The models used in fiber orientation prediction have three major groupings: micro-mechanics models, thermal expansion coefficient models, and fiber closure approximation models. Additional general research is also considered.
Micro-mechanics models are the set of models used to predict the elastic properties of short-fiber reinforced composites from the knowledge of the matrix and the fiber elastic properties, fiber content, and fiber aspect ratio.
| Model | Reference |
|---|---|
| Halpin-Tsai | J.C. Halpin and J.L. Kardos, The Halpin-Tsai Equations: A review, Polym. Eng. Sci., 16(5), 345-352 (1976). |
| Tandon-Weng | G.P. Tandon and G.J. Weng, The Effect of Aspect Ratio of Inclusions on the Elastic properties of Unidirectionally Aligned Composites, Polym. Compos., 5(4), 327-333 (1984). |
| Krenchel | H. Krenchel, Fiber Reinforcement. Stockholm, Akademisk Vorlag, 1964. |
| Cox | H.L. Cox, The Elasticity and Strength of Paper and Other Fibrous Materials, British J. Appl. Phys., 3, 72-79 (1952). |
| Mori-Tanaka | Tucker, C. L. and Liang, E., Stiffness predictions for unidirectional short fiber composites: review and evaluation. Compos. Sci. Technol., 59, 655-71 (1999) |
| Ogorkiewicz-Weidmann-Counto |
R.M. Ogorkiewicz and G.W. Weidmann, Tensile Stiffness of a Thermoplastic Reinforced with Glass Fibers or Spheres, J. Mech. Sci., 16, 10 (1974). V.J. Counto, The Effect of the Elastic Modulus of the Aggregate on the Elastic Modulus Creep and Creep Recovery of Concrete, Mag. Concrete Res., 16, 129 (1964). |
Thermal expansion coefficient models are the set of models for predicting the longitudinal and transverse coefficients of thermal expansion of unidirectional fiber reinforced composites from the knowledge of the matrix and the fiber thermal expansion coefficients, fiber content and fiber aspect ratio.
| Model | Reference |
|---|---|
| Schapery | R.A. Schapery, Thermal Expansion Coefficients of Composite materials Based on Energy Principles, J. Compos. Mater., 2 (3), 380-404 (1968). |
| Chamberlain | D.E. Bowles and S.S. Tompkins, Prediction of Coefficients of Thermal Expansion for Unidirectional Composites, J. Comps. Mater., 23, 370-388 (1989). |
| Rosen-Hashin | B.W. Rosen and Z. Hashin, Effective Thermal Expansion Coefficients and Specific Heat of Composite Materials, Int. J. Eng. Sci., 8, 157-173 (1970). |
Closure approximation is a formula that approximates the fourth-order orientation tensor in terms of a second-order tensor. A variety of different forms of closure approximations have been proposed.
| Model | Reference |
|---|---|
| Hybrid | S.G. Advani and C.L. Tucker, The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites, J. Rheol., 31, 751-784 (1987). |
| Orthotropic 1 | Moldflow Bi-linear model based on J.S. Cintra and C.L. Tucker, Orthotropic Closure Approximations for Flow-induced Fiber Orientation, J. Rheol., 39, 1095-1122 (1995). |
| Orthotropic 2 | ORF (orthotropic fitted), see J.S. Cintra and C.L. Tucker, Orthotropic Closure Approximations for Flow-induced Fiber Orientation, J. Rheol., 39, 1095-1122 (1995). |
| Orthotropic 3 | Moldflow Bi-quadratic model based on J.S. Cintra and C.L. Tucker, Orthotropic Closure Approximations for Flow-induced Fiber Orientation, J. Rheol., 39, 1095-1122 (1995). |
| Orthotropic 4 | ORL (orthotropic, fitted for low Ci), see J.S. Cintra and C.L. Tucker, Orthotropic Closure Approximations for Flow-induced Fiber Orientation, J. Rheol., 39, 1095-1122 (1995). |
Jeffery, G.B., The Motion of Ellipsoidal Particles Immersed in Viscous Fluid, Proc. Roy. Soc., A102, p.161 (1922).
J.C. Halpin and J.L. Kardos, The Halpin-Tsai Equations: A review, Polym. Eng. Sci., 16(5), 345-352 (1976).
Folgar, F.P. and C.L. Tucker, Orientation Behavior of Fibers in Concentrated Suspensions, J. Reinf. Plas. Compos., 3, p.98 (1984).
Dinh, S.M. and Armstrong, R.C., A Rheological Equation of State for Semi-Concentrated Fiber Suspensions. J. Rheol., 28, p207 (1984).
Tandon, G.P. and Weng, G.T., Polym. Comp., 327-333 (1984).
Bay, R.S., Fiber Orientation in Injection Molded Composites: A Comparison of Theory and Experiment. PhD thesis, University of Illinois at Urbana-Champaign (1991).
Tucker, C.L. and Liang, E., Stiffness predictions for unidirectional short fiber composites: review and evaluation. Compos. Sci. Technol., 59, 655-71 (1999).
J. Wang, J.F. O’Gara, and C.L. Tucker III, An Objective Model for Slow Orientation Dynamics in Concentrated Fiber Suspensions: Theory and Rheological Evidence. Journal of Rheology, 52(5):1179-1200 (2008).
Phelps, J. and C. L. Tucker III, An Anisotropic Rotary Diffusion Model for Fiber Orientation in Short- and Long-Fiber Thermoplastics. Journal of Non-Newtonian Fluid Mechanics 156(3): 165–176 (2009).
Phelps, J.H., Processing-microstructure Models for Short- and Long-fiber Thermoplastic Composites. PhD thesis, University of Illinois at Urbana-Champaign (2009).