注射成型短纤维增强复合材料纤维取向分布的预测
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摘要
在纤维增强注射成型过程中，纤维取向对成型制品的力学性能有很大的影响，使制品的性质呈现各向异性，或在固化制品中产生残余应力而产生翘曲变形。并且，纤维取向也是制品微观结构的主要特征。因此纤维取向的预测，对与纤维取向相关的力学性能进行分析，从而达到预测和控制产品性能的要求，对此类产品的生产具有非常重要的意义。
论文针对短纤维增强注射成型过程，采用数值方法预测纤维增强注射成型制品的取向分布，对纤维增强复合材料熔体流动以及增强纤维的取向进行分析，预测最终制件中的纤维取向分布，不仅可以为产品设计提供重要的依据，还可以建立成型工艺条件与最终制件中的纤维取向之间的定量关系。主要工作包括：
(1)理论研究一个浸没在Newton流体中刚性的椭圆形质点(纤维)的动力学特征，分析了纤维在稳态剪切流和简单拉仲流中纤维的运动，解析解表明：剪切流动使纤维沿流动方向排列，而拉仲流动趋向于使纤维沿拉仲方向排列。
(2)重点研究取向张量的性质，取向张量和取向分布函数之间的关系，取向张量的描述精度，以及取向张量的闭合近似理论的精度。
(3)在注射成型流动引起的纤维取向的数值预测中，将短纤维增强的热塑性熔体近似为浓悬浮液，采用Hele-Shaw近似来计算型腔中的速度场，然后假设纤维为圆柱形刚体，利用取向分布函数描述空间点的取向状态，并采用Folgar-Tucker取向模型描述纤维的取向行为。
(4)采用有限元法预测纤维增强注射成型制品的取向分布，对纤维增强复合材料熔体流动以及增强纤维的取向进行分析，预测成型过程中熔体充填流动模式、以及最终制件中的纤维取向分布。
Prediction of fiber orientation distributing in short-fiber-reinforced composites injection molding
During injection molding of the fiber reinforced composites, fiber orientation can significantly affect the mechanical property of parts, which either made parts developing anisotropic property or develop residual stress due to which solidified in the parts cause parts to warp deformation. Fiber orientation is the main properties of the parts'microstructure.So a prediction of the fiber orientation can analyze mechanical properties with relation to fiber orientation,which satisfy with the need of controling and prediction parts' properties.Therefore,an accurate prediction in producting the parts is very important.
Aiming at the progress of injection molding the short fiber reinforced composites, we predict the orientation distributing of the final parts by numerical methods.To analyze fiber orientation and predict the orientation distributing of the final parts, which not only provide the important criterion for the part-designed ,but also building a quantitative relation between the molding technics and the fiber orientation of the final parts.The main result are as follow:
1) To study dynamics properties of an elliptical shape mass point(fiber) immersed in Newton fluid .To analyze the motion of the fiber in steady shearing flow and simple stretching flow.The analytic solution showed:shearing flow tend to align fibers in the direction of flow, stretching flows tend to align fibers in the direction of stretching.
2) The important purpose is to study the properties of orientation tensor, the relation between orientation tensor and orientation distribution function,the description accuracy of orientation tensor, and the accuracy of the closure approximation of orientation tensor.
3) During numerical prediction of fiber orientation induced by injection molding flow, considering the short fiber reinforced composites melt as concentrated suspension, adopting Hele-Shaw model approximate the velocity field in cavity.We believe that the fiber is cylindric rigid body,describing the orientation state of spatial point by ODE,and demonstrating the behavior of the fiber
orientation by adopting Folgar-Tucker orientation model.
4) A finite-element/finite-difference program is employed to predict the orientation distributing of fiber reinforced injection molding parts.To predict the filling pattern of the melt in the molding progress and the fiber orientation distribution of the final parts by analyzing the flow of the fiber reinforced composites melt and fiber orientation.
论文针对短纤维增强注射成型过程，采用数值方法预测纤维增强注射成型制品的取向分布，对纤维增强复合材料熔体流动以及增强纤维的取向进行分析，预测最终制件中的纤维取向分布，不仅可以为产品设计提供重要的依据，还可以建立成型工艺条件与最终制件中的纤维取向之间的定量关系。主要工作包括：
(1)理论研究一个浸没在Newton流体中刚性的椭圆形质点(纤维)的动力学特征，分析了纤维在稳态剪切流和简单拉仲流中纤维的运动，解析解表明：剪切流动使纤维沿流动方向排列，而拉仲流动趋向于使纤维沿拉仲方向排列。
(2)重点研究取向张量的性质，取向张量和取向分布函数之间的关系，取向张量的描述精度，以及取向张量的闭合近似理论的精度。
(3)在注射成型流动引起的纤维取向的数值预测中，将短纤维增强的热塑性熔体近似为浓悬浮液，采用Hele-Shaw近似来计算型腔中的速度场，然后假设纤维为圆柱形刚体，利用取向分布函数描述空间点的取向状态，并采用Folgar-Tucker取向模型描述纤维的取向行为。
(4)采用有限元法预测纤维增强注射成型制品的取向分布，对纤维增强复合材料熔体流动以及增强纤维的取向进行分析，预测成型过程中熔体充填流动模式、以及最终制件中的纤维取向分布。
Prediction of fiber orientation distributing in short-fiber-reinforced composites injection molding
During injection molding of the fiber reinforced composites, fiber orientation can significantly affect the mechanical property of parts, which either made parts developing anisotropic property or develop residual stress due to which solidified in the parts cause parts to warp deformation. Fiber orientation is the main properties of the parts'microstructure.So a prediction of the fiber orientation can analyze mechanical properties with relation to fiber orientation,which satisfy with the need of controling and prediction parts' properties.Therefore,an accurate prediction in producting the parts is very important.
Aiming at the progress of injection molding the short fiber reinforced composites, we predict the orientation distributing of the final parts by numerical methods.To analyze fiber orientation and predict the orientation distributing of the final parts, which not only provide the important criterion for the part-designed ,but also building a quantitative relation between the molding technics and the fiber orientation of the final parts.The main result are as follow:
1) To study dynamics properties of an elliptical shape mass point(fiber) immersed in Newton fluid .To analyze the motion of the fiber in steady shearing flow and simple stretching flow.The analytic solution showed:shearing flow tend to align fibers in the direction of flow, stretching flows tend to align fibers in the direction of stretching.
2) The important purpose is to study the properties of orientation tensor, the relation between orientation tensor and orientation distribution function,the description accuracy of orientation tensor, and the accuracy of the closure approximation of orientation tensor.
3) During numerical prediction of fiber orientation induced by injection molding flow, considering the short fiber reinforced composites melt as concentrated suspension, adopting Hele-Shaw model approximate the velocity field in cavity.We believe that the fiber is cylindric rigid body,describing the orientation state of spatial point by ODE,and demonstrating the behavior of the fiber
orientation by adopting Folgar-Tucker orientation model.
4) A finite-element/finite-difference program is employed to predict the orientation distributing of fiber reinforced injection molding parts.To predict the filling pattern of the melt in the molding progress and the fiber orientation distribution of the final parts by analyzing the flow of the fiber reinforced composites melt and fiber orientation.
引文
1. M.Gupta,K.K.Wang, Fiber orientation and mechanical properties of short-fiber-reinforced injection-molded composites:simulated and experimental results,Polym.Compos., 1993,14:367-382
2. Bay Randy S. Tucker Charlers L. Fiber orientation in simple injection molding,Partl:Theory and numerical methods. Polymer Composites., 1992,13(4):317-331
3. Jeffery G.B. The Motion of Ellipsodial Particles immersed in a Viscous Fluid.Proc.Roy.Soc.,1922,A102:161-193
4. Seok Won Lee. Jae Ryoun Youn. Jae Chun Hyun, Prediction of fiber orientation structure for injection molded short fiber composites, Mat Res Innovat., 2002, 6:189-197
5. F. Folgar, C.L. Tucker, Orientation behavior of fibers in concentrated suspensions, J. Reinf. Plast. Compos. ,1984,3:98-119
6. S.G. Advani, C.L. Tucker, The use of tensors to describe and predict fiber-orientation in short fiber composites,J.Rheol., 1987,31:751-784
7. J.S. Cintra Jr., C.L. Tucker, Orthotropic closure approximation for flow-induced fiber orientation, J. Rheol., 1995,39:1095-1122.
8. S.G. Advani and C. L.Tucker Ⅲ,Closure approximation for three-dimensional structure tensors,J.Rheol., 1990,34(3):367-386
9．林兰芬，马择恩，彭玉生，，注射成型中充填流动对短纤维取向影响的研究，西北工业大学学报，1997，15(2)
10．郭建娟，晏石林，纤维取向分析的数学模型，武汉理工大学学报，2001，23(1)：56-59
11. S.T.Chung,T.H.Kwon, Numerical simulation of fiber orientation in injection molding of short-fiber-reinforced thermoplastics, Polym.Eng.Sci., 1995, 25:604-618
12. R.S.Bay and C.L.Tucker, Ⅲ, Fiber orientation in simple injection moldings. PartⅠ: Theory and numerical method.,Polym.Compos., 1992,13(4):317-331
13. R.S.Bay and C.L.Tucker, Ⅲ, Fiber orientation in simple injection moldings. Part Ⅱ: Experimental results.,Polym. Compos., 1992,13(4):332-342
14. S.T.Chung,T.H. Kwon, Coupled analysis of injection molding filling and fiber orientation including in-plane velocity gradient effect, Polymer Composites., 1996,17 (6): 859-872
15. G.C. Lipscomb, Ⅱ, M. M. Denn, D. U. Hur, and D. V. Boger, The flow of fiber suspensions in complex geometries. J. Non-Newtonian Fluid Mech., 1988, 26:297-325
16. C.L. Tucker, Flow regimes for fiber suspensions in narrow gaps, J. Non-Newtonian Fluid Mech, 1991,39:239-268
17. G.P.Greene, J.O. Wilkes, Numerical analysis of injection molding of glass fiber reinforced thermoplastics part 1: Injection pressure and flow, Polym.Eng.Sci., 1997,37 (6):1019-1035.
18. J.M.Wille, J.J. McGrath, Determination of 3D fiber orientation distribution in
thermoplastic injection molding, Composites Science and Technology., 1995,53(2):133-143
19. H.Henry de Frahan,V.Veedeye,F.Dupret,and M.J Crochet, Numerical prediction if fiber orientation in injection molding, Polym.Eng.Sci.,1992,32(4):254-266
20. L.R.Schmidt, A special mold and tracer technique for studying shear and extensional flows in a mold cavity during injection molding, Polym. Eng. Sci., 1974,14:797
21. M.R.Kamal and S.Kenig, The injection molding of thermo-plastics part1: theoretical model, Polym.Eng.Sci.,1972,12(4):294-301
22．黄峡宏，周持兴．高分子粘弹性熔体注射成型非等温保压过程的模拟，上海交通大学学报，1999，33(2)
23．王敏中，弹性力学教程，北京：北京大学出版社，2002
24. V.W. Wang, C. A. Hieber, and K. K. Wang, Dynamic Simulation and Graphics for the Injection Molding of Three-Dimensional Thin Parts, Journal of Polymer Engineering., 1986, 7(1): 21-45.
25. Hieber CA (1987) Melt-viscosity characterization and application to injection molding. In: Isayev AI (ed) Injection molding and compression molding fundamentals. MarDekker, New York, pp 61-78
26．冯金海，短纤维复合材料加工中的纤维取向研究，玻璃钢／复合材料，1995，2：15-18
27. Greene,Joseph Polym.Eng.Sci.,P, Wilkes,Jamea O, Numerical ananlysis of injection molding of glass fiber reinforced thermoplastics.Part2:fiber orientation, Polym.Eng.Sci., 1997, 37(6):1019-1035
28. Y.Yokoi, S. Kamata and T. Kanematsu, Visual observation of three-dimension melt flow inside a mold cavity by gate-magnetization method, SPE Technical Papers, 1991, 37:358
29. Gerard.P,J.Pabiot.J,Characterization of fiber and molecular orientaton and their interaction in composite injection molding., Polym.Eng.Sci., 1998,17(10):922-934
30. Kyeong H,Yong M. Modified Hybrid Closure Approxim for Prediction of Flow-induced Orientation.J Rheo., 1999(43):567-592
31. Fu SY, Lauke B,Effects of fiber length and fiber orientation distribution on the tensile strength of short-fiber-reinforced polymers.,Comp Sci Technol.,1998,58:61-72
32. Saito,Makoto,Kukula.Stefan,Kataoka.Yasuto,Practical use of the statistically modified laminate model for injection molding.Partl :method and verification, 1998,19(5):497-505
33. C.A. Hieber, S.F. Shen, A finite-element/finite-difference simulation of the injection-molding filling process, J. Non-Newt. Fluid Mech., 1980,7:1-32
34. K.-H. Hanb, Y.-T. Ima, Numerical simulation of three-dimensional fiber orientation in short-fiber-reinforced injection-molded parts, Journal of Materials Processing Technology., 2002,124:366-371
35. R.M.Christensen and K.H.Lo,Solution for effective shear properties in three phase aphere and cylinder models,J.Mech.Phys.Solids, 1979,27,315-330
36．徐士良，计算机常用算法，北京：清华大学出版社，1995
37. F. Dupret and L. Vandershuren. Calculation of the temperature field in injection molding. AIChE J., 1988,34(12): 1959-1972
38. C.Hirt,B.Nichols,Volume of fluid(VOF)method for dynamics of free boundaries,Journal of Computational physics., 1981,39:201-225
39. Charles L.Tucker Ⅲ,Erwin Liang,Stiffness prediction for unidirectional short-fiber composites:Review and evaluation,Composites Science and Technology, 1999, 59, 655-671
40. Gupta M,Santhanam N,Chiang H H,et al, Prediction of Fiber Orientation and Mechanical Properties in short-fiber Reinforced Injection-molded Composites,in Computer Aided Design in Composite Material Technology, Advani s G.Blain W R, Wilde W p,et al,eds,London,New York,1993
41．林兰芬．短纤维增强塑料注射成型中三维纤维取向的数值预测，材料科学与工艺，1998，6(2)
42．吴望一编著，流体力学(上)，北京：北京大学出版社，1983
2. Bay Randy S. Tucker Charlers L. Fiber orientation in simple injection molding,Partl:Theory and numerical methods. Polymer Composites., 1992,13(4):317-331
3. Jeffery G.B. The Motion of Ellipsodial Particles immersed in a Viscous Fluid.Proc.Roy.Soc.,1922,A102:161-193
4. Seok Won Lee. Jae Ryoun Youn. Jae Chun Hyun, Prediction of fiber orientation structure for injection molded short fiber composites, Mat Res Innovat., 2002, 6:189-197
5. F. Folgar, C.L. Tucker, Orientation behavior of fibers in concentrated suspensions, J. Reinf. Plast. Compos. ,1984,3:98-119
6. S.G. Advani, C.L. Tucker, The use of tensors to describe and predict fiber-orientation in short fiber composites,J.Rheol., 1987,31:751-784
7. J.S. Cintra Jr., C.L. Tucker, Orthotropic closure approximation for flow-induced fiber orientation, J. Rheol., 1995,39:1095-1122.
8. S.G. Advani and C. L.Tucker Ⅲ,Closure approximation for three-dimensional structure tensors,J.Rheol., 1990,34(3):367-386
9．林兰芬，马择恩，彭玉生，，注射成型中充填流动对短纤维取向影响的研究，西北工业大学学报，1997，15(2)
10．郭建娟，晏石林，纤维取向分析的数学模型，武汉理工大学学报，2001，23(1)：56-59
11. S.T.Chung,T.H.Kwon, Numerical simulation of fiber orientation in injection molding of short-fiber-reinforced thermoplastics, Polym.Eng.Sci., 1995, 25:604-618
12. R.S.Bay and C.L.Tucker, Ⅲ, Fiber orientation in simple injection moldings. PartⅠ: Theory and numerical method.,Polym.Compos., 1992,13(4):317-331
13. R.S.Bay and C.L.Tucker, Ⅲ, Fiber orientation in simple injection moldings. Part Ⅱ: Experimental results.,Polym. Compos., 1992,13(4):332-342
14. S.T.Chung,T.H. Kwon, Coupled analysis of injection molding filling and fiber orientation including in-plane velocity gradient effect, Polymer Composites., 1996,17 (6): 859-872
15. G.C. Lipscomb, Ⅱ, M. M. Denn, D. U. Hur, and D. V. Boger, The flow of fiber suspensions in complex geometries. J. Non-Newtonian Fluid Mech., 1988, 26:297-325
16. C.L. Tucker, Flow regimes for fiber suspensions in narrow gaps, J. Non-Newtonian Fluid Mech, 1991,39:239-268
17. G.P.Greene, J.O. Wilkes, Numerical analysis of injection molding of glass fiber reinforced thermoplastics part 1: Injection pressure and flow, Polym.Eng.Sci., 1997,37 (6):1019-1035.
18. J.M.Wille, J.J. McGrath, Determination of 3D fiber orientation distribution in
thermoplastic injection molding, Composites Science and Technology., 1995,53(2):133-143
19. H.Henry de Frahan,V.Veedeye,F.Dupret,and M.J Crochet, Numerical prediction if fiber orientation in injection molding, Polym.Eng.Sci.,1992,32(4):254-266
20. L.R.Schmidt, A special mold and tracer technique for studying shear and extensional flows in a mold cavity during injection molding, Polym. Eng. Sci., 1974,14:797
21. M.R.Kamal and S.Kenig, The injection molding of thermo-plastics part1: theoretical model, Polym.Eng.Sci.,1972,12(4):294-301
22．黄峡宏，周持兴．高分子粘弹性熔体注射成型非等温保压过程的模拟，上海交通大学学报，1999，33(2)
23．王敏中，弹性力学教程，北京：北京大学出版社，2002
24. V.W. Wang, C. A. Hieber, and K. K. Wang, Dynamic Simulation and Graphics for the Injection Molding of Three-Dimensional Thin Parts, Journal of Polymer Engineering., 1986, 7(1): 21-45.
25. Hieber CA (1987) Melt-viscosity characterization and application to injection molding. In: Isayev AI (ed) Injection molding and compression molding fundamentals. MarDekker, New York, pp 61-78
26．冯金海，短纤维复合材料加工中的纤维取向研究，玻璃钢／复合材料，1995，2：15-18
27. Greene,Joseph Polym.Eng.Sci.,P, Wilkes,Jamea O, Numerical ananlysis of injection molding of glass fiber reinforced thermoplastics.Part2:fiber orientation, Polym.Eng.Sci., 1997, 37(6):1019-1035
28. Y.Yokoi, S. Kamata and T. Kanematsu, Visual observation of three-dimension melt flow inside a mold cavity by gate-magnetization method, SPE Technical Papers, 1991, 37:358
29. Gerard.P,J.Pabiot.J,Characterization of fiber and molecular orientaton and their interaction in composite injection molding., Polym.Eng.Sci., 1998,17(10):922-934
30. Kyeong H,Yong M. Modified Hybrid Closure Approxim for Prediction of Flow-induced Orientation.J Rheo., 1999(43):567-592
31. Fu SY, Lauke B,Effects of fiber length and fiber orientation distribution on the tensile strength of short-fiber-reinforced polymers.,Comp Sci Technol.,1998,58:61-72
32. Saito,Makoto,Kukula.Stefan,Kataoka.Yasuto,Practical use of the statistically modified laminate model for injection molding.Partl :method and verification, 1998,19(5):497-505
33. C.A. Hieber, S.F. Shen, A finite-element/finite-difference simulation of the injection-molding filling process, J. Non-Newt. Fluid Mech., 1980,7:1-32
34. K.-H. Hanb, Y.-T. Ima, Numerical simulation of three-dimensional fiber orientation in short-fiber-reinforced injection-molded parts, Journal of Materials Processing Technology., 2002,124:366-371
35. R.M.Christensen and K.H.Lo,Solution for effective shear properties in three phase aphere and cylinder models,J.Mech.Phys.Solids, 1979,27,315-330
36．徐士良，计算机常用算法，北京：清华大学出版社，1995
37. F. Dupret and L. Vandershuren. Calculation of the temperature field in injection molding. AIChE J., 1988,34(12): 1959-1972
38. C.Hirt,B.Nichols,Volume of fluid(VOF)method for dynamics of free boundaries,Journal of Computational physics., 1981,39:201-225
39. Charles L.Tucker Ⅲ,Erwin Liang,Stiffness prediction for unidirectional short-fiber composites:Review and evaluation,Composites Science and Technology, 1999, 59, 655-671
40. Gupta M,Santhanam N,Chiang H H,et al, Prediction of Fiber Orientation and Mechanical Properties in short-fiber Reinforced Injection-molded Composites,in Computer Aided Design in Composite Material Technology, Advani s G.Blain W R, Wilde W p,et al,eds,London,New York,1993
41．林兰芬．短纤维增强塑料注射成型中三维纤维取向的数值预测，材料科学与工艺，1998，6(2)
42．吴望一编著，流体力学(上)，北京：北京大学出版社，1983