Some approximate equations useful in the phenomenological treatment of linear viscoelastic data

Ninomiya, Kazuhiko; Ferry, John D.

doi:10.1016/0095-8522(59)90067-4

Cited by 200 publications

(68 citation statements)

References 6 publications

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“…Nevertheless, the methods proposed by Schwarzl (1970) should be highlighted also since both interconversions can be achieved. More recently, other authors have proposed other methods (Emri and von Bernstorff 2005;Schapery 1999a, 1999b;Kulik et al 2009;Maheri and Adams 2002;Jahani and Nobari 2008;Chen 2000;Ninomiya and Ferry 1959;Fernández et al 2011;Schwarzl 1970;Sorvari and Malinen 2007). Nevertheless, that of Leblanc (2005) should be highlighted, as his work focuses on the employment of the Fourier transform but in order to investigate non-linear viscoelastic materials.…”

Section: Introductionmentioning

confidence: 99%

“…The advantage of this method is a direct employment of the fast Fourier transform (FFT) algorithm to experimental data, in opposition to other existing methods (Emri and von Bernstorff 2005;Schapery 1999a, 1999b;Kulik et al 2009;Maheri and Adams 2002;Jahani and Nobari 2008;Chen 2000;Ninomiya and Ferry 1959;Fernández et al 2011;Schwarzl 1970;Sorvari and Malinen 2007) based on fitting models or theoretical functions. Concretely, the proposed method is valuable when a Prony series cannot be properly fitted to the experimental data in time or frequency domains.…”

Section: Introductionmentioning

confidence: 99%

“…The most widely applied methods (Emri and von Bernstorff 2005) for material functions conversion from time to frequency domains are those based on Prony series (Chen 2000), and the opposed conversion can be achieved through the algorithms proposed by Ninomiya and Ferry (1959). The former can be obtained by fitting the experimental data by means of a generalized Maxwell model , whereas the latter is based on experimental data fitting.…”

Section: Introductionmentioning

confidence: 99%

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Relaxation modulus—complex modulus interconversion for linear viscoelastic materials

García-Barruetabeña

Cortés

Abete

et al. 2012

Mech Time-Depend Mater

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This paper is aimed at exploring the interconversion path between the relaxation modulus E(t) and the corresponding complex modulus E * (ω) for linear viscoelastic solid materials. In contrast to other approximate methods, the fast Fourier transform (FFT) algorithm is directly applied on the time-dependent part of the viscoelastic response R(t). Firstly, the method foundations are presented. Then, a theoretical example is performed by means of a generalized Maxwell model, where the influence of sampling conditions and eventual experimental error and data dispersion is analyzed. Finally, an application example using experimental data is carried out to assess the method. As a result, the proposed procedure allows obtaining the complex modulus by means of relaxation tests, and vice versa.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Relaxation modulus—complex modulus interconversion for linear viscoelastic materials

García-Barruetabeña

Cortés

Abete

et al. 2012

Mech Time-Depend Mater

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show abstract

“…Although the theoretical study of the different interconversion methods is welldocumented in the specialist literature (Tschoegl 1989;Emri et al 2005;Schapery 1999a, 1999b;Lakes and Wineman 2006;Tschoegl et al 2002;Sorvari and Malinen 2007;Shames and Cozzarelli 1997;Lakes 1998;Ninomiya and Ferry 1959), it is not easy to find experimental data to estimate the error made when used these methods. The aim of this work is, therefore, to obtain the experimental axial moduli in cases of relaxation (static and dynamic) and creep (static) for a linear viscoelastic material and to compare them with moduli deduced analytically from the interconversions.…”

Section: Introductionmentioning

confidence: 99%

“…For this reason, alternative methods of interconversion have been developed, such as application of the generalized methods of Maxwell and Kelvin, or even experimental interconversion meth-ods (Ninomiya and Ferry 1959). The scope or limitations of each method depend on the theoretical substrate and the assumptions and simplifications adopted in each case.…”

Section: Introductionmentioning

confidence: 99%

Study of the interconversion between viscoelastic behaviour functions of PMMA

Pelayo

Rodriguez

Lamela

et al. 2010

Mech Time-Depend Mater

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The use of polymers and polymer-based composites in mechanical, civil and electronic engineering has been growing owing to advances in the technology of materials. The different applications and working conditions of these materials require knowledge about their viscoelastic material functions: relaxation modulus, compliance, complex modulus, etc. Interconversion between these functions may be required for different reasons such as the impossibility of direct experimentation under certain excitation conditions. In this work, a DMA is used to calculate the experimental viscoelastic functions of a linear viscoelastic material (PMMA). The same functions are estimated by interconversion methods and compared with experimental ones. The results show that the interconversion functions fit properly the experimental functions.

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Propriétés de copolymères triséquencés poly(isoprène‐seq. méthacrylate d'alcoyle)

Pascault

Guyon

Essel

et al. 1978

Angew. Makromol. Chem.

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RESUME:Nous avons etudie des copolymbes triskquenc6.s de I'isoprhe et de differents mkthacrylates d'alcoyles. Les comportements viscotlastiques de ces 'matkriaux sont ceux des elastomtres thermoplastiques du type SBS. La valeur du facteur de perte (tg6) de la phase caoutchoutique depend du pourcentage de la phase plastique et du procedt de mise en oeuvre du film. Nous avons Cgalement ttudie I'influence de la nature de la sequence ester (methyl, ethyl, propyl, butyl, isobutyl et diphhyl) et montrer son interaction sur la morphologie des materiaux et leurs modes de relaxations. SUMMARY:Block copolymers with a central sequence of polyisoprene (12% of 1-4 structure) and poly(alky1-methacrylates) have been studied. The viscoelastic properties of these compounds are those of thermoplastic rubbers of the SBS type. The loss factor (tg6) of the rubbery phase changes with the ratio of plastic compound and with the processing of the films. We studied the influence of the ester sequences (methyl, ethyl, propyl, butyl, isobutyl and diphenyl methacrylates). We correlated the viscoelastic behaviour and relaxation processes of the materials with the nature of the sequence together with the morphology observed by electron microscopy.

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Some approximate equations useful in the phenomenological treatment of linear viscoelastic data

Cited by 200 publications

References 6 publications

Relaxation modulus—complex modulus interconversion for linear viscoelastic materials

Relaxation modulus—complex modulus interconversion for linear viscoelastic materials

Study of the interconversion between viscoelastic behaviour functions of PMMA

Propriétés de copolymères triséquencés poly(isoprène‐seq. méthacrylate d'alcoyle)

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