繊維配向予測で使用するモデルは、大きく 3 つのグループに分類できます。これは、マイクロメカニックス モデル、熱膨張係数モデル、およびファイバー完結近似モデルです。これ以外の一般的な研究内容も考慮されています。
マイクロメカニックス モデルは、マトリックスとファイバーの弾性、含有ファイバー、およびファイバーのアスペクト比に関する情報に基づいて、短繊維強化複合材料の弾性を予測するための一連のモデルです。
| モデル | 参照 |
|---|---|
| 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). |
熱膨張係数モデルは、マトリックスとファイバーの熱膨張係数、含有ファイバー、およびファイバーのアスペクト比に関する情報に基づいて、一方向ファイバー強化複合材料の縦および横の熱膨張係数を予測するための一連のモデルです。
| モデル | 参照 |
|---|---|
| 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). |
完結近似は、4 次配向テンソルを 2 次テンソルの観点から近似化する式です。さまざまな完結近似形式が提案されています。
| モデル | 参照 |
|---|---|
| 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).