Correlation of large longitudinal deformations with different strain histories

Zapas, L. J.; Craft, T.

doi:10.6028/jres.069a.058

Cited by 91 publications

(26 citation statements)

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“…As indicated by the asymptotic results, the fit to stress growth and strain recovery changes, as 7' changes, less for shear than for elongation and in shear is generally as good without as with the modified nonequilibrium potential; see figs. [8][9][10]. Thus the Leonov model can quantitatively match both elongationäl and shear data for Melt I nearly as well as the Wagner model, if 0~ is taken to be an empirical function of elastic strain.…”

Section: Results and Diseussionmentioning

confidence: 78%

Elongational-flow predictions of the Leonov constitutive equation

Larson¹

1983

Rheol Acta

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Abstract:The basic thermodynamic ideas from rubber-elasticity theory which Leonov employed to derive his constitutive model are herein summarized. Predictions of the single-mode version are presented for homogeneous elongational flows including stress growth following start-up of steady flow, stress decay following sudden stretching and following cessation of steady flow, elastic recovery following cessation of steady flow, energy storage in steady-stäte flow, and the velocity profile in constantforce spinning. Using parameters of the multiple-mode version which fit the linearviscoelastic data, the Leonov-model predictions of elongational stress growth during, and elastic recovery following, steady elongation are calculated numerically and compared to the experimental results for Melt I and to the Wagner model. It is found that the Leonov model, as originally formulated, agrees qualitatively with the data, but not quantitatively; the Wagner model gives quantitative agreement, but requires much nonlinear data with whieh to fit model parameters. Quantitative agreement can be obtained with the Leonov model, if the nonequilibrium potential which relates recoverable strain to strain rate is adjusted empirically. This can most simply be done by making each relaxation time dependent upon the reeoverable strain. The Leonov model, unlike the Wagner model, is derived from an entropic constitutive equation, which is advantageous for calculating stored elastic energy or viscous dissipation. The Leonov model also has an appealingly simple differential form, similar to the upperconvected Maxwell model, which, in numerical calculations, may be an important advantage over the integral Wagner model. Key words:Leonov constitutive model, Wagner model, elongational flow, nonequilibrium potential, Melt I IntroduetionOflate, the emphasis in the development of constitutive equations for polymeric liquids has been on singleintegral strain equations, particularly those whose kernel is separable into a product of a tensor strain-history measure and a strictly time-dependent scalar memory function. The Wagner model [1][2], which is an example of this class of constitutive equations, has been particularly successful at predicting the viscoelastic response of one particular low-density polyethylene melt [3][4][5][6]. While the class of single-integral models has a theoretical basis in continuum mechanics [7] and is general enough to be consistent with all but the most stringent of rheological tests [3-6, 8, 9], such equations can be difficult to handle numerically, particularly with respect to boundary conditions, and considerable linear (small-deformation) and nonlinear (large-deformation) measurements must ordinarily be made to fully specify them. Basis of the Leonov ModelLeonov arrived at his constitutive equation for incompressible concentrated polymeric systems by

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Section: Results and Diseussionmentioning

confidence: 78%

Elongational-flow predictions of the Leonov constitutive equation

Larson¹

1983

Rheol Acta

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“…40 The nonlinear viscoelastic modulus G(c,t À t 0 ) can be divided into a linear viscoelatic modulus G(t À t 0 ) and a straindependent function as given as,…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Investigation and prediction on the nonlinear viscoelastic behaviors of nylon1212 toughened with elastomer

Wang

Cao

et al. 2011

J of Applied Polymer Sci

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Studies on the nonlinear viscoelastic behaviors of nylon1212 toughened with styrene-[ethylene-(ethylene-propylene)]-styrene block copolymer (SEEPS) were carried out. The linear relaxation curves at relatively low shear strains show good overlap, the relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model. The nonlinear relaxation curves of nylon1212 blends at different shear strains have been obtained and their damping functions were evaluated. Meanwhile, it is found that most blends in the experimental windows follow the strain-time separation principle and Laun double exponential model can predict damping curves well. The successive start-up of shear behavior was investigated. The results showed that Wagner model, derived from the K-BKZ (Kearsley-Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data of nylon 1212 blend with 10 wt % SEEPS well, but there exists some deviation for experiment data of nylon1212 blends with high SEEPS concentrations.

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“…In a recent pa per [1],1 excelle nt agree me nt was shown be twee n expe rime ntal res ults a nd pre di ction s of the BKZ elastic fluid theory [2]. This theory involves a pote ntial fun ction, U, but leaves it unspecified .…”

Section: Introductionmentioning

confidence: 99%

“…Encouraged by th ese results [1], I con stru cted a form of U with whi c h the BKZ elas ti c fluid theor y could quantitatively describe biaxial strain at large deforma tion, biaxial cree p, and simple exte nsion of vulcanized rubbers. This form of U involv es three material prop erties .…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic behavior under large deformations

Zapas¹

1966

J. RES. NATL. BUR. STAN. SECT. A.

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The BKZ elas ti c Auid th eo ry is used to correlate experim ental res ults obtained in biaxial strain and steady simple s hea r. With a he uri sti c potenti a l fun cti on involving three material properti es, excell ent agree ment is obtained betw ee n theory and experiment. In the spec ial case whe re on e of the mate rial prope rti es is domin ant , th e be havi or in ste ady simple shear is cal culated from dynami c meas ure me nts in th e infinites imal range and is compared with ac tual data.

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Correlation of large longitudinal deformations with different strain histories

Cited by 91 publications

References 1 publication

Elongational-flow predictions of the Leonov constitutive equation

Elongational-flow predictions of the Leonov constitutive equation

Investigation and prediction on the nonlinear viscoelastic behaviors of nylon1212 toughened with elastomer

Viscoelastic behavior under large deformations

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