Linear viscoelastic model for elongational viscosity by control theory |
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Authors: | Tommi Borg Esko J Pääkkönen |
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Institution: | 1.TomCoat Oy,Evij?rvi,Finland;2.Laboratory of Plastics and Elastomer Technology,Tampere University of Technology,Tampere,Finland |
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Abstract: | Flows involving different types of chain branches have been modelled as functions of the uniaxial elongation using the recently
generated constitutive model and molecular dynamics for linear viscoelasticity of polymers. Previously control theory was
applied to model the relationship between the relaxation modulus, dynamic and shear viscosity, transient flow effects, power
law and Cox–Merz rule related to the molecular weight distribution (MWD) by melt calibration. Temperature dependences and
dimensions of statistical chain tubes were also modelled. The present study investigated the elongational viscosity. We introduced
earlier the rheologically effective distribution (RED), which relates very accurately and linearly to the viscoelastic properties.
The newly introduced effective strain-hardening distribution (REDH) is related to long-chain branching. This REDH is converted to real long-chain branching distribution by melt calibration and a simple relation formula. The presented procedure
is very effective at characterizing long-chain branches, and also provides information on their structure and distribution.
Accurate simulations of the elongational viscosities of low-density polyethylene, linear low-density polyethylene and polypropylene,
and new types of MWDs are presented. Models are presented for strain-hardening that includes the monotonic increase and overshoot
effects. Since the correct behaviour at large Hencky strains is still unclear, these theoretical models may aid further research
and measurements. |
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