A Constitutive Relation for the Viscous Flow of an Oriented Fiber Assembly

Abstract

A constitutive relation for an equivalent, homogeneous fluid is developed for the anisotropic viscous flow of an oriented assembly of discontinuous fibers suspended in a viscous fluid. The anisotropic viscous compliance matrix can be expressed in terms of three constants by assuming the equivalent fluid to be incompressible and the micro-structure to have axial symmetry (transversely isotropic). By means of a micromechanics analysis, the three terms of the constitutive relation are expressed in terms of the viscosity of the matrix fluid, the fiber aspect ratio, and the fiber volume fraction. A comparison of the viscosity terms reveals that the elongational viscosity in the fiber direction varies as the square of the fiber aspect ratio and a complex function of the fiber volume fraction. Further, the ratio of the axial elongational viscosity to the transverse elongational viscosity and both axial and transverse shear viscosities was shown to be 10⁴-10⁶ for fiber aspect ratio of 10²-10³, except at extreme values of the fiber volume fraction.

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References

1. Smiley, A. J. and R. B. Pipes . 1987. “Simulation of the Diaphragm Forming of Carbon Fiber/Thermoplaslic Composite Laminates”, Proceedings of the American Society far Composites. Second Technical Conference, Lancaster, Pa: Technomic Publishing Co., p. 218.

2. O'Bradaigh. C. M. and P. J. Mallon . 1989. “Effect of Forming Temperature on the Properties of Polymerica Diaphragm Formed Thermoplastic Components”, Composites Science and Technology, 35: 235–255.

3. Cogswell, F. N. 1987. “The Processing Science of Thermoplastic Structural Composites”, International Polymer Processing, 1(4):157–165.

4. Cogswell, F. N. and D. J. Groves . 1988. “The Melt Rheology of Continuous Fibre Reinforced Structural Composite Materials”, Proceedings of the Xth International Conference on Rheology, Sydney, Australia.

5. Barnes, J. A. and F. N. Cogswell . 1989. “Transverse Flow Processes in Continuous Fibre-Reinforced Thermoplastic Composites”, Composites, 20: 38–12.

6. Mallon, P. J. and C. M. O'Bradaigh . 1988. “Development of a Pilot Autoclave for Polymeric Diaphragm Forming of Continuous Fiber Reinforced Thermoplastics”, Composites, 19: 37–47.

7. O'Bradaigh, C. M. , B. A. Regan , R. B. Pipes and P. J. Mallon . 1990. “Investigation of Shear Buckling in Diaphragm Forming of Continuous Fiber Thermoplastics Composites.” Paper 20, SPI Composites Institute Annual Conference, Washington, Dc.

8. Mallon, P. J. , C. M. O'Bradaigh and R. B. Pipes . 1989. “Polymeric Diaphragm Forming of Complex-Curvature Thermoplastic Composite Parts.” Composites, 20: 48–56.

9. Okine, R. K. , D. H. Edison and N. K. Little . 1990. “Properties and Formability of an Aligned Discontinuous Fiber Thermoplastic Composite Sheet”, Journal of Reinforced Plastics and Composites, 8: 70–90.

10.

10. Metzner, A. B. 1985. “Rheology of Suspensions in Polymeric Liquids”, J. of Rheology, 29(6): 739–775.

11.

11. Rogers, T. G. 1989. “Rheological Characterization of Anisotropic Materials”, Composites, 20(1):21–27.

12.

12. Gibson, A. G. 1989. “Die Entry of Reinforced Polymers”, Composites, 20(1):57–64.

13.

13. Batchelor, G. K. 1971. “The Stress Generated in Non-dilute Suspensions of Elongated Particles by Pure Straining Motion”, Journal of Fluid Mechanics, 46(4):813–829.

14.

14. Goddard, J. D. 1976. “Tensile Stress Contributions of Flow Oriented Slender Particles in Non-Newtonian Fluids”, Journal of Non-Newtonian Fluid Mechanics, 1: 1–17.

15.

15. Aerivos. A. and E. S. G. Shaqfch . 1988. “The Effective Thermal Conductivity and Elongational Viscosity of a Nondilute Suspension of Aligned Slender Rods”, Physics of Fluids, 31(7):1841–1844.

16.

16. Cogswell, F. N. “An Interpretation of the Flow of Composite Materials Measured under Oscillatory Shear”, Ici Materials Centre, paper 87/87, Wilton. United Kingdom.

17.

17. Balasubramanyan. R. , R. S. Jones and A. B. Wheeler . 1989. “Modeling Transverse Flows of Reinforced Thermoplastic Materials”, Composites, 20(1):33–37.