Abstract
A viscoelastic plastic model for suspension of small particles in polymer melts has been developed. In this model, the total stress is assumed to be the sum of stress in the polymer matrix and the filler network. A nonlinear viscoelastic model along with a yield criterion were used to represent the stresses in the polymer matrix and the filler network, respectively. The yield function is defined in terms of differential equations with an internal parameter. The internal parameter models the evolution of structure changes during floc rupture and restoration. The theoretical results were obtained for steady and oscillatory shear flow and compared with experimental data for particle filled thermoplastic melt. The experimental data included the steady state shear strress over a wide range of shear rates, the transient stress in a start up shear flow, stress relaxation after cessation of a steady state shear flow, the step shear and the oscillatory shear flow at various amplitudes.
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References
Bingham EC (1922) Fluidity and Plasticity. McGraw Hill Book Company, New York, NY
Cheng DC-H, Evans F (1965) Phenomenological Characterization of the Rheological Behavior of Inelastic Reversible Thixotropic and Antithixotropic Fluids. Br J App Phys 16:1599–1617
Cheng DC-H (1966) Cone and Plate Viscometry: Explicit Formulae for Shear Stress and Shear Rate and the Determination of Inelastic Thixotropic Properties. Br J Appl Phys 17:253–263
Cheng DC-H (1973) A Differential Form of Constitutive Relation for Thixotropy. Rheol Acta 12:228–233
Cheng DC-H (1986) Yield Stress: A Time Dependent Property and How to Measure It. Rheol Acta 25:542–554
Coussot P, Leonov AI, Piau JM (1993) Rheology of Concentrated Dispersed System in a Low Molecular Weight Matrix. J Non-Newt Fluid Mech 46:179–217
Dee Kee D, Kaloni (1986) Recent Developments in Structured Continua. Longman Science & Technical
Doraiswamy D, Mujumdar AN, Tsao I, Beris AN, Danforth SC, Metzner AB (1991) The Cox-Merz Rule Extended: a Rheological Model for Concentrated Suspensions and Other Materials With a Yield Stress. J Rheol 35:647–685
Fan X (1991) Rheological Properties and Model for Particle Filled Polymer Melts. A Dissertation Presented to the Graduate Faculty of the University of Akron
Giacomin AJ, Jeyaseelan RS, Samurkas T, Dealy JM (1993) Validity of Separable BKZ model for Large Amplitude Oscillatory Shear. J Rheol 37 (5):811–826
Harris J (1967) A Continuum Theory of Time Dependent Inelastic Flow. Rheol Acta 6:6–12
Hutton JF (1975) On Using the Weissenberg Rheogoniometer to Measure Normal Stresses in Lubricating Greases as Examples of Materials Which Have a Yield Stress. Rheol Acta 14:979–992
Isayev AI, Yanovsky Yu G, Vinogradov GV, Gordievsky LJ (1970) Mechanical parameters of dispersed systems under cyclic deformation with various amplitude. J Eng Phys 18:675–678
Isayev AI, Zolotarev VA, Vinogradov GV (1975) Viscoelastic properties of bitumens in continuous and cyclic deformation. Rheol Acta 14:135–144
Isayev AI, Hieber CA (1982) Oscillatory Shear Flow of Polymeric Systems. J Polym Sci 20:423–440
Isayev AI, Fan X (1990) Viscoelastic Plastic Constitutive Equation for Flow of Particle Filled Polymers. J Rheol 34:35–54
Isayev AI, Fan X (1994) Steady and Oscillatory Flows of Silicon-Polypropylene Ceramic Compound. J Mater Sci 29:2931–2938
Kamal MR, Mutel A (1985) Rheological Properties of Suspensions in Newtonian and Non-Newtonian Fluids. J Polym Sci No 4:293–382
Kemblowski Z, Perera J (1979) Rheological Characterization of Thixotropic Fluids. Rheol Acta 18:702–710
Kemblowski Z, Perera J (1980) A Generalized Rheological Model of Thixotropic Materials. Rheol Acta 19:529–538
Leonov AI (1976) Nonequilibrium Thermodynamics and Rheology of Viscoelastic Polymer Media. Rheol Acta 15:85–98
Leonov AI, Lipkina EH, Paskhin ED, Prokunin AN (1976) Theoretical and Experimental Investigations of Shearing in Elastic Polymer Liquids. Rheol Acta 15:411–426
Leonov AI (1990) On the Rheology of Filled Polymers. J Rheol 34:1039–1068
Metzner AB (1985) Rheology of Suspensions in Polymeric Liquids. J Rheol 29 (6):739–775
Mewis J (1979) Thixotropy — A General Review. J Non-Newtonian Fluid Mech 6:120
Montes S, White JL (1993) Rheological Models of Rubber-Carbon Black Compounds: Low Interaction Viscoelastic Models and High Interaction ThixotropicPlastic-Viscoelastic Models. J Non-Newton Fluid Mech 49:277–298
Philippoff W (1966) Vibrational measurements with large amplitudes. Trans Soc Rheol 10:317–334
Prager W, Hohenemser K (1932) Über die Ansatze der Mechanik der Continua. Zeitschrift für Angewandte Mathematik und Mechanik 12:216
Schwedoff T (1900) Recherches Experimentales Sur la Cohesion des Liquids. Congres de Physique 1:478
Simhambhatla M, Leonov AI (1995) On the Rheological Modeling of Viscoelastic Polymer Liquids with Stable Constitutive Equations. Rheol Acta 34:259–273
Simhambhatla A (1994) The Rheological Modeling of Simple Flows of Unfilled and Filled Polymers. Ph D Dissertation, The University of Akron
Slibar A, Parsley PR (1959) Retarded Flow of Bingham Materials. J Appl Mech 29:107–113
Slibar A, Parsley PR (1962) On the Analytical Description of Flow of Thixotropy Materials. Proc Intern Symp on Second Order Effects in Elasticity, Plasticity and Fluid Dynamics, Haifa, pp 314–330
Suetsugu Y, White JL (1984) A Theory of Thixotropic Plastic Viscoelastic Fluids With Time Dependent Yield Surface and Its Comparison to Transient and Steady State Experiments on Small Particle Filled Polymer Melts. J Non-Newton Fluid Mech 14:121–140
Treloar L (1975) Physics of Rubber Elasticity, 3rd ed. Oxford University Press, Oxford
Upadhyay RK, Isayev AI, Shen SF (1981) Transient Shear Flow Behavior of Polymeric Fluids According To the Leonov Model. Rheol Acta 20:443–457
Vinogradov GV, Yanovsky Yu G, Isayev AI (1970) Viscoelastic Behavior of an Amorphous Polymer under Oscillations of Large Amplitude. J Polym Sci A 8:1239–1259
Vinogradov GV, Yanovsky Yu G, Isayev AI, Shatalov VP, Shalganova VG (1971) Influence of Vibrations on the Viscoelastic Behavior of Monodisperse Polybutadienes. Intern J Polym Mater 1:17–30
Vinogradov GV, Isayev AI, Zolotarev VA, Verebskaya EA (1977) Rheological Properties of Road Bitumens. Rheol Acta 16:266–281
White JL (1979) A Plastic-Viscoelastic Constitutive Equation To Represent the Rheological Behavior of Concentrated Suspensions of Small Particle in Polymer Melts. J Non-Newt Fluid Mech 5:177–190
White JL (1981) Approximate Constitutive Equations for Slow Flow of Rigid Plastic Viscoelastic Fluids. J Non-Newt Fluid Mech 8:195–202
White JL, Lobe VM (1982) Comparison of the Predictions of Viscoelastic and Plastic-Viscoelastic Fluid Model to the Rheological Behavior of Polystyrene and Polystyrene-Carbon Black Compounds. Rheol Acta 21:167–175
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Sobhanie, M., Isayev, A.I. & Fan, Y. Viscoelastic plastic rheological model for particle filled polymer melts. Rheol Acta 36, 66–81 (1997). https://doi.org/10.1007/BF00366725
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DOI: https://doi.org/10.1007/BF00366725