Elastic Extension

The next stop is to cool the nylon below its Tg without removing the stress, retaining its molecular orientation. The nylon becomes rigid with a much higher elastic modulus in the tension direction [15,000 to 20,000 MPa (2 to 3 x 106 psi)]. This is nearly ten times the elastic modulus of the unoriented nylon-66 plastic. The stress for any elastic extension must work against the rigid backbone of the nylon molecule and not simply unkink molecules. This procedure has been commonly used in the commercial production of man-made fibers since the 1930s via DuPont. 

The extension of an amorphous material under a tensile force can be resolved into three parts first, an immediate elastic extension. Which is immediately recoverable on removing the tensile force Mcondly, a delayed elastic extension which is recoverable slowly and thirdly, a plastic extension, viscous flow, or creep, which cannot be glteovered. With glass at ordinary temperatures, this plastic exten- ion is practically absent. A very slow delayed elastic extension OOCUrs. This effect can be troublesome in work with torsion fibres. The delayed elastic effect in vitreous silica fibres is 100 times less than in other glass fibres, and viscous flow of silica is negligible below OO C (N. J. Tighe, 1956). For exact work vitreous sihea torsion flbres are therefore used. 

In order to simplify the discussion and keep the derivation of the formulae tractable, a fibre with a single orientation angle is considered. In a creep experiment the tensile deformation of the fibre is composed of an immediate elastic and a time-dependent elastic extension of the chain by the normal stress ocos20(f), represented by the first term in the equation, and of an immediate elastic, viscoelastic and plastic shear deformation of the domain by the shear stress, r =osin0(f)cos0(f), represented by the second term in Eq. 106. 

Elastomers are polymeric substances with rubber-like behavior at ambient temperatures. This means they are more or less elastic, extensible, and flexible. They can be exfended by relafively small force and return to the original length (or near it) after the force is removed. Rubber-like behavior can be observed in plastics, but under different conditions, such as at elevated temperatures or in swollen state. These are not true elastomers, however. 

Fig. 20. Effect of annealing of HDPE (X = 15) on the heat of elastic extension 8). 1 — initial unannealed sample 2 — after isometric annealing at 1 32 °C for 30 min 3 — after free annealing at 132 °C for 30 min...

FIGURE 31.16 Effect of emollient BW on elastic properties of skin, as measured using Dermal Torque Meter, over a 6-h period following a single wash event. Ue and Ur refer to the immediate elastic extension and recovery, respectively. 

The protein libers of connective tissue can exist in either of two forms in the presence of water (1) a form with high tensile strength but little elastic extensibility and (2) a form with rubberlike extensibility and low modulus... 

This equation can be combined conceptually with the viscous behavior of Eq. (11-9) in either of two ways. If the stresses causing elastic extension and viscous flow are considered to be additive, then... 

This friction behaviour has been related to the three-dimensionally cross-linked structure of the ion-irradiated polymer material, since, with increasing fluence, the polymer surface becomes harder and less elastic due to a greater extent of cross-linking. The stick-slip behaviour is thus caused by the adhesion of the two surfaces, and the periodic elastic extension and sudden release of the cross-linked structure of the implanted layer. The microfriction results have been correlated with nanoindentation hardness measurements, which are an indirect measure of the extent of cross-linking (Rao etal, 1995). 

It can be demonstrated [6.27] that Elnl(N, m) has its maximum at m N/2, when the elastic compression fields generated by partial interstitials essentially compensate for the elastic extension fields surrounding partial vacancies. At m as N/2, the configurational entropy of the complex is also maximum. Therefore, m w N/2 is the most probable number of atoms disposed in the complex of N noncoincident sites, so that nearly one half of the noncoincident sites is occupied by atoms, and another half is vacant. The existence of two-level systems, high diffusion mobility of atoms along non-coincidence sections, low-energy structural fluctuations in polyclusters is connected with this circumstance (Sect. 6.6). 

Under some artificial conditions, however, plants freeze intracellu-larly due to the much more rapid freezing (e.g., a cooling rate of 1°/ min) which does not permit sufficient time for the water to diffuse out of the cells to the extracellular loci of ice. Even then, cell rupture does not normally occur because of the elastic extensibility of the cell walls. The intracellular ice crystals may, however, pierce the cell membranes. This leaves holes on thawing, allow the cell contents to diffuse out, resulting in death of the cell. 

Figure 8-8. Flair fiber elastic extension versus linear density.

Note Work to 20% extension is g x cm, Hookean slope is in gforce/mm elastic extension, Hookean limit is g, and force to 20% extension is g. 

The elasticity of rubbers is very different from that of materials such as metals or even glassy or semicrystalline polymers. Young s moduli for metals are typically of the order of 10 MPa (see table 6.1) and the maximum elastic extension is usually of order 1% for higher extensions fracture or permanent deformation occurs. The elastic restoring force in the metal is due to interatomic forces, which fall off extremely rapidly with distance, so that even moderate extension results in fracture or in the slipping of layers of atoms past each other, leading to non-elastic, i.e. non-recoverable, deformation. 

Carefully hanging a weight on the fully swollen elastic band causes elastic extension sufficient to support a light load. The elastic force, / within the band that supports the load is comprised of two components, an internal energy component,/b, and an entropy component,/s, that is. 

OuwELTjES on account of his researches on the elastic extension and the liquefaction temperature of gelatin gels as affected by added salts, discusses at length the hypothesis that the partition between the amorphous and the crystalline portions of the gel framework is shifted according to the lyotropic value of the salt. The phenomena to be explained are also consistent with the assumption that there is a corresponding shift either of the number or of the cohesive energies of the non crystalline junction points in the amorphous portion of the gel, or of both. We shall revert to these problems later. 

Most authors do not discriminate between Tr and but consider Tg as the freezing temperature of the rubbery state. This is not exact however, because there is a transition between the rubbery clastic and the rigid state, namely the highly elastic state (elastic extensibility between 1 and 100%. 

The data for a semicrystalline sample of polystyrene are also shown in the graph of Fig. 4.145. They show a much higher Ethan the rubbery plateau. Here the crystals form a dense network between the parts of the molecules that become liquid at the glass transition temperature. This network prohibits flow beyond the rubber elastic extension of the liquid parts of the molecules. Unimpeded flow is possible only after the crystals melt in the vicinity of 5(X) K. 

Kinetically one can compare the rubber elastic extension to the compression of a gas, as illustrated in Fig. 5.167. The thermodynamic equations reveal that reversible rabber contraction can just as well drive a heat pump as reversible gas expansion. Raising temperature, increases the pressure of a gas, analogously it takes a greater force to keep a rabber band extended at higher temperature. The two equations for this fact are known as the ideal gas law p = PoTV(/(ToV) with PoV/r = R, the gas... 

To change the rope balance a certain amount of oil must be transferred from one cylinder to the other. This can be estimated from the change in rope stretch caused by the change in load. For a typical six strand triangular rope of suitable size and weight, elastic extension would be calculated from ... 

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