섬유 배향 예측에 사용되는 모델에는 3개의 주요 그룹인 마이크로공학 모델, 열팽창 계수 모델 및 섬유 클로저 근사치 모델이 있습니다. 추가 일반 연구도 고려됩니다.
마이크로공학 모델은 매트릭스 및 섬유 탄성 속성, 섬유 함량 및 섬유 종횡비에 대한 지식으로 짧은 섬유 강화 컴포지트의 탄성 속성을 예측하는 데 사용되는 모델 집합입니다.
| 모델 | 기준 |
|---|---|
| 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). |
열팽창 계수 모델은 매트릭스 및 섬유 열팽창 계수, 섬유 함량 및 섬유 종횡비에 대한 지식으로 단방향 섬유 강화 컴포지트의 세로 및 횡단 열팽창 계수를 예측하는 모델 세트입니다.
| 모델 | 기준 |
|---|---|
| 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). |
클로저 근사치는 2차 텐서 측면에서 4차 배향 텐서의 근사치를 구하는 공식입니다. 다양한 형태의 클로저 근사치가 제안되었습니다.
| 모델 | 기준 |
|---|---|
| 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).