Shear pliability

FIGURE 2 Dependence of equilibrium shear pliability on temperature (a) dependence of front-factor on n / (b). 

Operator in glassy and hyperelastic states of cross-linked polymers is equal to from 0 to 1, respectively, and in transition region between these conditions from 0 to 1. Therefore Equations (1) and (2) reproduce change of concerned cross-linked polymers hyperelastic properties in all their physical states in hyperelastic, where is being momentary a-process, shear pliability s relaxation operator is equal to equilibrium shear pliability in glassy, where is only local conformational mobility of polymeric mesh s cross-site chains, shear phabihty s relaxation operator is equal to shear pliability of glassy state in transition region between these states, where both... 

From Equation (7) follows conclusion about the same relaxation spectrum for strain electromagnetic susceptibility and shear pliability. This means that deOied cooperative mobility of polymer meshe s points a-relaxation times spectrum reproduces both strain and electromagnetic response of cross-linked polymer system to external mechanical force. It should be noted that as well as shear pUability s relaxation operator, strain electromagnetic susceptibility s relaxation operator generalizes in it is record all physical states of cross-linked polymers. 

Equilibrium shear pliability of cross-linked polymers with spatially homogeneous topological structure is inversely proportional to absolute temperature T (K) [2]... 

Parameters of a-relaxation times spectrum were determined using the least-squares method by isothermal creep s and photocieep curves that were obtained for several temperamres in glass transition regioa Experimentally was proved, that relaxation spectrum for shear pliability and strain electromagnetic susceptibility is identical. More one evidence of shear pliability s and strain electromagnetic susceptibility s spectrums coincidence may be slight discrepancy not more than 10% of photocreep s values, converted to mechanical scale (with use of relaxation spectmm s parameters defined by creep s curves) by dependence from the real experimental values. 

Presented in this chapter, mathematical description of interconnected cross-linked polymers viscoelastic and electromagnetic properties was developed on the base of common heredity s theory. In the main new and key moment was momentary components of shear pliability and strain electromagnetic susceptibility modeling with the... 

So as strain electromagnetic susceptibility s and shear pliability s relaxation spectmms coincide [1,2], theoretical account of o-ielaxation times at specified temperature was made with the use of temperature function [2], In the capacity of a-mode width s value analog [3] was taken 0.5. 

For description strain electromagnetic aiusotropy of densely polymer meshes in all their physical states include strain electromagnetic susceptibility relaxation operators C (MPa ), electromagnetic susceptibility elastic and shear pliability J(MPa ) coef- cients and consider that they are interconnected as appropriate equihbrium properties in Equation (3)... 

Then, in concordance with Equation (5), shear pliability and strain electromagnetic susceptibility relaxational spectrums are identical. In conclusion of mathematical model s account it should be noted that operator C in it is record deOies strain electromagnetic susceptibility in every physical state of densely cross-linked polymers, so as operator / [4],... 

It was supposed that experimental restored relaxation spectrams of strain electromagnetic susceptibility and shear pliability operators are identical. Additional argument for equality of strain electromagnetic susceptibility and shear pliability relaxation spectrums was exact coincidence in practice of photocreep curves, converted according to the equation in mechanical scale and experimental received creep curves (difference between calculated and experimental points was not more than 10%). 

As long as, contribution of equilibrium volumetric pliability strain tensor is negligibly small for cross-linked polymers consider shear pliability [1]. 

In Equation (1) J = relaxation operator of shear pliability, MPa % = tensor of shear tension, MPa = equilibrium volumetric pliability, MPa" P = pressure, MPa = Krokener s symbol. 

Model constants were found by the results of solid expansion and mechanical researches on installation [4] (measuring error was less than 3%). In Drst case models were chilled from 150 to 25°C with ratio 0.4°C/mim Relaxation operator of shear pliability was determined by Equation (1) on the base of experimental meastrred deformation of model and known value of applied mechanical tension. For exception of thermal prehistory inOtence on properties of experimental objects before each test models were heated to 150°C, were kept at that temperatirre 3 hr and chilled with ratio 0.2°C/min to temperature 25°C. 

FIGURE 2 Temperature dependence of the equilibrium shear pliability (a) Front factor s dependence of y (b). 

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