Elastic effect

As discussed above, polymer chains tend to be disentangled and oriented under shear. One important result of the disentanglement and molecular orientation under shear is the decrease of viscosity with increasing shear rate. However, the flow of polymers is not pure viscous flow, and it has elastic component since the change of chain conformations is not completely irreversible. Upon the release of the shear, the polymer chains tend to recoil and be pulled back by the restraining force. Such elastic response has significant effect on the fiber formation processes. 

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Common experimental evidence shows that the viscosity of polymers varies as they flow. Under certain conditions however, elastic effects in a polymeric flow can be neglected. In these situations the extra stress is again expressed, explicitly, in terms of the rate of deformation as... 

For nonnewtonian fluids, pressure readings with taps may also be low because of fluid-elasticity effects. This error can be largely eliminated by using flush-mounted diaphragms. 

The shock-induced micromechanical response of <100>-loaded single crystal copper is investigated [18] for values of (WohL) from 0 to 10. The latter value results in W 10 Wg at y = 0.01. No distinction is made between total and mobile dislocation densities. These calculations show that rapid dislocation multiplication behind the elastic shock front results in a decrease in longitudinal stress, which is communicated to the shock front by nonlinear elastic effects [pc,/po > V, (7.20)]. While this is an important result, later recovery experiments by Vorthman and Duvall [19] show that shock compression does not result in a significant increase in residual dislocation density in LiF. Hence, the micromechanical interpretation of precursor decay provided by Herrmann et al. [18] remains unresolved with existing recovery experiments. 

Such elastic effects are of great importance in polymer processing. They are dominant in determining die swell and calender swell via the phenomenon often... 

As demonstrated, Eq. (7) gives complete information on how the weight fraction influences the blend viscosity by taking into account the critical stress ratio A, the viscosity ratio 8, and a parameter K, which involves the influences of the phenomenological interface slip factor a or ao, the interlayer number m, and the d/Ro ratio. It was also assumed in introducing this function that (1) the TLCP phase is well dispersed, fibrillated, aligned, and just forms one interlayer (2) there is no elastic effect (3) there is no phase inversion of any kind (4) A < 1.0 and (5) a steady-state capillary flow under a constant pressure or a constant wall shear stress. 

Elastic modulus Up to the fracture stress, glass behaves, for most practical purposes, as an elastic solid at ordinary temperatures. Most silicate-based commercial glasses display an elastic modulus of about 70GNm", i.e. about 1/3 the value for steel. If stress is applied at temperatures near the annealing range, then delayed elastic effects will be observed and viscous flow may lead to permanent deformation. 

Because of the melt-elasticity effects of the material, it does not draw down in a simple proportional manner thus, the draw-down process is a source of errors in the profile. Errors are significantly reduced in a balanced situation such as circular extrudate. These errors must be corrected by modifying the die and takeoff equipment. 

Networks obtained by anionic end-linking processes are not necessarily free of defects 106). There are always some dangling chains — which do not contribute to the elasticity of the network — and the formation of loops and of double connections cannot be excluded either. The probability of occurrence, of such defects decreases as the concentration of the reaction medium increases. Conversely, when the concentration is very high the network may contain entrapped entanglements which act as additional crosslinks. It remains that, upon reaction, the linear precursor chains (which are characterized independently) become elastically effective network chains, even though their number may be slightly lower than expected because of the defects. 

Parameter k e is termed as the viscosity-to-elasticity ratio here, which labels the relative ratio of viscosity to elasticity. In the typical case of EHL, this value is strong enough to assure it pertinent to omit the elastic effect. But in the typical TFL case, its order of magnitude is close to one and the elasticity must be taken into account. 

The angular momentum conservation equation couples the viscous and the elastic effects. The angular profiles of the director and the effective viscosity data are computed for one set of material parameters based on published data in literature. The velocity profiles are also attained from the same dataset. The results show that the alignment of molecules has a strong influence on the lubrication properties. 

It is possible to calculate a number of different kinds of "effective" crosslink densities. Bauer et al have used a quantity they termed the "elastically effective crosslink density " (Cel) correlate cure with solvent resistance and other physical properties of coatings (7-10). The correlation was basically empirical. Formally, the is a calculation of the number of functional groups attached to the infinite network for which there are at least two other paths out to the network on the given polymer or crosslinker. Thus, chains with only one or two paths to the infinite network are excluded. The following expression can be written for... 

PRINT "THE OLD ELASTICALLY EFFECTIVE CROSSLINK DENSITY EXPRESSION OF BAUER" 150 PRINT "AND BUDDE. THE SECOND CALCULATES A CROSSLINK DENSITY WHICH IN" THEORY SHOULD BE PROPORTIONAL TO THE RUBBERY ELASTIC MODULUS."... 

PRINT "THE OLD ELASTICALLY EFFECTIVE CROSSLINK DENSITY - CEL 3330 PRINT... 

In this case, the crosslinking density is the sum of the effective crosslinking density and the secondary cyclization, since both crosslinkages are elastically effective. The calculation conditions are the same as Figure 1 except that the number of secondary cycles formed per effective crosslinkage T) is 20. 

For the elastically effective number of chain elements, taken as twice the number of closed circuits, we have... 

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. 

Efficiency of the cross-linking reaction can be defined as the ratio of effective cross-link density, px, to the theoretical cross-link density, p(. Theoretical cross-link density assumes that all of the cross-linker added to the formulation created elastically effective cross-links however, it cannot be defined for nonchemical methods. Thus the theoretical cross-link density, p is given as... 

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