Anisotropic Viscosities of an Oriented Fiber Composite with a Power-Law Matrix
Abstract
Models for the prediction of the longitudinal and transverse elongational viscosities and the inplane and transverse shearing viscosities have been developed for an oriented assembly of discontinuous fibers suspended in both a Newtonian fluid and a power-law fluid with finite yield stress. The present theory is shown to be increasingly ac curate as the fiber volume fraction is increased in contrast to the work of suspension rheology which is largely relegated to dilute and semiconcentrated systems. The approach taken is to assume the fiber kinematics, calculate the resulting fluid motion and determine directly the effective properties of the composite. Solutions are shown to compare favor ably with the results of Batchelor [2] and Christensen [6].
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References
Pipes, R.B. et al. 1991. "A Constitutive Relation for the Viscous Flow of an Oriented Fiber Assembly," Journal of Composite Materials, 25(9):1204-1217.
Batchelor, G.K. 1971. "The Stress Generated in a Non-Dilute Suspension of Elongated Particles by Pure Straining Motion," Journal of Fluid Mechanics, 46(part 4):813-829.
Mewis, J. and A.B. Metzner. 1974. "The Rheological Properties of Suspensions in Newtonian Fluids Subjected to Extensional Deformations," Journal of Fluid Mechanics, 62(part 3):593-600.
Pipes, R.B. et al. 1991. "Influence of Fiber Length on the Viscous Flow of an Oriented Fiber Assembly," Journal of Composite Materials, 25(10):1379-1390.
Cogswell, F.N. "An Interpretation of the Flow of Composite Materials Measured under Oscillary Shear," ICI Materials Centre, paper 87/82, Wilton United Kingdom.
Christensen, R.M. and K.H. Lo . 1979. "Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models," Journal of Mechanics and Physics of Solids, 27:315-330.
Christensen, R.M. and K.H. Lo . 1986. Erratum, Journal of Mechanics and Physics of Solids, 34(6):639.
Christensen, R.M. 1990. Private communication.
Cogswell, F.N. 1990. Private communcation.
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Article first published: October 1992
Issue published: October 1992
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