rheometric technique involves the simultaneous assessment of force, and deformation and/or rate as a function of temperature. Through the appropriate rheometrical equations, such basic measurements are converted into quantities of rheological interest, for instance, shear or extensional stress and rate in isothermal condition. The rheometrical equations are established by considering the test geometry and type of flow involved, with respect to several hypotheses dealing with the nature of the fluid and the boundary conditions the fluid is generally assumed to be homogeneous and incompressible, and ideal boundaries are considered, for instance, no wall slip. 

It is clear in Fig. 1.10 that the distribution of Kuroko deposits is restricted in a narrow zone in the Green tuff region which was called a Kuroko belt by Inoue (1969). This belt was formed by rapid subsidence under the extensional stress regime and is thought to have been a back-arc depression zone at middle Miocene age. The relationship between tectonic setting and formation of Kuroko deposits is discussed in section 1.5. 

Figure 1.146, Stre.ss trajectory map.s of southern Northeast Honshu in the late Cenozoic period, after Tsunakawa and Takeuchi (1986) with a slight addition. oh, . trajectory is drawn by smoothing the inferred stress orientations from the selected dike-swarms with K-Ar dates. Selected major faults with age estimation are also shown for indicating types of stress fields. T Extensional stress field, where ay > a 2>cth , and normal or gravity faulting is preferable. P Compre.ssional, oh > ay, reverse or thrust faulting...

During Miocene age most of this province was in a submarine environment. Violent submarine volcanism (bimodal and basic type) took place at Miocene age in this province. This geologic environment may be related to an extensional stress regime (Uyeda and Kanamori, 1979). The Kuroko deposits have been formed related to this tectonic situation. 

In any model, back-arc basins form under the extensional stress regime and are associated by Mariana-type subduction by Uyeda and Kanamori (1979) rather than Chilean-type subduction. 

It seems likely that epithermal Au mineralization (low sulfidation-type) forms in volcanic depression zone (back-arc on land) under the extensional stress regime rather than compressional stress regime. 

These deposits are characterized by polymetallic (Cu, Pb, Zn, Au, Ag, etc.) mineralization and formation in extensional stress fields. Ore fluids responsible for these ore deposits are dominated by seawater origin, considering isotopic and chemical composition of ore fluids. 

Extensional flow describes the situation where the large molecules in the fluid are being stretched without rotation or shearing [5]. Figure 4.3.3(b) illustrates a hypothetical situation where a polymer material is being stretched uniaxially with a velocity of v at both ends. Given the extensional strain rate e (= 2v/L0) for this configuration, the instantaneous extensional viscosity r e is related to the extensional stress difference (oxx-OyY), as... 

Now let us take a look at a recent NMR imaging experiment of Fano flow, in which the local velocities in the tubeless column were mapped out quantitatively and nondestructively [20], For such a set-up, the weight force of the column is balanced by the extensional stress difference azz - axx associated with the vertical velocity gradient (dvz/dz), as... 

The stress is simply defined as the force divided by the area over which it is applied. Pressure is a compressive bulk stress. When we hang a weight on a wire, we are applying an extensional stress and when we slide a piece of paper over a gummed surface to reach the correct position, we are applying a shear stress. We will focus more strongly on this latter stress because most of our instruments are designed around this format. The units of stress are Pascals. 

Fig. E11.2c Extensional stress-strain response of the PE-GMA, PE-MAH, and 256 multilayer films at 140°C and extension rate of 0.1 s. [Reproduced by permission from T. Saito and C. W. Macosko, Interfacial Cross-linking and Diffusion via Extensional Rheometry, Polym. Eng. Sci., 42, 1-9 (2002).]...

Recently, Muliawan et al. (52), who have been studying melt fracture, and in particular sharkskin extrudate instabilities over the last decade, have presented interesting experimental results relating the extensional stress-Hencky strain behavior of polymer melts to their sharkskin (exit) and gross (capillary entrance) melt fracture behavior. For the purposes of this discussion, results obtained with two Nova Chemicals... 

If we exclude the pressure from the relation for the stresses (9.58) under the considered uniaxial deformation, we can obtain an expression for the extensional stress... 

When relations (9.67) and (9.68) are used, the invariant can be expressed in terms of the elongational velocity gradient or extensional stress... 

For correct measurements, the extensional rate of strain is in general controlled and the extensional stress is measured. 

The instantaneous extensional stress W(e, t) is the force F(e, t) along the cylinder axis required to pull the cylinder ends apart, divided by the instantaneous cross-sectional area A s, t) of the cylinder thus a(e, r) = F e, t)/A(e, t). The time-dependent extensional viscosity, rj(e, t), is then ct( , t)/e. If this viscosity reaches a time-independent value within the duration of the experiment, that value is called the steady-state extensional viscosity, r ( ). 

Figure 1.12 Rotating clamp device used by Meissner to impose a uniaxial extensional strain on a cylindrical filament of polymer of length Lq. Leaf springs in one of the sets of rotating clamps allow the extensional stress to be measured. (From Meissner 1971, reprinted with permission from Steinkopff Publishers.)...

In Sections 1.3.1 and 1.3.2, we discussed the shear stress and the extensional stress in shearing flows and extensional flows, respectively. These are components of the three-dimensional state-of-stress tensor T. The ith row of T is the force per unit area that material exterior to a unit cube exerts on a surface perpendicular to the tth coordinate axis (see Fig. 1-18). In general, if F is the force per unit area acting on a surface perpendicular to an arbitrary outward-directed unit vector, n, then... 

Figure 6.26 Extensional stress au — 022 versus extension rate for glass fibers of aspect ratios 282, 586, and 1259 suspended in Newtonian polybutene oil (viscosity 283 P) at the volume percents shown. The straight lines have slopes of unity the data are in excellent agreement with the equation of Batchelor (1971), Eq. (6-57). [From Macosko 1994 (adapted from Mewis andMetzner 1974), with permission from Cambridge University Press.]...

Joint— A fracture in bedrock across which there has not been significant displacement, but that forms as a result of extensional stresses. 

The melt viscosity of LCPs is sensitive to thermal and mechanical histories. Quite often, instrumental influences are important in the value of viscosity measured. For example, the viscosity of HBA/HNA copolyesters are dependent on the die diameter in capillary flow (59). LCP melts or solutions are very efficiently oriented in extensional flows, and as a result, the influence of the extensional stresses at the entrance to a capillary influence the shear flow in the capillary to a much greater extent than is usually found with non-LC polymers. 

Blends. There has been considerable research in recent years on polymer blends that contain an LCP. This subject was recently reviewed by Dutta et al. (67). The addition of an LCP to another thermoplastic melt effectively lowers the melt viscosity and improves processability. In addition, if the flow field contains an extensional stress component, the LCP dispersed phase is extended into a fibrous morphology and oriented in the flow direction. This microstructure can be retained in the solidified blend to provide self-reinforcement. 

Surfactant additives have been studied intensively in recent years because of the self-reparability or self-assembly of their micro structures after degradation by mechanical or extensional stresses. This ability has led to many studies of their applications in DHC recirculation systems. Classifications of surfactant DR As and their self-assembly nature are described. Also discussed in this section are the main research results on microstructures, rheological properties, HTR of surfactant DR solutions, and approaches to enhance heat transfer coefficients. Significant field tests around the world are reviewed. 

Triassic or Tertiary NNW-SSE fractures formed in an ambient E-W to ENE-WSW extensional stress regime would be expected to show evidence of sinistral rather than dextral transtension. Kerr (1987) noted the evidence for late-stage dextral shear reactivation of the NNW-SSE faults, which he ascribed to a short-lived change in the Tertiary stress field. However, Tertiary veins in the Cretaceous carbonates near Ballycastle are dominated by NE-SW to ENE-WSW orientations, with a subordinate NNW-SSE to N-S set. Both are filled by multiple calcite cements with no evidence of fer-... 

To avoid problems with pressure that might be applied to the outside of the sample, it is customary to define the extensional stress crE in terms of the difference between the two applied stresses, thus... 

The new metallocene catalysis leads to isomer purity in excess of 96%. It is also possible to produce branched, high melt strength PP, with extensional stress hardening, similar to that of LDPE [Phillips et al., 1992]. The new PP s show the melting point, T = 120-164°C. To enhance the performance, PP is usually blended (in the reactor or outside the reactor) with much more viscous PP-copolymers. As a consequence, one of the most serious industrial problem is homogenization of these materials [Luciani and Utracki, 1996 Utracki andLuciani, 1996]. 

Drop Deformability When a neutrally buoyant, initially spherical droplet is suspended in another liquid and subjected to shear or extensional stress, it deforms and then breaks up into smaller droplets. Taylor [1932,1934] extended the work of Einstein [1906, 1911] on dilute suspension of solid spheres in a Newtonian liquid to dispersion of single Newtonian liquid droplet in another Newtonian liquid, subjected to a well-defined deformational field. Taylor noted that at low deformation rates in both uniform shear and planar hyperbolic fields, the sphere deforms into a spheroid (Figure 7.9). 

Bousfield et al. [1986] studied the surface tension driven breakup of Newtonian and viscoelastic filaments. The authors found that disturbances grow more rapidly in viscoelastic filaments than in the Newtonian ones, but that there is a retardation of the growth and stabilization at long times, resulting from large extensional stresses (see Figure 7.16). The formation of satellite drops was found to be retarded by the elasticity. 

For capillary flow at 150°C, the extensional stress, Ojj = 50-800 kPa, at the entrance to capillary was calculated from [Cogswell, 1972] ... 

Since the tensile yield stress for solid PA-6 at 150°C was determined as = 15 kPa, independent of the rate of straining, the extensional stress in the capillary entrance was more than sufficient to deform the amorphous part of PA-6. Owing to crystallization, the elongated structures, once created, could neither disintegrate nor elastically retract to spherical shapes. 

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