An empirical constitutive equation of integral type for viscoelastic liquids

Steller, Ryszard

doi:10.1007/bf01332585

Cited by 4 publications

(6 citation statements)

References 21 publications

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“…Expressions (4a, b) differ from those originally published [16] in the assumption that Gy and 2 depend on the first invariant of the tensor product A = Ct-t 12t. It agrees with the principles of representation of symmetrical, isotropic tensor functions [28], since Ct -1 and 12t have been introduced into eq.…”

Section: Theoretical Considerationsmentioning

confidence: 93%

“…(5) are just the same as those from eq. (4) [16]. It has been found that they describe experimental data for many polymeric systems quite well [16].…”

Section: Correlations Between Materials Functionsmentioning

confidence: 96%

“…(4) [16]. It has been found that they describe experimental data for many polymeric systems quite well [16]. Although the material functions for simple and oscillatory shear flows, which follow from the constitutive eqs.…”

Section: Correlations Between Materials Functionsmentioning

confidence: 98%

“…Based on experimental data on stress relaxation in solid polymers, the following constitutive equation of the Oldroyd-Walters-Fredrickson (OWF) type has been derived [16]:…”

Section: Theoretical Considerationsmentioning

confidence: 99%

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A simple integral constitutive equation for polymeric liquids

Steller

1988

Rheol Acta

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An integral constitutive equation describing the strain history in terms of the Cauchy-Green and Finger tensors is presented. Its memory functions, which correspond to a flow-dependent continuous spectrum of relaxation times, depend on the invariants of the Cauchy-Green and Finger rate of strain tensors. Theoretical predictions resulting from this equation are compared with experimental data for some types of flow. Using the Laguerre polynomial expansion, the basic equation is generalized.

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Section: Theoretical Considerationsmentioning

confidence: 93%

“…(5) are just the same as those from eq. (4) [16]. It has been found that they describe experimental data for many polymeric systems quite well [16].…”

Section: Correlations Between Materials Functionsmentioning

confidence: 96%

Section: Correlations Between Materials Functionsmentioning

confidence: 98%

“…Based on experimental data on stress relaxation in solid polymers, the following constitutive equation of the Oldroyd-Walters-Fredrickson (OWF) type has been derived [16]:…”

Section: Theoretical Considerationsmentioning

confidence: 99%

See 2 more Smart Citations

A simple integral constitutive equation for polymeric liquids

Steller

1988

Rheol Acta

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“…polyisobutylene (PIB) solution at 0, 25 and 50°C (Schultheisz and Leigh 2002); polydimethylsiloxane (PDMS) at 0, 25 and 50°C (Schultheisz et al 2003); and high-density polyethylene (HDPE) and polypropylene (PP) melts at 200°C. The data for both melts were recalculated from quantitative material functions resulting from an integral constitutive equation, which was presented much earlier (Steller 1985).…”

Section: Introductionmentioning

confidence: 99%

Determination of the first normal stress difference from viscometric data for shear flows of polymer liquids

Steller

2016

Rheol Acta

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New equation for determination of the primary normal stress difference from viscosity curve is proposed, and the methods of calculations with the use of adequate viscosity models are discussed. Comparison of calculated and measured values of primary normal stress difference has shown that the proposed equation describes quite well experimental data but the calculations are not stable. For this reason, the proposed equation along with other equations of this type known from the literature was transformed into shear stress-dependent form. It was shown that such transformation makes it possible to represent the normal stress-to-shear stress ratio (Weissenberg number) as a unique function of the local slope of the flow curve, which is simultaneously temperature invariant. Such representation was confirmed using experimental data for eight systems comprising linear polymers and various measurement temperatures. It was found that new equation in the shear stress-dependent form is numerically stable and provides excellent description of experimental data. The general structure of expressions, which may be used for description of the elasticity of polymer liquids based on the flow curve shape, was discussed from the point of view of dimensional analysis. Obtained results made it possible to modify other expressions known from the literature in such way that they also provide an excellent fit to experimental data.

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Structure development in melt spinning of poly(ethylene‐co‐octene) filaments with various comonomer contents

Shan

White

2004

J of Applied Polymer Sci

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An experimental study of the spinnability and the variation in crystallinity and orientation of melt spinning of poly(ethylene-co-octene) with different contents of comonomers was carried out. The spinning behavior of these polymers was investigated under different drawdown ratios and temperatures and correlated to spinline stress. The melt-spun filaments were characterized by wideangle X-ray diffraction birefringence, and differential scanning calorimetry. S-1 is a high-density polyethylene and S-2, S-3, and S-4 have 16, 22, and 38 wt % octene. An orthorhombic unit cell was found in all four polymers, but a dominant hexagonal structure (perhaps mesophase) was found for the highest octene level (S-4). The orientation factors for the a-, b-, and c-axis of the orthorhombic crystal structure and a-axis of the hexagonal phase were then calculated. The crystalline orientation behavior of the lower octene copolymers (S-1, S-2, and S-3) are similar and can be represented as a "rownucleated" structure. However, the orientation behavior of S-4 was different. The uniaxial mechanical properties were also measured. The Young's modulus and tensile strength generally increased with birefringence for all polymers. With increasing content of octene, the Young's modulus showed a decrease from semicrystalline thermoplastic toward an elastomer.

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An empirical constitutive equation of integral type for viscoelastic liquids

Cited by 4 publications

References 21 publications

A simple integral constitutive equation for polymeric liquids

A simple integral constitutive equation for polymeric liquids

Determination of the first normal stress difference from viscometric data for shear flows of polymer liquids

Structure development in melt spinning of poly(ethylene‐co‐octene) filaments with various comonomer contents

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