SMC模压流动中纤维取向的研究与模拟
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摘要
片状模塑料(简称SMC)模压成型工艺是近年来在国内外受到普遍重视的短纤维增强复合材料成型工艺。在模塑料从熔融状态到固体状态的过程中，纤维／基体混合物在模具中发生流动变形，变形改变了纤维的取向。在流动结束后，纤维的最终取向也将保留在固体部件中，纤维的取向状态对部件的力学和物理性能都有很大的影响。因而研究短纤维增强聚合物的流变性能，流动过程中的纤维取向就显得极为重要。同时，准确的模拟对目前的加工过程中的错误诊断以及流程控制都有重要意义。本文在国家自然科学基金项目的资助下，研究了SMC的模压流动及其充模过程中的纤维取向行为。
在文章的理论部分，首先分析了SMC熔体的流变行为，基于流体力学基本理论，引用广义Hele-Shaw模型作为SMC模压流动的理论模型。接着研究了在流动的悬浮液中描述和预测纤维取向的理论，导出了二维流场中纤维取向的数学模型。在数值计算与分析中，根据SMC模压流动分析和纤维定向分析的数学模型，编制SMC模压流动及充模过程中纤维取向的计算机程序。程序中用有限单元控制体方法模拟模压流动，用表征纤维取向的张量和有限元伽辽金方法来解决瞬时纤维取向方程，用计算机图形原理编程实现对SMC流动轨迹、纤维取向分布的计算机模拟。最后通过实例对二维薄板在恒定合模速率下的纤维取向进行了计算机模拟计算，其结果对SMC铺料的方式、模具设计以及压制工艺参数的最终确定具有一定的理论指导意义。
As an important process of fibre-reinforced composites, sheet molding compound (SMC) technology draws worldwide attention recently. The orientation of the reinforcing fibres changes during the deformation process, and when the matrix solidifies the final orientation pattern is retained in the part. This orientation plays a key role in determining the mechanical and physical properties of the finished product. Therefore, it is very important to have some insight into the change of fibre orientation during flow.
At first the rheology behavior of SMC is analyzed and a Generalized Hele-Shaw model (GHS), based on the theory of fluid mechanics, is adopted as theory model of compression molding. Then theories of describing and predicting fibre orientation in flowing suspensions are investigated and a mathematics model of planar orientation in a two-dimensional domain is derived. In the numerical methods section, a finite element/control volume mold filling simulation, a tensor representation of fibre orientation and a finite element solution of the transient fibre orientation equations are combined in the program. The input data and output results are visualized by means of finite element software. Finally the orientation states of 2-D thin plate are simulated in a certain velocity. The numerical results will be of a certain theoretical function to placement of SMC charge, design of mold and optimization of the technological parameters.
在文章的理论部分，首先分析了SMC熔体的流变行为，基于流体力学基本理论，引用广义Hele-Shaw模型作为SMC模压流动的理论模型。接着研究了在流动的悬浮液中描述和预测纤维取向的理论，导出了二维流场中纤维取向的数学模型。在数值计算与分析中，根据SMC模压流动分析和纤维定向分析的数学模型，编制SMC模压流动及充模过程中纤维取向的计算机程序。程序中用有限单元控制体方法模拟模压流动，用表征纤维取向的张量和有限元伽辽金方法来解决瞬时纤维取向方程，用计算机图形原理编程实现对SMC流动轨迹、纤维取向分布的计算机模拟。最后通过实例对二维薄板在恒定合模速率下的纤维取向进行了计算机模拟计算，其结果对SMC铺料的方式、模具设计以及压制工艺参数的最终确定具有一定的理论指导意义。
As an important process of fibre-reinforced composites, sheet molding compound (SMC) technology draws worldwide attention recently. The orientation of the reinforcing fibres changes during the deformation process, and when the matrix solidifies the final orientation pattern is retained in the part. This orientation plays a key role in determining the mechanical and physical properties of the finished product. Therefore, it is very important to have some insight into the change of fibre orientation during flow.
At first the rheology behavior of SMC is analyzed and a Generalized Hele-Shaw model (GHS), based on the theory of fluid mechanics, is adopted as theory model of compression molding. Then theories of describing and predicting fibre orientation in flowing suspensions are investigated and a mathematics model of planar orientation in a two-dimensional domain is derived. In the numerical methods section, a finite element/control volume mold filling simulation, a tensor representation of fibre orientation and a finite element solution of the transient fibre orientation equations are combined in the program. The input data and output results are visualized by means of finite element software. Finally the orientation states of 2-D thin plate are simulated in a certain velocity. The numerical results will be of a certain theoretical function to placement of SMC charge, design of mold and optimization of the technological parameters.
引文
[1]梁国正，顾媛娟．．模压成型技术，北京：化学工业出版社，1999．
[2]P. Hubert and A. Poursatip.. A review of flow and compaction modelling relevant to thermoset matrix laminate processing, Journal of Reinforced plastic and composites, V17,No.4,1998.
[3]Owen, M. J., Thomas, D. H Flow, fibre orientation and mechanical properties relationships in polyester DMC PROC. 33rd Ann.Tech conf., SPIRP/Cdiv., Sect.20-B(1978)
[4]X. T. Pham and F. Trochu.. Simulation of compression resin transfer molding to manufacture thin composite shells, Polymer Composites, V20,No.3, 1999
[5]顾国芳，浦鸿汀，聚合物流变学基础，上海：同济大学出版社．2000．
[6]C. C. Lee, F.Folgar and C. L. Tucker..Simulation of compression molding for fiber-reinforced thermosetting polymers. Journal of Engineering for Industry, Vol.26, 1984.
[7]C. L. Tucker and F. Folgar..A moldel of compression mold filling. Polymer Engineering and Science, Vol.23,No.2,1983.
[8]S. M. Dinh and R. C. Armstrong.. A Rheoloical Equation of State foe Semiconcentrated Fibre Suspensions, Journal of Rheolog, 28(3). 207-227(1984)
[9]K. O. and F. R. Young. Prediction of Fibre Orientation in the Thickness Plane During Flow Molding of Short Fibre Composites. Polymer Composites. April 1995,Vol.16,No.
[10]Takaaki Matsuoka and Hideroh Taahashi.. Prediction of Fibre Orientation in Injection Molded Parts of Short-Fibre-Reinforced Thermoplastics. Polymer Engineering and Science, August 1990, Vol.30, No. 1
[11]H. D. Frahan, and M. J. Crochet. Numerical Prediction of Fibre Orientation in Injection Molding. Polymer Engineering and Science Febreary. 1992,Vol.32, No. 4
[12]TSEUDO HIRAI.Rheology of Carbon Fibre Composite Prepreg Materials. Doshisha University,Kyoto,Japan.
[13]林兰芬 董金祥．．纤维增强塑料的充模流动和纤维取向的耦合仿真模型，化工学报，1999年8月，第50卷第4期。
[14]陈兴 李德群 卢义强．．注塑流动过程中的计算机模拟，中国塑料，1997年5月，第11卷第3期。
[15]B.Mlekusch.. Fibre Orientation in Short-fibre-reinforced Thermoplastics Ⅱ. Quantitative Measurements by Image Analysis Composites Science and
Technology, 59 (1999) 547-560
[16] J.Hine and R_A.Duckett.. Measuring the Development of Fibre Orientation during the Melt Extrusion of Short Glass Fiber Reinforced polypropylene Composites, PART A 28A (1997) 949-958
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[22] V.R.Voller and S.Peng ..An Algorithm for Analysis of Polymer Filling of Molds. Polymer Engineering and Science, November 1995,Vol.35,No.22
[23] Xjuan-tan Pham and F.Trochu. Simulation of compression Resin Transfer Molding to Manufacture Thin composite Shells. Polymer Composites, June 1999,Vol.20,No,3
[24] M. Pinfold and G. Calvert..The Effect of Material Flow on the Stress Analysis of an SMC Component. Composites Structure, 32 (1995) 549-555
[25] B.R.Whiteside and P.D.Coates..Glass Fiber Orientation within Injection Moulded Automotive Pedal Simulation and Experimental Studies.Plastics, Rubber and Composites,.2000 Vol.29, No. 1
[26] G.Ausias and J.F.Agassant.. Rheology of Short Glass Fiber Reinforced Polypropylene.J. Rhelo..36(4) , May 1992
[27] C. L. Tucker III..Heat transfer and reaction issues in liquid composite molding, Polymer Composites, V17, No. 1,1996．
[28] D. R. Calhoun, S. Yalvac, D. G. Wetters and C. A. Raeck..Critical issues in moldel verification for the resin transfer molding process, Polymer Composites,V17,No.l,1996．
[29] M. A. dweib and C. M. 0 Bradaigh.. anisotropic modeling of isothermal sqeezing flow of glass-mat reinforced thermoplastic(GMT), Polymer Composites, V19,No.5,1998．
[30] G.Kotsikos, J.H.bland and A.G. Gibson..Rheological characterization of commercial glass mat thermoplastic(GMTs) by squeeze flow testing, Polymer Composites, V20, No. 1,1999．
[31] M. D. Wakeman, T. A. cain, C. D. Rudd, R. Brooks and A. C. Long.. Compression moulding of glass and polypropylene composites for optimised macro-and micro-mechanical properties-1 commingled glass and polypropylene, Composites Science and Technology, V58,1998
[32] R. Blancon, J. J. Martinez-vega, G. Merle, M. Revellino, G. Camino, A. Y. Polishchuk and M. P. Luda..Durability of sheet molding compounds., influence of hydrothermal aging on morphology and molecular mobility at microscopic scale, Polymer engineering and science, V37,No. 10, 1997．
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[34] Glettler, L.T.. Flow orientation of short fibres composites JOURNEL OF COMPOSITES MATERRIAL Vol. 3,p.244(1969)
[35] F.Folgar and C.L.Tucker.. Orientation behavior of fibres in concentrated suspensions, J. Renif. Plast. Compos., Vol. 3,pp.98-119 (1984)
[36] Jeffery, G. B..The motion of ellipsoidal particles immersed in a viscous fluid Proc..Roy.Soc.,A102,P. 161(1923)
[37] F.Folgar and C. L.Tucker.. Orientation behavior of fibres in concentrated suspensions, J. Renif. Plast. Compos., Vol. 3,pp.98-119 (1984)
[38] Scidhar Ranganatnan and S.C.Advani..Fibre-fibre interactions in homogeneous flows of nondilute suspensions, J Rheol 35(8) , 1499-1522(1991)
[39] Advani ,S.G. and Tucker ,C.L..A tensor description of fibre orientation in short fibre composites, SPE Tech .pap., Vol. 31, pp. 1113-1118(1985)
[40] Folkes ,M.J.and Russell..Orientation effects during the flow of short fibre reinforced thermoplasticsm, Polymer, Vol. 29,pp.751-753(1980)
[41] Kyeong-hee Han and Yong-taek IM ..Modified Hybrid closure Approximation for Prediction of Flow-induced Orientation. J. Rheol,43(3) .May/June 1999．
[42] 晏石林，梅启林，沈大荣，吴代华，片状模塑料模压流动仿真分析，复合材料学 报,V14 (2) ,1997．
[43]晏石林，梅启林，王建平．．SMC成型加工中的计算机模拟，西安公路交通大学学报，V17，1997．
[44]林兰芬，董金祥．．纤维增强塑料的充模流动和纤维取向的耦合仿真模型，化工学报，V50，No．4，1999．
[45]梅启林．．酚醛SMC的流变性及模压流动的计算机模拟研究，武汉工业大学硕士学位论文，1992．
[46]朱以文等．．微机有限元前后处理系统ViziCAD及其应用，北京：科学技术文献出版社，1993．
[47]P. Lazzarin, G. Molina, L. Molinari and M. Quaresimin.. Numerical simulation of SMC component moulding, Engineering Materials, V144,1998.
[48]M. R. Barone and T. A. Osswald.. A boundary element analysis of flow in sheet molding compound, Polymer Composites, V9,No.2, 1988.
[49]C. M. Lin and C. I. Weng.. Simulation of compression molding for sheet molding compound considering the anisotropic effect, Composites,V27A(12),1996
[50]E. W. Liang and C. W. Tucker.. A finite element method for flow in compression molding of thin and thick parts, Composites,V27A(12),1996
[51]H. Hamada K. Futamata and H.Naito.. Curing and deformation analysis in SMC compression molding, Composites Processing and Microstructure, ICCM-11, Gold Coast, Australia, 14th-18th July 1997.
[52]G. Kotsikos, J. H. Bland and A. G. Gibson.. Squeeze flow testing of glass mat thermoplastic material, Composites,V27A(12),1996.
[53]Y. E Chen, V. R. Voller and K. A. Stelson.. Time-implicit fixed and deforming grid solutions for compression molding filling, Polymer Composites V17,No.3, 1996.
[54]J. M. Castro and R. M. Griffith.. Sheet molding compound compression-molding flow, Polymer engineering and science, V29,No.10, 1989.
[55]G. Kotsikos and A. G. Gibson.. Investigation of the squeeze flow behaviour of sheet molding compounds (SMC), Composites,V29A, 1998.
[56]G. Lielens, P. Pirotte, A. Couniot, F. Dupret and R. Keunings.. Prediction of thermo-mechanical properties for compression moulded composites, Composites,V29A,1998.
[57]T. Mei and M. R. Piggott.. Mesostructure development during molding of sheet molding compounds, Polymer Composites V17,No.4, 1996.
[58]C. M. Lin, C. I. Weng and C. T. Ho.. Anisotropy in sheet molding compounds during compression molding, Polymer Composites, V18,No., 1997.
[59]G. Grasso, G. L. Rosa, S. M. Oliveri and A. Ristano.. thermoelastic analysis of element in composite material, Key engineering materials, V144, 1998.
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[61]M. R. Barone and T. A. Osswald.. Boundary integral equations for analysis the flow of a chopped fiber reinforced polymer compound in compression molding, Journal of non-newtonian fluid mechanics, V26,1987.
[62]L. M. Matuana, C. B. Papk and J. J. Balatinecz.. The effect of low levels of plasticizer on the rheological and mechanical properties of polyvinyl chloride/newsprint-fiber composites, Journal of Vinyl & Additive technology, V3,No.4, 1997.
[63]S. L. Yan, Z. G. Tang and M. Liu.. Numerical simulation of sheet molding compound in compression molding process. Second Asian-Australiasian Conference on Composite Materials "Composites Technologies for the New Millennium", 2000.
[64]唐致刚，晏石林，郭建娟．．SMC模压流动模拟的固定网格法，固体力学学报(计算力学专辑)，2000．
[65]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，Vol，23，NO．11
[66]唐致刚，片状模塑料模压流动与计算机模拟研究，武汉理工大学硕士论文，2001
[2]P. Hubert and A. Poursatip.. A review of flow and compaction modelling relevant to thermoset matrix laminate processing, Journal of Reinforced plastic and composites, V17,No.4,1998.
[3]Owen, M. J., Thomas, D. H Flow, fibre orientation and mechanical properties relationships in polyester DMC PROC. 33rd Ann.Tech conf., SPIRP/Cdiv., Sect.20-B(1978)
[4]X. T. Pham and F. Trochu.. Simulation of compression resin transfer molding to manufacture thin composite shells, Polymer Composites, V20,No.3, 1999
[5]顾国芳，浦鸿汀，聚合物流变学基础，上海：同济大学出版社．2000．
[6]C. C. Lee, F.Folgar and C. L. Tucker..Simulation of compression molding for fiber-reinforced thermosetting polymers. Journal of Engineering for Industry, Vol.26, 1984.
[7]C. L. Tucker and F. Folgar..A moldel of compression mold filling. Polymer Engineering and Science, Vol.23,No.2,1983.
[8]S. M. Dinh and R. C. Armstrong.. A Rheoloical Equation of State foe Semiconcentrated Fibre Suspensions, Journal of Rheolog, 28(3). 207-227(1984)
[9]K. O. and F. R. Young. Prediction of Fibre Orientation in the Thickness Plane During Flow Molding of Short Fibre Composites. Polymer Composites. April 1995,Vol.16,No.
[10]Takaaki Matsuoka and Hideroh Taahashi.. Prediction of Fibre Orientation in Injection Molded Parts of Short-Fibre-Reinforced Thermoplastics. Polymer Engineering and Science, August 1990, Vol.30, No. 1
[11]H. D. Frahan, and M. J. Crochet. Numerical Prediction of Fibre Orientation in Injection Molding. Polymer Engineering and Science Febreary. 1992,Vol.32, No. 4
[12]TSEUDO HIRAI.Rheology of Carbon Fibre Composite Prepreg Materials. Doshisha University,Kyoto,Japan.
[13]林兰芬 董金祥．．纤维增强塑料的充模流动和纤维取向的耦合仿真模型，化工学报，1999年8月，第50卷第4期。
[14]陈兴 李德群 卢义强．．注塑流动过程中的计算机模拟，中国塑料，1997年5月，第11卷第3期。
[15]B.Mlekusch.. Fibre Orientation in Short-fibre-reinforced Thermoplastics Ⅱ. Quantitative Measurements by Image Analysis Composites Science and
Technology, 59 (1999) 547-560
[16] J.Hine and R_A.Duckett.. Measuring the Development of Fibre Orientation during the Melt Extrusion of Short Glass Fiber Reinforced polypropylene Composites, PART A 28A (1997) 949-958
[17] P.Lazzarin and M.Quaresimin,. Numerical Simulation of SMC Component Moulding, Key Engineering Materials,. Vol. 144(1998) pp. 191-200
[18] Chao-Ming L and Cheng-I W... Simulation of Compression Molding for sheet Molding compound considering the Anisotropic Effect,.Polymer Composites, February 1999, Vol.20, No. 1
[19] M.Gupta and K.K.Wang... Fibre Orientation and Mechanical Properties of Short-fibre-reinforced Injection-Molded Composites.. Simulated and Experimental Results. Polymer Composites, October 1993,Vol. 14,No.5
[20] F.FOLGAR and C.L.TUCKER..Simulation of Compression Molding for Fibre-Reinforced Thermosetting Polymers. Transactions of the ASME May.l984,Vol.l06
[21] B.Mlekusch, and W.Geymayer.Fibre Orientation in short-fibre-reinforced thermoplastics I. Contrast enhancement for image analysis. Composites Science and Technology ,59(1999)
[22] V.R.Voller and S.Peng ..An Algorithm for Analysis of Polymer Filling of Molds. Polymer Engineering and Science, November 1995,Vol.35,No.22
[23] Xjuan-tan Pham and F.Trochu. Simulation of compression Resin Transfer Molding to Manufacture Thin composite Shells. Polymer Composites, June 1999,Vol.20,No,3
[24] M. Pinfold and G. Calvert..The Effect of Material Flow on the Stress Analysis of an SMC Component. Composites Structure, 32 (1995) 549-555
[25] B.R.Whiteside and P.D.Coates..Glass Fiber Orientation within Injection Moulded Automotive Pedal Simulation and Experimental Studies.Plastics, Rubber and Composites,.2000 Vol.29, No. 1
[26] G.Ausias and J.F.Agassant.. Rheology of Short Glass Fiber Reinforced Polypropylene.J. Rhelo..36(4) , May 1992
[27] C. L. Tucker III..Heat transfer and reaction issues in liquid composite molding, Polymer Composites, V17, No. 1,1996．
[28] D. R. Calhoun, S. Yalvac, D. G. Wetters and C. A. Raeck..Critical issues in moldel verification for the resin transfer molding process, Polymer Composites,V17,No.l,1996．
[29] M. A. dweib and C. M. 0 Bradaigh.. anisotropic modeling of isothermal sqeezing flow of glass-mat reinforced thermoplastic(GMT), Polymer Composites, V19,No.5,1998．
[30] G.Kotsikos, J.H.bland and A.G. Gibson..Rheological characterization of commercial glass mat thermoplastic(GMTs) by squeeze flow testing, Polymer Composites, V20, No. 1,1999．
[31] M. D. Wakeman, T. A. cain, C. D. Rudd, R. Brooks and A. C. Long.. Compression moulding of glass and polypropylene composites for optimised macro-and micro-mechanical properties-1 commingled glass and polypropylene, Composites Science and Technology, V58,1998
[32] R. Blancon, J. J. Martinez-vega, G. Merle, M. Revellino, G. Camino, A. Y. Polishchuk and M. P. Luda..Durability of sheet molding compounds., influence of hydrothermal aging on morphology and molecular mobility at microscopic scale, Polymer engineering and science, V37,No. 10, 1997．
[33] C. C. Lee, F.Folgar and C. L. Tucker.. Simulation of compression molding for fiber-reinforced thermosetting polymers, Journal of Engineering for Industry, V106, 1984．
[34] Glettler, L.T.. Flow orientation of short fibres composites JOURNEL OF COMPOSITES MATERRIAL Vol. 3,p.244(1969)
[35] F.Folgar and C.L.Tucker.. Orientation behavior of fibres in concentrated suspensions, J. Renif. Plast. Compos., Vol. 3,pp.98-119 (1984)
[36] Jeffery, G. B..The motion of ellipsoidal particles immersed in a viscous fluid Proc..Roy.Soc.,A102,P. 161(1923)
[37] F.Folgar and C. L.Tucker.. Orientation behavior of fibres in concentrated suspensions, J. Renif. Plast. Compos., Vol. 3,pp.98-119 (1984)
[38] Scidhar Ranganatnan and S.C.Advani..Fibre-fibre interactions in homogeneous flows of nondilute suspensions, J Rheol 35(8) , 1499-1522(1991)
[39] Advani ,S.G. and Tucker ,C.L..A tensor description of fibre orientation in short fibre composites, SPE Tech .pap., Vol. 31, pp. 1113-1118(1985)
[40] Folkes ,M.J.and Russell..Orientation effects during the flow of short fibre reinforced thermoplasticsm, Polymer, Vol. 29,pp.751-753(1980)
[41] Kyeong-hee Han and Yong-taek IM ..Modified Hybrid closure Approximation for Prediction of Flow-induced Orientation. J. Rheol,43(3) .May/June 1999．
[42] 晏石林，梅启林，沈大荣，吴代华，片状模塑料模压流动仿真分析，复合材料学 报,V14 (2) ,1997．
[43]晏石林，梅启林，王建平．．SMC成型加工中的计算机模拟，西安公路交通大学学报，V17，1997．
[44]林兰芬，董金祥．．纤维增强塑料的充模流动和纤维取向的耦合仿真模型，化工学报，V50，No．4，1999．
[45]梅启林．．酚醛SMC的流变性及模压流动的计算机模拟研究，武汉工业大学硕士学位论文，1992．
[46]朱以文等．．微机有限元前后处理系统ViziCAD及其应用，北京：科学技术文献出版社，1993．
[47]P. Lazzarin, G. Molina, L. Molinari and M. Quaresimin.. Numerical simulation of SMC component moulding, Engineering Materials, V144,1998.
[48]M. R. Barone and T. A. Osswald.. A boundary element analysis of flow in sheet molding compound, Polymer Composites, V9,No.2, 1988.
[49]C. M. Lin and C. I. Weng.. Simulation of compression molding for sheet molding compound considering the anisotropic effect, Composites,V27A(12),1996
[50]E. W. Liang and C. W. Tucker.. A finite element method for flow in compression molding of thin and thick parts, Composites,V27A(12),1996
[51]H. Hamada K. Futamata and H.Naito.. Curing and deformation analysis in SMC compression molding, Composites Processing and Microstructure, ICCM-11, Gold Coast, Australia, 14th-18th July 1997.
[52]G. Kotsikos, J. H. Bland and A. G. Gibson.. Squeeze flow testing of glass mat thermoplastic material, Composites,V27A(12),1996.
[53]Y. E Chen, V. R. Voller and K. A. Stelson.. Time-implicit fixed and deforming grid solutions for compression molding filling, Polymer Composites V17,No.3, 1996.
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