Extensional

The features created by crustal movements may be mountain chains, like the Himalayas, where collision of continents causes extensive compression. Conversely, the depressions of the Red Sea and East African Rift Basin are formed by extensional plate movements. Both type of movements form large scale depressions into which sediments from the surrounding elevated areas ( highs ) are transported. These depressions are termed sedimentary basins (Fig. 2.3). The basin fill can attain a thickness of several kilometres. 

Since faults are zones of inherent weakness they may be reactivated over geologic time. Usually, faulting occurs well after the sediments have been deposited. An exception to this is a growth feu/f (also termed a syn-sedimentary fault), shown in Figure 5.7. They are extensional structures and can frequently be observed on seismic sections through deltaic sequences. The fault plane is curved and in a three dimensional view has the shape of a spoon. This type of plane is called listric. Growth faults can be visualised as submarine landslides caused by rapid deposition of large quantities of water-saturated... 

Extensional viscosity Extension cord External lubricant External plasticizers Exterol Exter press Exton... 

Film. By far the largest appHcation for LLDPE resins (over 60% in the United States) is film. Because LLDPE film has high tensile strength and puncture resistance, it is able to compete with HDPE film for many uses. The toughness and low temperature properties of LLDPE film also exceed those of conventional LDPE. Furthermore, because LLDPE resins exhibit relatively low strain hardening in the molten state and lower extensional viscosity, it can be produced at high rates with Httle risk of bubble breaks. 

Extensional Viscosity. In addition to the shear viscosity Tj, two other rheological constants can be defined for fluids the bulk viscosity, iC, and the extensional or elongational viscosity, Tj (34,49,100—107). The bulk viscosity relates the hydrostatic pressure to the rate of deformation of volume, whereas the extensional viscosity relates the tensile stress to the rate of extensional deformation of the fluid. Extensional viscosity is important in a number of industrial processes and problems (34,100,108—110). Shear properties alone are insufficient for the characterization of many fluids, particularly polymer melts (101,107,111,112). 

Extensional flows occur when fluid deformation is the result of a stretching motion. Extensional viscosity is related to the stress required for the stretching. This stress is necessary to increase the normalized distance between two material entities in the same plane when the separation is s and the relative velocity is ds/dt. The deformation rate is the extensional strain rate, which is given by equation 13 (108) ... 

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified and measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ... 

Fig. 14. Shear viscosity, Tj, and extensional viscosity, Tj as a function of deformation rate of a low density polyethylene (LDPE) at 150°C (111). To convert...

Extensional Viscosity. AH three types of extensional viscosity can be measured (101,103) uniaxial, biaxial, and pure shear. Only a few commercial instmments are available, however, and most measurements are made with improvised equipment. Extensional viscosity of polymer melts can be estimated from converging flow (entrance pressure) or from a melt strength drawdown test (208). 

Another type of experiment involves a fluid filament being drawn upward against gravity from a reservoir of the fluid (101,213,214), a phenomenon often called the tubeless siphon. The maximum height of the siphon is a measure of the spinnabiUty and extensional viscosity of the fluid. Mote quantitative measures of stress, strain, and strain rate can be determined from the pressure difference and filament diameter. A more recent filament stretching device ia which the specimen is held between two disks that move apart allows measurements ia low viscosity Hquids (215). AH of these methods are limited to spinnable fluids under small total strains and strain rates. High strain rates tend to break the column or filament. 

A sliding plate rheometer (simple shear) can be used to study the response of polymeric Hquids to extension-like deformations involving larger strains and strain rates than can be employed in most uniaxial extensional measurements (56,200—204). The technique requires knowledge of both shear stress and the first normal stress difference, N- (7), but has considerable potential for characteri2ing extensional behavior under conditions closely related to those in industrial processes. 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

Extensional viscosity that results purely from shear deformation seems to be of less interest, but has been measured (108). The theology of several different polymer melts in terms of shear viscosity and uniaxial and biaxial extensional viscosity has been compared (231). Additional information on the measurement of extensional viscosity are also available (105,238—240). 

Additional complications can occur if the mode of deformation of the material in the process differs from that of the measurement method. Most fluid rheology measurements are made under shear. If the material is extended, broken into droplets, or drawn into filaments, the extensional viscosity may be a more appropriate quantity for correlation with performance. This is the case in the parting nip of a roUer in which filamenting paint can cause roUer spatter if the extensional viscosity exceeds certain limits (109). In a number of cases shear stress is the key factor rather than shear rate, and controlled stress measurements are necessary. 

Eor the case of high modulus fibers such as carbon fibers with = 240 GPa (3.5 x 10 psi), in a polymer matrix, such as epoxy resin with = 3.0 GPa (450,000 psi), the extensional modulus is approximately proportional to the fiber volume fraction and the modulus of the fibers ... 

Thus the addition of the stiff carbon fibers has a very great effect in stiffening the epoxy matrix. Eor the commonly used fiber volume fraction of 0.6 the unidirectional carbon—epoxy lamina has a predicted extensional stiffness E = 145 GPa (2.1 x 10 psi)-... 

The difference between the bounds defined by the simple models can be large, so that more advanced theories are needed to predict the transverse modulus of unidirectional composites from the constituent properties and fiber volume fractions (1). The Halpia-Tsai equations (50) provide one example of these advanced theories ia which the rule of mixtures expressions for the extensional modulus and Poisson s ratio are complemented by the equation... 

The melt-spinning process used to convert mesophase pitch into fiber form is similar to that employed for many thermoplastic polymers. Normally, an extruder melts the pitch and pumps it into the spin pack. Typically, the molten pitch is filtered before being extruded through a multi-holed spinnerette. The pitch is subjected to high extensional and shear stresses as it approaches and flows through the spinnerette capillaries. The associated torques tend to orient the liquid crystalline pitch in a regular transverse pattern. Upon emerging from the... 

A] is the Extensional Stiffness Matrix although it should be noted that it also contains shear terms. 

Having obtained all the terms for the extensional stiffness matrix [A], this may then be inverted to give the compliance matrix [a]. 

This is called the Extensional Stiffness Matrix and the similarity with that derived earlier for the single ply should be noted. 

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

Referring to the terminology in Fig. 5.9 and using analysis similar to that for the coni-cylindrical die, it may be shown that the shear, extensional and die entry pressure losses are given by... 

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