Bulk longitudinal deformation

One-Dimensional Extension in Infinite Medium (Bulk Longitudinal Deformation)... 

Viscoelastic behavior in simple extension or in bulk longitudinal deformation will in general combine the features of shear and bulk viscoelasticity, since the moduli E t) and M t) depend on both (7(0 and K t), as shown by equations 51 and 58 of Chapter 1 ( and analogous relations for E and M ). However, as already pointed out, shear effects predominate in E(t) and E. and bulk effects predominate... 

It is well known that under static conHning pressure the viscosities of ordinary liquids are increased. The same effect is observed for the steady flow viscosity of polymers and for viscoelastic relaxation times, though the latter have been usually studied in bulk deformation or bulk longitudinal deformation rather than in shear. Qualitatively this behavior can be understood in terms of the dependence of segmental mobility on the fractional free volume, since the free volume must decrease with increasing pressure just as it does with decreasing temperature. Quantitative relations analogous to equations 32 and 34 can be readily derived, not only for pressure dependence but also for dependence on certain other variables that affect the free volume. 

Deformation Simple Shear Bulk Compression Simple Extension" Bulk Longitudinal... 

The two basic types of mechanical deformation, from a physical and molecular standpoint, are shear and dilatation. The experimental methods described in the preceding three chapters yield information primarily about shear only in extension measurements on hard solids does a perceptible volume change influence the results. By combining shear and extension measurements, the bulk properties can be calculated by difference, as for example in creep by equation 55 of Chapter 1, but the subtraction is unfavorable for achieving a precise result. Alternatively, bulk properties can be measured directly, or they can be obtained by combining data on shear and bulk longitudinal def ormations (corresponding to the modulus M discussed in Chapter 1), where the subtraction does not involve such a loss of precision. Methods for such measurements will now be described. They have been reviewed in more detail by Marvin and McKinney. ... 

Elasticity of solids determines their strain response to stress. Small elastic changes produce proportional, recoverable strains. The coefficient of proportionality is the modulus of elasticity, which varies with the mode of deformation. In axial tension, E is Young s modulus for changes in shape, G is the shear modulus for changes in volume, B is the bulk modulus. For isotropic solids, the three moduli are interrelated by Poisson s ratio, the ratio of traverse to longitudinal strain under axial load. 

Thus, the speetral funetions, Fi(A), are comprehensively studied both experimentally and theoretically. The behavior of relaxation functions, G2(t) and G3(t), is still much less known. The properties of the function, G2(t), were mainly studied in experiments with longitudinal ultrasound waves.It has been found that relaxation mechanisms manifested in shear and bulk deformations are of a similar nature. In particular, polymeric solutions are characterized by close values of the temperature-shift factors and similar relaxation behavior of both shear and bulk viscosity. The data on the function, F3(A), indicate that relaxation behavior of isotropic deformation at thermal expansion can be neglected for temperatures well above the glass-transition temperature. ... 

Where a is the longitudinal stress, e is corresponding strain, and E is called Young s modulus (or the modulus of elasticity). Similarly, in shear deformation, the modulus is called the shear modulus or the modulus of rigidity (G). When a hydrostatic force is applied, a third elastic modulus is used the modulus of compressibility or bulk modulus (K). It is defined as the ratio of hydrostatic pressure to volume strain. A deformation (elongation or compression) caused by an axial force is always associated with an opposite deformation (contraction or expansion) in the lateral direction. The ratio of the lateral strain to the longitudinal strain is the fourth elastic constant called Poisson s ratio (v). For a small deformation, elastic parameters can be correlated in the following way ... 

In order to visualize the development of pucker, a model (Figure 3.3(a) and (b)) is shown to understand the deformation of fabric stmcmre due to the insertion of a seam in it. This stitching line or a seam has to find a position on and in the plane of the fabric. In order to accommodate the bulk of stitch, the fabric yam in both directions gets displaced around this juncture. Depending on the physical and mechanical properties of the fabric, the sewing thread may have no resistance from the fabric and would manifest in different types of yam movements (distortions) in the fabric structure otherwise due to resistance from the fabric, only compression of the thread and fabric yam may take place. The former causes severe pucker and the latter causes little or no pucker. It is either the yams parallel to the seam, or the ones perpendicular to the seam, that absorb the longitudinal and lateral... 

Emission. When the fiber and pumping are long and large enough to obtain gain, emission spectra are deformed by amplification by stimulated emission (ASE) (fig. 36). So, observed longitudinal emission spectra may be very different from bulk... 

In the compound systems described above, the polymer is subjected to com-pressional stress only, with no shear components, because the confining liquid transmits no perceptible shear stresses. If, however, longitudinal waves are propagated in a continuous specimen of polymer with at least one dimension large compared with the wavelength, the sample experiences both bulk and shear stresses and deformations which are combined in a manner dependent on the sample shape. 

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