A rheological model for a short fiber suspension in polymeric liquid is proposed according to irreversible thermodynamics of viscoelastic deformation of polymers with the effect of fiber orientation taken into account. In this model, the evolution of elastic deformation tensor, namely, reversible Finger strain tensor, is governed by not only the reversible Finger strain tensor but also the fiber orientation tensor in a manner of a positive entropy production. The final form of stress tensor combines the viscoelasticity of polymeric matrix of the Leonov model and the fiber contribution of the Dinh–Armstrong model. The Folgar–Tucker model is employed for fiber orientation kinematics along with an invariant-based optimal fitting closure approximation. The rheological behavior of the model is comprehensively studied using steady and transient shear flows.
REFERENCES
1.
Advani
, S. G.
, Flow and Rheology in Polymer Composites Manufacturing
(Elsevier Science
, Amsterdam
, 1994
).2.
Advani
, S. G.
, and C. L.
Tucker
, “The use of tensors to describe and predict fiber orientation in short fiber composites
,” J. Rheol.
31
, 751
–784
(1987
).3.
Ait-Kadi
, A.
, and M.
Grmela
, “Modelling the rheological behavior of fibre suspensions in viscoelastic media
,” J. Non-Newtonian Fluid Mech.
53
, 65
–81
(1994
).4.
Azaiez
, J.
, “Constitutive equations for fiber suspensions in viscoelastic media
,” J. Non-Newtonian Fluid Mech.
66
, 35
–54
(1996
).5.
Batchelor
, G. K.
, “The stress system in a suspension of force-free particles
,” J. Fluid Mech.
41
, 545
–570
(1970
).6.
Batchelor
, G. K.
, “The stress generated in a non-dilute suspension of elongated particles by pure straining motion
,” J. Fluid Mech.
46
, 813
–829
(1971
).7.
Beris
, A. N.
, and B. J.
Edwards
, Thermodynamics of Flowing Systems with Internal Microstructure
(Oxford University Press
, New York
, 1994
).8.
Bird
, R. B.
, P. J.
Dotson
, and N. L.
Johnson
, “Polymer solution rheology based on a finitely extensible bead-spring chain model
,” J. Non-Newtonian Fluid Mech.
7
, 213
–235
(1980
).9.
Chan
, Y.
, J. L.
White
, and Y.
Oyanagi
, “A fundamental study of rheological properties of glass-fiber-reinforced polyethylene and polystyrene melts
,” J. Rheol.
22
, 507
–524
(1978
).10.
Christensen
, R. M.
, Theory of Viscoelasticity: An Introduction
(Academic Press
, New York
, 1982
).11.
Chung
, D. H.
, and T. H.
Kwon
, “Improved model of orthotropic closure approximation for flow induced fiber orientation
,” Polym. Compos.
22
, 636
–649
(2001
).12.
Chung
, D. H.
, and T. H.
Kwon
, “Invariant-based optimal fitting closure approximation for the numerical prediction of flow-induced fiber orientation
,” J. Rheol.
46
, 169
–194
(2002
).13.
Chung
, S. T.
, and T. H.
Kwon
, “Numerical simulation of fiber orientation in injection molding of short-fiber-reinforced thermoplastics
,” Polym. Eng. Sci.
35
, 604
–618
(1995
).14.
Cintra
, J. S.
, and C. L.
Tucker
, “Orthotropic closure approximations for flow-induced fiber orientation
,” J. Rheol.
39
, 1095
–1122
(1995
).15.
Dinh
, S. M.
, and R. C.
Armstrong
, “A rheological equation of state for semiconcentrated fiber suspensions
,” J. Rheol.
28
, 207
–227
(1984
).16.
Eberle
, A. P. R.
, D. G.
Baird
, and P.
Wapperom
, “Rheology of non-Newtonian fluids containing glass fibers: A review of experimental literature
,” Ind. Eng. Chem. Res.
47
, 3470
–3488
(2008
).17.
Eberle
, A. P. R.
, D. G.
Baird
, P.
Wapperom
, and G. M.
Vélez-García
, “Using transient shear rheology to determine material parameters in fiber suspension theory
,” J. Rheol.
53
(3
), 685
–705
(2009
).18.
Eberle
, A. P. R.
, G. M.
Vélez-García
, D. G.
Baird
, and P.
Wapperom
, “Fiber orientation kinetics of a concentrated short glass fiber suspension in startup of simple shear flow
,” J. Non-Newtonian Fluid Mech.
165
, 110
–119
(2010
).19.
Eslami
, H.
, M.
Grmela
, and M.
Bousmina
, “A mesoscopic rheological model of polymer/layered silicate nanocomposites
,” J. Rheol.
51
(6
), 1189
–1222
(2007
).20.
Eslami
, H.
, M.
Grmela
, and M.
Bousmina
, “A mesoscopic tube model of polymer/layered silicate nanocomposites
,” Rheol. Acta
48
, 317
–331
(2009
).21.
Folgar
, F.
, and C. L.
Tucker
, “Orientation behavior of fibers in concentrated suspensions
,” J. Reinf. Plast. Compos.
3
, 98
–119
(1984
).22.
Guo
, R.
, J.
Azaiez
, and C.
Bellehumeur
, “Rheology of fiber filled polymer melts: Role of fiber-fiber interactions and polymer-fiber coupling
,” Polym. Eng. Sci.
45
, 385
–399
(2005
).23.
Huq
, A. M. A.
, and J.
Azaiez
, “Modeling of fiber-polymer coupling for suspensions of mono-modal fibers
,” Polym. Compos.
27
, 82
–91
(2006
).24.
Hyunh
, H. M.
, “Improved fiber orientation predictions for injection-molded composites
,” M.S. thesis, University of Illinois at Urbana-Champaign
, 2001
.25.
Jack
, D. A.
, B.
Schache
and D. E.
Smith
“Neural network-based closure for modeling short-fiber suspensions
,” Polym. Compos.
31
, 1125
–1141
(2009
).26.
Jeffery
, G. B.
, “The motion of ellipsoidal particles immersed in a viscous fluid
,” Proc. R. Soc. London, Ser. A
102
, 161
–179
(1922
).27.
Kwon
, T. H.
, and S. F.
Shen
, “A unified constitutive theory for polymeric liquids I. Basic considerations and a simplified model
,” Rheol. Acta
23
, 217
–230
(1984
).28.
Kwon
, Y.
, and A. I.
Leonov
, “Stability constraints in the formulation of viscoelastic constitutive equations
,” J. Non-Newtonian Fluid Mech.
58
, 25
–46
(1995
).29.
Laun
, H. M.
, “Orientation effects and rheology of short glass fiber-reinforced thermoplastics
,” Colloid Polym. Sci.
262
, 257
–269
(1984
).30.
Leonov
, A. I.
, “Nonequilibrium thermodynamics and rheology of viscoelastic polymer media
,” Rheol. Acta
15
, 85
–98
(1976
).31.
Leonov
, A. I.
, “On a class of constitutive equations for viscoelastic liquids
,” J. Non-Newtonian Fluid Mech.
25
, 1
–59
(1987
).32.
Leonov
, A. I.
, E. H.
Lipkina
, E. D.
Paskhin
, and A. N.
Prokunin
, “Theoretical and experimental investigation of shearing in elastic polymer liquids
,” Rheol. Acta
15
, 411
–426
(1976
).33.
Petrie
, C. J. S.
, “The rheology of fibre suspensions
,” J. Non-Newtonian Fluid Mech.
87
, 369
–402
(1999
).34.
Rajabian
, M.
, C.
Dubois
, and M.
Grmela
, “Suspensions of semiflexible fibers in polymeric fluids: Rheology and thermodynamics
,” Rheol. Acta
44
, 521
–535
(2005
).35.
Ramazani
, A.
, A.
Ait-Kadi
, and M.
Grmela
, “Rheological modelling of short fiber thermoplastic composites
,” J. Non-Newtonian Fluid Mech.
73
, 241
–260
(1997
).36.
Ramazani
, A.
, A.
Ait-Kadi
, and M.
Grmela
, “Rheology of fiber suspensions in viscoelastic media: Experiments and model predictions
,” J. Rheol.
45
(4
), 945
–962
(2001
).37.
Sepehr
, M.
, G.
Ausias
, and P. J.
Carreau
, “Rheological properties of short fiber filled polypropylene in transient shear flow
,” J. Non-Newtonian Fluid Mech.
123
, 19
–32
(2004
a).38.
Sepehr
, M.
, P. J.
Carreau
, M.
Moan
, and G.
Ausias
, “Rheological properties of short fiber model suspensions
,” J. Rheol.
48
(5
), 1023
–1048
(2004
b).39.
Shaqfeh
, E. S. G.
, and G. H.
Fredrickson
, “The hydrodynamic stress in a suspension of rods
,” Phys. Fluids A
2
, 7
–24
(1990
).40.
Tucker
, C. L.
, “Flow regimes for fiber suspensions in narrow gaps
,” J. Non-Newtonian Fluid Mech.
39
, 239
–268
(1991
).41.
Wang
, J.
, J. F.
O’Gara
, and C. L.
Tucker
, “An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence
,” J. Rheol.
52
(5
), 1179
–1200
(2008
).© 2011 The Society of Rheology.
2011
The Society of Rheology
You do not currently have access to this content.
