纤维取向预测中使用的模型主要分三类：微机械模型、热膨胀系数模型和纤维闭合近似模型。还需要考虑其他的综合研究成果。
微机械模型是一组用于根据基材和纤维弹性属性以及纤维含量和纤维的纵横比预测短纤维加强型组合物的弹性属性的模型。
| 模型 | 参考 |
|---|---|
| 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). |
热膨胀系数模型是一组用于根据基材和纤维热膨胀系数、纤维含量以及纤维纵横比预测单向纤维加强型组合物的纵向和横向热膨胀系数的模型。
| 模型 | 参考 |
|---|---|
| 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). |
闭合近似是用于根据第二顺序张量逼近第四顺序取向张量的公式。已提出多种不同形式的闭合近似。
| 模型 | 参考 |
|---|---|
| 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).