Constitutive Model of a Transversely Isotropic Bingham Fluid

[+] Author and Article Information
D. N. Robinson

Department of Civil Engineering, University of Akron, Akron, OH 44325

K. J. Kim, J. L. White

Institute of Polymer Engineering, University of Akron, Akron, OH 44325

J. Appl. Mech 69(5), 641-648 (Aug 16, 2002) (8 pages) doi:10.1115/1.1483831 History: Received January 03, 2000; Revised December 14, 2001; Online August 16, 2002
Copyright © 2002 by ASME
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Chapman,  F. M., and Lee,  T. S., 1970, “Effect of Talc Filler on the Melt Rheology of Polypropylene,” SPE J., 26, pp. 37–40.
Vinogradov,  G. V., Malkin,  A. Y., Plotnikova,  E. P., Sabsai,  O. Y., and Nikolayeva,  N. E., 1972, “Viscoelastic Properties of Filled Polymers,” Int. J. Polym. Mat., 2, pp. 1–27.
Suetsugu,  Y., and White,  J. L., 1983, “The Influence of Particle Size and Surface Coating of Calcium Carbonate on the Rheological Properties of Its Suspensions in Molten Polystyrene,” J. Appl. Polym. Sci., 28, pp. 1481–1501.
Osanaiye,  G., Leonov,  A. I., and White,  J. L., 1993, “Investigations of the Rheological Behavior of Rubber Carbon-Black Compounds Over a Wide-Range of Stresses Including Very-Low Stresses,” J. Non-Newtonian Fluid Mech., 49, pp. 87–101.
Toki,  S., and White,  J. L., 1982, “Rheological and Solid Boundary Condition Characterization of Unvulcanized Elastomers and Their Compounds,” J. Appl. Polym. Sci., 27, pp. 3171–3184.
Montes,  S., and White,  J. L., 1982, “A Comparative Rheological Investigation of Natural and Systhetic Cis-1,4 Polyisoprenes and Their Carbon Black Compounds,” Rubber Chem. Technol., 55, pp. 1354–1369.
Kim,  K. J., and White,  J. L., 1999, “Rheological Investigations of Suspensions of Talc, Calcium Carbonate and Their Mixtures in a Polystyrene Melt,” Polym. Eng. Sci., 39, pp. 2189–2198.
Bingham, E. C., 1922, Fluidity and Plasticity, McGraw-Hill, New York.
Hohenemser,  K., and Prager,  W., 1932, “Über die ansätze der mechanik isotroper kontinua,” Z. Angew. Math. Mech., 12, pp. 216–226.
Oldroyd,  J. G., 1947, “A Rational Formulation of the Equations of Plastic Flow for a Bingham Solid,” Proc. Cambridge Philos. Soc., 43, pp. 100–105.
Prager, W., 1961, Introduction to Mechanics of Continua, Ginn and Co., Boston.
White,  J. L., 1979, “A Plastic-Viscoelastic Constitutive Equation to Represent the Rheological Behavior of Concentrated Suspensions of Small Particles in Polymer Melts,” J. Non-Newtonian Fluid Mech., 5, pp. 177–190.
White,  J. L., and Lobe,  V. M., 1982, “Comparison of the Prediction of Viscoelastic and Plastic-Viscoelastic Fluid Model to the Rheological Behavior of Polystyrene and Polystyrene-Carbon Black Compounds,” Rheol. Acta, 21, pp. 167–175.
Ericksen,  J. L., 1961, “Poiseuille Flow of Certain Anisotropic Fluids,” Arch. Ration. Mech. Anal., 8, pp. 1–8.
White,  J. L., and Suh,  C. H., 1997, “A Theory of Transversely Isotropic Plastic Viscoelastic Fluids to Represent the Flow of Talc and Similar Disc-Like Particle Suspensions in Thermoplastics,” J. Non-Newtonian Fluid Mech., 69, pp. 15–27.
Hill,  R., 1949, “A Theory of the Yielding and Plastic Flow of Anisotropic Metals,” Proc. R. Soc. London, Ser. A, A193, pp. 281–428.
Hill,  R., 1949, “The Theory of Plane Plastic Strain for Anisotropic Metals,” Proc. R. Soc. London, Ser. A, A193, pp. 428–437.
Hill, R., 1950, The Mathematical Theory of Plasticity, Oxford University Press, Oxford, UK.
White,  J. L., Kim,  K. J., and Robinson,  D. N., 1999, “Alternate Models for a Transversely Isotropic Plastic Viscoelastic Fluid,” J. Non-Newtonian Fluid Mech., 83, pp. 19–32.
Spencer, A. J. M., 1971, Continuum Physics, A. C. Eringen, ed., Academic Press, San Diego, CA.
Spencer, A. J. M., 1972, Deformations of Fiber-Reinforced Materials, Clarendon Press, Oxford, England.
Spencer, A. J. M., 1984, Continuum Theory of Fiber-Reinforced Composites, Springer-Verlag, New York.
Spencer,  A. J. M., 1992, “Plasticity Theory for Fiber-Reinforced Composites,” J. Eng. Math., 26, pp. 107–118.
Lance,  R. H., and Robinson,  D. N., 1971, “A Maximum Shear Stress Theory of Plastic Failure for Fiber-Reinforced Materials,” J. Mech. Phys. Solids, 19, pp. 49–60.
Robinson,  D. N., and Duffy,  S. F., 1990, “Continuum Deformation Theory for High Temperature Metallic Composites,” J. Eng. Mech., 116(4), pp. 832–844.
Poitou,  A., Chinesta,  F., and Bernier,  G., 2001, “Orienting Fibers by Extrusion in Reactive Powder Concrete,” J. Eng. Mech., 127(6), pp. 593–598.
Advani, S. G., 1994, Flow and Rheology in Polymer Composites Manufacturing, Elsevier Science, Amsterdam.
Robinson,  D. N., and Pastor,  M. S., 1992, “Limit Pressure of a Circumferentially Reinforced SiC/Ti Ring,” Composites Eng., 2(4), pp. 229–238.
von Mises,  R., 1928, “Mechanik der plastischen formänderung von kristallen,” Z. Angew. Math. Mech., 8, pp. 161–185.
Perzyna,  P., 1966, “Fundamental Problems in Viscoplasticity,” Adv. Appl. Mech., 9, pp. 243–377.
Drucker,  D. C., 1959, “A Definition of Stable Inelastic Material,” ASME J. Appl. Mech., 26, pp. 101–106.
Drucker, D. C., 1962, “Stress-Strain-Time Relations and Irreversible Thermodynamics,” Proc. of the International Symposium on Second Order Effects in Elasticity, Plasticity and Fluid Mechanics, Haifa, Pergamon, London, pp. 331–351.
Ziegler,  H., 1958, “An Attempt to Generalize Onsager’s Principle,” Z. Angew. Math. Phys., 9b, pp. 748–763.
Betten, J., 1981, “On the Representation of the Plastic Potential of Anisotropic Solids,” Plastic Behavior of Anisotropic Solids, Proc. CNRS Internat. Colloquium, J. P. Boehler, ed., Villard-de-Lans, Editions du Centre National de la Recherche Scientifique, pp. 213–228.
Robinson, D. N., Bininda, W. K., and Ruggles, M. B., 2001, “Creep of Polymer Matrix Composites (PMC), Norton/Bailey Creep Law for Transverse Isotropy,” submitted for publication.


Grahic Jump Location
“Natural” stress states
Grahic Jump Location
Combined shear stress (LS) and normal stress (TN)
Grahic Jump Location
Threshold curves in normalized σ/KL,τ/KL space. PS/TALC 40V%–0.474, Isotropic–0.577.
Grahic Jump Location
Family of curves Φ=const. (F=const.,μ̄=const.) for PS/Talc 40V%. Illustrates normality.
Grahic Jump Location
Fluid elements showing preferential and flow directions; (a) disk-like filler particles, (b) elongated fiber filler particles
Grahic Jump Location
Apparent viscosity (Pa-S) versus stress (Pa) for PS/TALC 20% (symbols). Correlation of shear flow (LS)–(solid curve). Prediction of elongational flow (TN)–(dashed curve).
Grahic Jump Location
Apparent viscosity (Pa-S) versus stress (Pa) for PS/TALC 40% (symbols). Correlation of shear flow (LS)–(solid curve). Prediction of elongational flow (TN)–(dashed curve).
Grahic Jump Location
Convex Ω=const. surfaces in σ , V space. Threshold surface F=0(μ̄=∞). Illustrates normality.




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