Modeling nonlinear rheology of unentangled polymer melts based on a single integral constitutive equation

2020 ◽  
Vol 64 (1) ◽  
pp. 129-140 ◽  
Author(s):  
Esmaeil Narimissa ◽  
Manfred H. Wagner
Keyword(s):  
Constitutive Equation ◽  
Polymer Melts ◽  
Nonlinear Rheology ◽  
Single Integral ◽  
Integral Constitutive Equation

A Single‐Integral Constitutive Equation

1969 ◽  
Vol 13 (1) ◽  
pp. 103-109 ◽  
Author(s):  
Alden H. Emery ◽  
Michael L. White
Keyword(s):  
Constitutive Equation ◽  
Single Integral ◽  
Integral Constitutive Equation

Bulge initiation in tubes of time-dependent materials

2015 ◽  
Vol 22 (4) ◽  
pp. 636-648 ◽  
Author(s):  
Alan S Wineman
Keyword(s):  
Constitutive Equation ◽  
Linear Viscoelasticity ◽  
Time Dependent ◽  
Branching Time ◽  
Deformation History ◽  
Thermally Induced ◽  
Relaxation Effects ◽  
Non Linear ◽  
Single Integral ◽  
Integral Constitutive Equation

This work considers the inflation and extension of an elastomeric tubular membrane when its material exhibits a time-dependent response. Three different models for time-dependent response are considered: finite linear viscoelasticity, Pipkin–Rogers non-linear viscoelasticity, and thermally induced chemorheological degradation. The first two are based on different assumptions about stress relaxation effects while the third accounts for time-dependent microstructural changes due to simultaneous scission and re-cross-linking of macromolecular network junctions. Each of these models describes a material response that softens with time. It is shown that the constitutive equations for all three models are included in a general non-linear single-integral constitutive equation. In previous work, for elastic membranes, the material is fixed and a localized bulge may form as the load increases. In this work, the load is specified, and a localized bulge may form as the membrane material undergoes a time-dependent response. It is assumed that the extension and inflation histories are initially uniform, but there may be a time when a localized bulge-like deformation starts to form. This is treated as branching from the uniform extension and inflation history. For times beyond this ‘branching time’, the governing equations are satisfied by both the continuation of the initial uniform deformation history and the branched deformation history for the bulge. A unified condition for determining this branching time, applicable to all three models, is derived in terms of the general non-linear single-integral constitutive equation. Post-branching response is not considered here.

Viscosity Models Based on Network Theory for Polymer Melts

2010 ◽  
Vol 129-131 ◽  
pp. 1244-1247
Author(s):  
Hai Hang Xu ◽  
Lei Zhong
Keyword(s):  
Experimental Data ◽  
Kinetic Equation ◽  
Constitutive Equation ◽  
Polymer Composites ◽  
Network Theory ◽  
Polymer Melts ◽  
Structure Parameter ◽  
Viscosity Models ◽  
Model Predictions ◽  
Good Agreement

New shear and extensional viscosity models based on Fredrickson kinetic equation coupled with Dewitt constitutive equation were established to predict viscosities of polymer melts. The experimental data of 125°C LDPE and LDPE filled with 35% glass beads reported from references were compared with the model predictions. The predictions showed good agreement with the measurements. The models are simple and easy to use. Because they contain no structure parameter, they are capable to describe the viscosities of pure polymer and polymer composites.

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