Effects of extrudate swell and nozzle geometry on fiber orientation in Fused Filament Fabrication nozzle flow

Love, 2014, The importance of carbon fiber to polymer additive manufacturing, J. Mater. Res., 29, 1893, 10.1557/jmr.2014.212 J. Nixon, B. Dryer, D. Chiu, I. Lempert, D.I. Bigio, Three Parameter Analysis of Fiber Orientation In Fused Deposition Modeling Geometries, (2014) 985–995. Advani, 1987, The use of tensors to describe and predict fiber orientation in short fiber composites, J. Rheol., 31, 751, 10.1122/1.549945 Tucker, 1994 Lee, 2016, Numerical stimulation of extrudate swell of semi-concentrated fiber suspensions, vol. 153, 87 VerWeyst, 2002, Fiber suspensions in complex geometries: flow-orientation coupling, Can. J. Chem. Eng., 80, 1093, 10.1002/cjce.5450800611 Baloch, 1995, A computer simulation of complex flows of fibre suspensions, Comput. Fluids, 24, 135, 10.1016/0045-7930(94)00023-R Ausias, 1994, Flow and fiber orientation calculations in reinforced thermoplastic extruded tubes, Intern. Polym. Process., 9, 51, 10.3139/217.940051 Uematsu, 2013, Effect of carbon fiber on the capillary extrusion behaviors of high-density polyethylene, Polym. J., 45, 449, 10.1038/pj.2012.167 Wagner, 1996, Extrudate swell behavior of glass fiber filled polyamide 6, J. Polym. Compos., 17, 840, 10.1002/pc.10677 Stabik, 2004, Influence of filler particle geometry on die swell, Intern. Polym. Process., 19, 350, 10.3139/217.1840 Becraft, 1992, The rheology, fiber orientation, and processing behavior of fiber-filled fluids, J. Rheol., 36, 143, 10.1122/1.550359 Georgiou, 1995, The compressible newtonian extrudate swell problem, Int. J. Numer. Methods Fluids, 20, 255, 10.1002/fld.1650200305 Reddy, 1978, Finite element solution of viscous jet flows with surface tension, Comput. Fluids, 6, 83, 10.1016/0045-7930(78)90009-9 Mitsoulis, 2012, A study of various factors affecting newtonian extrudate swell, Comput. Fluids, 57, 195, 10.1016/j.compfluid.2011.12.019 Mitsoulis, 2012, Annular extrudate swell of fluoropolymer melt, Intern. Polym. Process., 27, 535, 10.3139/217.2601 Kanvisi, 2014, Numerical investigation and experimental observation of extrudate swell for viscoelastic polymer melts, Intern. Polym. Process., 29, 227, 10.3139/217.2840 Halpin, 1976, The Halpin-Tsai equations: a review, Polym. Eng. Sci., 16, 344, 10.1002/pen.760160512 Tandon, 1984, The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites, Polym. Compos., 5, 327, 10.1002/pc.750050413 Camacho, 1990, Stiffness and thermal expansion predictions for hybird short fiber composites, Polym. Compos., 11, 229, 10.1002/pc.750110406 Jack, 2006, The effect of fiber orientation closure approximations on mechanical property predictions, Compos. Part A Appl. Sci. Manuf., 38, 975, 10.1016/j.compositesa.2006.06.016 Folgar, 1984, Orientatrion behavior of fibers in concentrated suspensions, J. Reinf. Plast. Compos., 3, 98, 10.1177/073168448400300201 Cintra, 1995, Orthotropic closure approximations for flow-Induced fiber orientation, J. Rheol., 39, 1095, 10.1122/1.550630 Wetzel, 1999, Area tensors for modeling microstructure during laminar liquid-liquid mixing, Int. J. Multiphase Flow, 25, 35, 10.1016/S0301-9322(98)00013-5 Jeffery, 1923, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. London A, 102, 161, 10.1098/rspa.1922.0078 Zhang, 2013, Flow-induced micro- and nano-fiber suspensions Wang, 2008, An objective model for slow orientation kinetics in concentrated fiber suspensions: theory and rheological evidence, J. Rheol., 52, 1179, 10.1122/1.2946437 Phelps, 2009, An anisotropic rotary diffusion model for fiber orientation in short and long fiber thermoplastics, J. Nonnewton Fluid Mech., 156, 165, 10.1016/j.jnnfm.2008.08.002 Bay, 1991 Montgomery-Smith, 2011, The fast exact closure for Jeffery’s equation with diffusion, J. Nonnewton Fluid Mech., 166, 343, 10.1016/j.jnnfm.2010.12.010 Montgomery-Smith, 2011, Exact tensor closures for the three dimensional Jeffery’s equation, J. Fluid Mech., 680, 321, 10.1017/jfm.2011.165 Chung, 1996, Coupled analysis of injection molding filling and fiber orientation, including in-plane velocity gradient effect, Polym. Compos., 17, 859, 10.1002/pc.10679 VerWeyst, 1998 Tucker, 1999, Stiffness predictions for unidirectional short-fiber composites: review and evaluation, Compos. Sci. Technol., 59, 655, 10.1016/S0266-3538(98)00120-1 Eshelby, 1957, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. London A., 241, 376, 10.1098/rspa.1957.0133 Mori, 1973, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall. Mater., 21, 571, 10.1016/0001-6160(73)90064-3 Hill, 1952, The elastic behaviour of a crystalline aggregate, Proc. R. Soc. London A., 65, 349, 10.1088/0370-1298/65/5/307 Heller, 2015