A constitutive theory is presented for a transversely isotropic, viscoplastic (Bingham) fluid. The theory accounts for threshold (yield) and viscous flow characteristics through inclusion of a potential function serving the dual role of a threshold function and a viscous flow potential. The arguments and form of the potential function derive from the theory of tensorial invariants. The model reduces to a transversely isotropic model of perfect plasticity in the limit of vanishing viscosity. In the limit of isotropy, it reduces to the Hohenemser-Prager generalization of Bingham’s model. A characterization procedure is prescribed based on correlation with experiments conducted under simple states of stress. Application is made to polymer melts filled with talc particles.
Issue Section:
Technical Papers
1.
Chapman
, F. M.
, and Lee
, T. S.
, 1970
, “Effect of Talc Filler on the Melt Rheology of Polypropylene
,” SPE J.
, 26
, pp. 37
–40
.2.
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
.3.
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
.4.
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
.5.
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
.6.
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
.7.
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
.8.
Bingham, E. C., 1922, Fluidity and Plasticity, McGraw-Hill, New York.
9.
Hohenemser
, K.
, and Prager
, W.
, 1932
, “U¨ber die ansa¨tze der mechanik isotroper kontinua
,” Z. Angew. Math. Mech.
, 12
, pp. 216
–226
.10.
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
.11.
Prager, W., 1961, Introduction to Mechanics of Continua, Ginn and Co., Boston.
12.
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
.13.
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
.14.
Ericksen
, J. L.
, 1961
, “Poiseuille Flow of Certain Anisotropic Fluids
,” Arch. Ration. Mech. Anal.
, 8
, pp. 1
–8
.15.
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
.16.
Hill
, R.
, 1949
, “A Theory of the Yielding and Plastic Flow of Anisotropic Metals
,” Proc. R. Soc. London, Ser. A
, A193
, pp. 281
–428
.17.
Hill
, R.
, 1949
, “The Theory of Plane Plastic Strain for Anisotropic Metals
,” Proc. R. Soc. London, Ser. A
, A193
, pp. 428
–437
.18.
Hill, R., 1950, The Mathematical Theory of Plasticity, Oxford University Press, Oxford, UK.
19.
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
.20.
Spencer, A. J. M., 1971, Continuum Physics, A. C. Eringen, ed., Academic Press, San Diego, CA.
21.
Spencer, A. J. M., 1972, Deformations of Fiber-Reinforced Materials, Clarendon Press, Oxford, England.
22.
Spencer, A. J. M., 1984, Continuum Theory of Fiber-Reinforced Composites, Springer-Verlag, New York.
23.
Spencer
, A. J. M.
, 1992
, “Plasticity Theory for Fiber-Reinforced Composites
,” J. Eng. Math.
, 26
, pp. 107
–118
.24.
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
.25.
Robinson
, D. N.
, and Duffy
, S. F.
, 1990
, “Continuum Deformation Theory for High Temperature Metallic Composites
,” J. Eng. Mech.
, 116
(4
), pp. 832
–844
.26.
Poitou
, A.
, Chinesta
, F.
, and Bernier
, G.
, 2001
, “Orienting Fibers by Extrusion in Reactive Powder Concrete
,” J. Eng. Mech.
, 127
(6
), pp. 593
–598
.27.
Advani, S. G., 1994, Flow and Rheology in Polymer Composites Manufacturing, Elsevier Science, Amsterdam.
28.
Robinson
, D. N.
, and Pastor
, M. S.
, 1992
, “Limit Pressure of a Circumferentially Reinforced SiC/Ti Ring
,” Composites Eng.
, 2
(4
), pp. 229
–238
.29.
von Mises
, R.
, 1928
, “Mechanik der plastischen forma¨nderung von kristallen
,” Z. Angew. Math. Mech.
, 8
, pp. 161
–185
.30.
Perzyna
, P.
, 1966
, “Fundamental Problems in Viscoplasticity
,” Adv. Appl. Mech.
, 9
, pp. 243
–377
.31.
Drucker
, D. C.
, 1959
, “A Definition of Stable Inelastic Material
,” ASME J. Appl. Mech.
, 26
, pp. 101
–106
.32.
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.
33.
Ziegler
, H.
, 1958
, “An Attempt to Generalize Onsager’s Principle
,” Z. Angew. Math. Phys.
, 9b
, pp. 748
–763
.34.
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.
35.
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.
Copyright © 2002
by ASME
You do not currently have access to this content.
