Numerical evaluation of single fiber motion for short-fiber-reinforced composite materials processing

Journal of Manufacturing Science and Engineering

Volumn 133, Issue 5, 2011, Pages

  Zhang, Dongdong ^a   Smith, Douglas E ^a   Jack, David A ^b   Montgomery Smith, Stephen ^c  

^a University of Missouri   (United States)

^b Baylor University   (United States)

^c UNIVERSITY OF MISSOURI   (United States)

Author keywords

axisymmetric fiber; cylindrical fiber; equivalent aspect ratio; fiber orientation; Jeffery's orbit; short fiber reinforced composite materials

Indexed keywords

ASPECT RATIO; FIBER REINFORCED MATERIALS; FIBER REINFORCED PLASTICS; MOLDS; NEWTON-RAPHSON METHOD; POLYMER MELTS; REINFORCEMENT; REYNOLDS NUMBER; RUNGE KUTTA METHODS; SHEET MOLDING COMPOUNDS; VISCOUS FLOW;

AXISYMMETRIC; COMPUTATIONAL APPROACH; CYLINDRICAL FIBERS; FUNCTION OF TIME; HYDRODYNAMIC FORCES; LOW REYNOLDS NUMBER; SHORT-FIBER-REINFORCED COMPOSITES; VISCOUS FLUIDS;

FIBERS;

DYNAMICS; FIBER ORIENTATION; FINITE ELEMENT ANALYSIS; MOLDING; MOLDS; POLYMERS; REINFORCED PLASTIC; SHEETS; SIMULATION; VISCOUS FLOW;

EID: 80052971863     PISSN: 10871357     EISSN: 15288935     Source Type: Journal    
DOI: 10.1115/1.4004831     Document Type: Article

References (32)

1. Jeffery, G. B., 1922, "The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid", Proc. R. Soc. London, 102(715), pp. 161-179.
2. Folgar, F., and Tucker III, C. L., 1984, "Orientation Behavior of Fibers in Concentrated Suspensions", J. Reinf. Plast. Compos., 3(2), pp. 98-119. (Pubitemid 14608955)
3. Advani, S. G., and Tucker III, C. L., 1987, "The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites", J. Rheol., 31(8), pp. 751-784.
4. Montgomery-Smith, S., Jack, D. A., and Smith, D. E., 2011, "The Fast Exact Closure for Jefferys Equation With Diffusion", J. Non-Newtonian Fluid Mech., 166(7-8), pp. 343-353.
5. Cintra, J. S., and Tucker III, C. L., 1995, "Orthotropic Closure Approximations for Flow-Induced Fiber Orientation", J. Rheol., 39(6), pp. 1095-1122.
6. Jack, D. A., and Smith, D. E., 2005, "An Invariant Based Fitted Closure of the Sixth-Order Orientation Tensor for Modeling Short-Fiber Suspensions", J. Rheol., 49(5), pp. 1091-1115. (Pubitemid 43066521)
7. Taylor, G. I., 1923, "The Motion of Ellipsoidal Particles in a Viscous Fluid", Proc. R. Soc. London, 103(720), pp. 58-61.
8. Trevelyan, B. J., and Mason, S. G., 1951, "Particle Motions in Sheared Suspensions. I. Rotations", J. Colloid Sci., 6, pp. 354-367.
9. Mason, S. G., and Manley, R. St. J., 1956, "Particle Motions in Sheared Suspensions: Orientation and Interactions of Rigid Rods", Proc. R. Soc. London, 238(1212), pp. 117-131.
10. Anczurowski, E., and Mason, S. G., 1968, "Particle Motions in Sheared Suspensions. XXIV. Rotation of Rigid Spheroids and Cylinders", J. Rheol., 12(2), pp. 209-215.
11. Wang, J., O'Gara, J. F., and Tucker III, C. L., 2008, "An Objective Model for Slow Orientation Kinetics in Concentrated Fiber Suspensions: Theory and Rheological Evidence", J. Rheol., 52(5), pp. 1179-1200.
12. Petrie, C. J. S., 1999, "The Rheology of Fibre Suspensions", J. Non-Newtonian Fluid Mech., 87(2-3), pp. 369-402. (Pubitemid 30015011)
13. Leal, L. G., 1980, "Particle Motions in a Viscous Fluid", Annu. Rev. Fluid Mech., 12(1), pp. 435-476.
14. Jia, L., 2006, "Flow-Induced Alignment Migration of Particles in Suspensions", Ph. D. thesis, Michigan State University, East Lansing, MI 48824.
15. Junk, M., and Illner, R., 2007, "A New Derivation of Jeffery's Equation", J. Math. Fluid Mech., 9(4), pp. 445-288.
16. Batchelor, G. K., 1970, "The Stress System in a Suspension of Force-Free Particles", J. Fluid Mech., 41, pp. 545-570.
17. Batchelor, G. K., 1970, "Slender Body Theory for Particles of Arbitrary Cross-Section in Stoke Flow", J. Fluid Mech., 44, pp. 419-440.
18. Yamamoto, S., and Matsuoka, T., 1993, "A Method for Dynamic Simulation of Rigid and Flexible Fibers in a Flow Field", J. Chem. Phys., 98(1), pp. 644-650.
19. Ross, R. F., and Klingenberg, D. J., 1997, "Dynamic Simulation of Flexible Fibers Composed of Linked Rigid Bodies", J. Chem. Phys., 106(7), pp. 2949-2960. (Pubitemid 127617033)
20. Wang, G., Yu, W., and Zhou, C., 2006, "Optimization of the Rod Chain Model to Simulate the Motions of a Long Flexible Fiber in Simple Shear Flows", Eur. J. Mech. B/Fluids, 25(3), pp. 337-347.
21. Switzer III, L. H., 2002, "Simulating Systems of Flexible Fibers", Ph. D. thesis, University of Wisconsin-Madison, WI 53706.
22. Bretherton, F. P., 1962, "The Motion of Rigid Particles in a Shear Flow at Low Reynolds Number", J. Fluid Mech., 14(2), pp. 284-304.
23. Petrich, M. P., Koch, D. L., and Cohen, C., 2000, "An Experimental Determination of the Stress-Microstructure Relationship in Semi-Concentrated Fiber Suspensions", J. Non-Newtonian Fluid Mech., 95(2-3), pp. 101-133.
24. Harris, J. B., and Pittman, J. F. T., 1975, "Equivalent Ellipsoidal Aspect Ratios of Slender Rod-Like Particles", J. Colloid Interface Sci., 50(2), pp. 280-282.
25. Cox, R. G., 1971, "The Motion of Long Slender Bodies in a Viscous Fluid. Part 2. Shear Flow", J. Fluid Mech., 45(4), pp. 625-657.
26. Sugihara-Seki, M., 1996, "The Motion of an Ellipsoid in Tube Flow at Low Reynolds Numbers", J. Fluid Mech., 324, pp. 287-308. (Pubitemid 126453656)
27. Chwang, A. T., 1975, "Hydromechanics of Low-Reynolds-Number Flow. Part 3. Motion of a Spheroidal Particle in Quadratic Flows", J. Fluid Mech., 72(1), pp. 17-34.
28. Feng, J., Hu, H. H., and Joseph, D. D., 1994, "Direction Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid, Part 2. Couette and Poiseuille Flows", J. Fluid Mech., 277, pp. 271-301. (Pubitemid 283941)
29. Hu, H. H., Joseph, D. D., and Crochet, M. J., 1992, "Direct Simulation of Fluid Particle Motions", Theor. Comput. Fluid Dyn., 3, pp. 285-306.
30. Lamb, H., Hydrodynamics (Cambridge University, Cambridge, 1916).
31. Chapra, S. C., Applied Numerical Methods With MATLAB for Engineers and Scientists-Second Edition (McGraw-Hill, New York, 2008).
32. Chaffey, C. E., Takano, M., and Mason, S. G., 1965, "Particle Motions in Sheared Suspensions. XVI. Orientations of Rods and Disks in Hyperbolic and Other Flows", Can. J. Phys., 43, pp. 1269-1287.