# Prediction of primary normal stress difference from shear viscosity data using a single integral constitutive equation

@article{Wagner1977PredictionOP,
title={Prediction of primary normal stress difference from shear viscosity data using a single integral constitutive equation},
author={Manfred H. Wagner},
journal={Rheologica Acta},
year={1977},
volume={16},
pages={43-50}
}
• M. Wagner
• Published 1977
• Materials Science
• Rheologica Acta
SummaryBased on a single integral constitutive equation with a strain-dependent memory function, a relation between the primary normal stress functionθ and the shear viscosity functionη is proposed. According to this theory, the primary normal stress functionθ can be obtained from viscosity data by simple differentiation of the viscosity functionη with respect to the shear rate $$\dot \gamma$$ , and multiplication by a factor (−1/n). The material parametern is thereby associated with the strain… Expand
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• 1978
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• Rheologica Acta
• 2012
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#### References

SHOWING 1-10 OF 17 REFERENCES
Comparison of network theory predictions with stress/time data in shear and elongation for a low-density polyethylene melt
• Chemistry
• 1973
SummaryExperimental data are presented which show the variation with time of the shear stress and primary normal stress difference during shear flow with a stepfunction shear rate; the materialExpand
Analysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-density branched polyethylene melt
SummaryA single integral constitutive equation is presented, which gives a reasonable description of the non-linear shear and elongational behavior of a low-density branched polyethylene melt atExpand
Prediction of melt elasticity from viscosity data
• Materials Science
• 1974
A simple method for predicting the primary normal stress function, θ, from viscosity data is proposed. A relation between θ and the viscosity function, θ, based on the Goddard-Miller rheologicalExpand
Analysis of stress-growth data for simple extension of a low-density branched polyethylene melt
SummaryBased onLodge's theory of rubberlike liquids, a two-constants memory function is presented, which gives a qualitative description of the non-linear elongational behavior of a low-densityExpand
Rheological Properties of Three Solutions. Part I. Non‐Newtonian Viscosity, Normal Stresses, and Complex Viscosity
• Materials Science
• 1967
Non‐Newtonian viscosity and the primary normal stress difference in steady simple shear flow and the dynamic viscosity and dynamic storage modulus in oscillatory simple shear flow were measured forExpand
Time‐Dependent Stress in Polymer Melts and Review of Viscoelastic Theory
• Materials Science
• 1972
New rheogoniometer data for stress development after initiation of a steady shear are presented for three polymer melts: a low‐density polyethylene, a high‐density polyethylene, and a polystyrene.Expand
Modifications of the weissenberg rheogoniometer for measurement of transient rheological properties of molten polyethylene under shear. Comparison with tensile data
Improvements to the Weissenberg rheogoniometer are necessary in order to measure the transient rheological properties of polymer melts correctly. The improvements reported concern the mechanicalExpand
The Shearing Flows of the BKZ Fluid
• Materials Science
• 1974
Available experimental data of shearing flows are used to test the BKZ fluid model. The strain‐energy function is assumed in the form of U=M(s)g(I1, I2), where M(s) is obtained from theExpand
An inverse for the Jaumann derivative and some applications to the rheology of viscoelastic fluids
• Mathematics
• 1966
SummaryBy using a generalization of the matrizant of matrix calculus, it is shown how one can construct formally an inverse, or integral, for the well-knownJaumann derivative of continuum mechanics.Expand
Comparison of rubberlike-liquid theory with stress-growth data for elongation of a low-density branched polyethylene melt
• Materials Science
• 1972
SummaryThe non-linear behavior observed byMeissner can be qualitatively described by the rubberlike-liquid constitutive equations when the constants in the memory function are chosen to fit the dataExpand