ISSN:
1435-1528
Keywords:
Mirror relation
;
nonlinear viscoelasticity
;
polyethylene
;
polypropylene
;
first normal-stress difference
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
,
Physics
Notes:
Abstract An attempt is made to incorporate into a quasilinear viscoelastic constitutive equation of the Boltzmann superposition type the two mirror relations of Gleissle, as well as his relation between the steady-state first normal-stress difference and the shear viscosity curve. It is shown that the three relations can hold separately within this constitutive model, but not simultaneously, because they require a different nonlinear strain measure, namelyS 12 (γ) =γ − a (γ − 1) (a = 0 forγ ≦ 1,a = 1 forγ ≧ 1) for the mirroring of the viscosities,S 12 (γ) =γ − a (γ−k 2/γ) (a = 0 forγ ≦k, a = 1 forγ ≧k) for the mirroring of the first normal-stress coefficients, and $$S_{12} (\gamma ) = \frac{1}{2}\gamma \{ 1 - erf [ln (\gamma /2 \sqrt k )/\sqrt {2 ln k} ]\}$$ for the third relation. Hereγ denotes the shear strain and erf the error function. Experimental data on melts of a low-density polyethylene, a high-density polyethylene and a polypropylene show that the mirror relations are passable approximations, but that the third relation meets reality surprisingly close if the right value ofk is used.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01333243
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