短纤维增强塑料充填过程中纤维取向的数值模拟和实验分析
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摘要
纤维增强复合材料的机械、物理性能很大程度上依赖于纤维增强的特性,如纤维的取向状态、纤维的长径比等,而纤维取向状态对复合材料物理性能影响的研究更为广泛。在世界范围内,注射成型在塑料制件的生产中都占据着十分重要的地位,而对注塑件中的纤维取向研究多集中于充填阶段。在实际的生产过程中,制件不同部位的纤维取向是差异很大的,当纤维沿某个方向固定取向时,容易引起局部的各向异性而引起制件内部残余应力不均,造成制件收缩不均、翘曲变形等不期望的结果。在众多的纤维悬浮流研究中,通常采用两个Euler角对纤维在空间中的取向状态进行描述,然后通过数值分析的方法获得它们随时间变化的函数表达式,即可获得不同类型流场中的纤维取向。
在本文中,主要有两方面的工作,首先对所建立的圆盘模型中的速度场进行化简并推导,然后在Jeffery运动方程的基础上,通过随体坐标系法和计算机编程对所建立的圆盘模型算例中的纤维取向状态进行数值求解。另一方面通过实验的方法利用偏光显微镜获得两个实际的圆盘制件中的纤维取向情况,并将实验结果与数值分析的结果进行对比讨论。通过数值模拟与实验相结合的方法,得到了圆盘模型中纤维取向的总体情况,主要有以下几点结论：
(1)圆盘模型流场中的纤维沿高度方向分别受到不同的剪切作用和拉伸作用,并且纤维取向不受初始取向角的影响。
(2)在模型的表面层,纤维只受到剪切作用,其取向主要是平行于流场方向,并在较长的时间内处于该取向方向,只在极短的时间内进行翻转。
(3)在模型的中心层,纤维只受到流场的拉伸作用,纤维的取向状态则主要是平行于拉伸方向即垂直于流场方向。
(4)在模型表层和中心层之间的中间层位置,纤维同时受到拉伸作用和剪切作用,其取向情况则是前面两种情况的组合,一部分纤维主要平行于流场方向取向,一部分主要垂直于流场方向取向。并且沿着高度方向,当剪切作用处于主导地位时,纤维将较多地平行于流场方向取向,当拉伸作用占主导地位时,纤维将较多地沿平行于拉伸方向取向。
The mechanical and physical properties of fiber reinforced composites are strongly dependant on the quality of their reinforcement, such as situation of fiber orientation, aspect of fiber and so on, but the research of the influence fiber orientation made on properties of fiber reinforced composites is especially wide. Injection molding still occupies an important position on productions of plastic parts all over the world, however a majority research about fiber orientation of molded parts concentrate on filling stage. In actual manufacturing processes, there is great difference on different position of parts, and that will bring imbalance residual stress due to anisotropy when fibers orient themselves along some direction, in finally some unexpected behavior will be produced, such as shrinkage, warp and so on. In most of research about suspending fluid of fiber, the situation of fiber orientation usually be described with two Euler angles in space, then after the function between the Euler angles and the time's change can be obtained, the situation of the fiber orientation can be got in kinds of flow field.
In this paper, there are mainly two aspects of work, firstly the velocity field of the Center-gated disk model will be reduced, then on the base of Jeffery motion function, the situation of fiber orientation of the model can be obtained through the Co-rotational coordinate system and computer programme. On the other hand, the fiber orientation of two actual disk models can be got through experiment by Polarized optical microscopy(POM), then there will be comparison and discussion between numerical simulation and experiment result. Through combination of numerical simulation and experiment, the general situation of fiber orientation can be got in the Center-gated disk model, and then there are some conclusions below:
(1) The fibers endure different shear action and stretcher action along the height of flow field in the Center-gated disk model, and there is no influence on velocity grads due to initial angle of fiber.
(2) In the surface layer of the model, under pure shear action, the fibers will mainly orient parallel the flow direction and keep along this direction for a long time, but overturn within quite short time.
(3) In the central layer of the model, only stretcher action acts on fibers, and the fiber orientation is mainly parallel the stretcher direction(i.e. perpendicular to the flow direction).
(4) In the layers between the surface layer and the central layer, the fibers will be influenced by both shear action and stretcher action, so the fiber orientation will be combination of two conditions in the front. Some fibers are parallel the flow direction, and others are perpendicular to the flow direction. Along the height of the flow field, most of the fibers will be parallel the flow direction when the shear action is on the dominance, but on the opposite way, the majority fiber will parallel the stretcher direction.
在本文中,主要有两方面的工作,首先对所建立的圆盘模型中的速度场进行化简并推导,然后在Jeffery运动方程的基础上,通过随体坐标系法和计算机编程对所建立的圆盘模型算例中的纤维取向状态进行数值求解。另一方面通过实验的方法利用偏光显微镜获得两个实际的圆盘制件中的纤维取向情况,并将实验结果与数值分析的结果进行对比讨论。通过数值模拟与实验相结合的方法,得到了圆盘模型中纤维取向的总体情况,主要有以下几点结论：
(1)圆盘模型流场中的纤维沿高度方向分别受到不同的剪切作用和拉伸作用,并且纤维取向不受初始取向角的影响。
(2)在模型的表面层,纤维只受到剪切作用,其取向主要是平行于流场方向,并在较长的时间内处于该取向方向,只在极短的时间内进行翻转。
(3)在模型的中心层,纤维只受到流场的拉伸作用,纤维的取向状态则主要是平行于拉伸方向即垂直于流场方向。
(4)在模型表层和中心层之间的中间层位置,纤维同时受到拉伸作用和剪切作用,其取向情况则是前面两种情况的组合,一部分纤维主要平行于流场方向取向,一部分主要垂直于流场方向取向。并且沿着高度方向,当剪切作用处于主导地位时,纤维将较多地平行于流场方向取向,当拉伸作用占主导地位时,纤维将较多地沿平行于拉伸方向取向。
The mechanical and physical properties of fiber reinforced composites are strongly dependant on the quality of their reinforcement, such as situation of fiber orientation, aspect of fiber and so on, but the research of the influence fiber orientation made on properties of fiber reinforced composites is especially wide. Injection molding still occupies an important position on productions of plastic parts all over the world, however a majority research about fiber orientation of molded parts concentrate on filling stage. In actual manufacturing processes, there is great difference on different position of parts, and that will bring imbalance residual stress due to anisotropy when fibers orient themselves along some direction, in finally some unexpected behavior will be produced, such as shrinkage, warp and so on. In most of research about suspending fluid of fiber, the situation of fiber orientation usually be described with two Euler angles in space, then after the function between the Euler angles and the time's change can be obtained, the situation of the fiber orientation can be got in kinds of flow field.
In this paper, there are mainly two aspects of work, firstly the velocity field of the Center-gated disk model will be reduced, then on the base of Jeffery motion function, the situation of fiber orientation of the model can be obtained through the Co-rotational coordinate system and computer programme. On the other hand, the fiber orientation of two actual disk models can be got through experiment by Polarized optical microscopy(POM), then there will be comparison and discussion between numerical simulation and experiment result. Through combination of numerical simulation and experiment, the general situation of fiber orientation can be got in the Center-gated disk model, and then there are some conclusions below:
(1) The fibers endure different shear action and stretcher action along the height of flow field in the Center-gated disk model, and there is no influence on velocity grads due to initial angle of fiber.
(2) In the surface layer of the model, under pure shear action, the fibers will mainly orient parallel the flow direction and keep along this direction for a long time, but overturn within quite short time.
(3) In the central layer of the model, only stretcher action acts on fibers, and the fiber orientation is mainly parallel the stretcher direction(i.e. perpendicular to the flow direction).
(4) In the layers between the surface layer and the central layer, the fibers will be influenced by both shear action and stretcher action, so the fiber orientation will be combination of two conditions in the front. Some fibers are parallel the flow direction, and others are perpendicular to the flow direction. Along the height of the flow field, most of the fibers will be parallel the flow direction when the shear action is on the dominance, but on the opposite way, the majority fiber will parallel the stretcher direction.
引文
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[3]苗利利,杨庆浩,黄方方.注塑工艺制备玻璃纤维增强聚合物研究[J].广州化工,2007,35(1)：28-30
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[6]Strand R, Kim S. Dynamics and rheology of a dilute suspension of dipolar non- spherical particles in an external flow[J]. Rheological Acta,1992,31:94-117
[7]Chung S T, Kwon T H. Coupled analysis of injection molding filling and fiber orientation including in-plane velocity gradient effect[J]. Polymer Composites,1996,17(6):859-872
[8]Greene CY P, Wilkes J O. Numerical analysis of injection molding of glass fiber reinforced thermoplastics part 1:Injection pressure and flow[J]. Polym. Eng. Sci.,1997,37(6): 1019-1035
[9]Givler RC, Crochet MJ, Pipes RB. Fiber Orientation Development in Molding of Polymer Composites[J]. J. Compos,1983,17:330
[10]Advani SG, Tucker Ⅲ CL. Rheological Characterization of Fiber-Filled Polymer Composit-es via Constitutive Modeling[J]. Journal of Rheology,1987,31:751-784
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[18]Dihn S M R C, Armstrong A. Rheological equation state for semi-concentrated fiber suspensions[J]. Journal of Rheology,1984,8(3):207-279
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[31]Altan M C, Rao B N. Closed-form solution for the orientation field in a centre-gated disk[J]. Journal of Rheology,1995,39(3):581-599
[32]Tang L, Altan M C. Entry flow of fibers suspension in a straight channel[J]. Journal of Non-Fluid Mechanics,1995,6:183-216
[33]Jay H. Phelps, Charles L. Tucker Ⅲ. An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics[J]. Journal of Non- newtonian Fluid Mechanic,2009,156:165-176
[34]Marko Hyensjo, Anders Dahlkild. Study of the rotational diffusivity coefficient of fibers in planar contraction flows with varying tubule levels[J]. International Journal of Multiphase Flow,2008,34:894-903
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[2]冯金海,吴靖,周达飞.短纤维复合材料加工中的纤维取向研究[J].玻璃钢/复合材料,1995,(2)：15-20
[3]苗利利,杨庆浩,黄方方.注塑工艺制备玻璃纤维增强聚合物研究[J].广州化工,2007,35(1)：28-30
[4]Gupta M., Wang K K. Fiber orientation and mechanical properties of short-fiber-reinforced injection-molded composites:simulated and experimental results[J]. Polymer Composites, 1993,14:367-382
[5]Leal G, Hinch E J. The rheology of a suspension of nearly spherical particles subject to Brownian rotations[J]. Journal of Fluid Mechanics,1972,55:745-765
[6]Strand R, Kim S. Dynamics and rheology of a dilute suspension of dipolar non- spherical particles in an external flow[J]. Rheological Acta,1992,31:94-117
[7]Chung S T, Kwon T H. Coupled analysis of injection molding filling and fiber orientation including in-plane velocity gradient effect[J]. Polymer Composites,1996,17(6):859-872
[8]Greene CY P, Wilkes J O. Numerical analysis of injection molding of glass fiber reinforced thermoplastics part 1:Injection pressure and flow[J]. Polym. Eng. Sci.,1997,37(6): 1019-1035
[9]Givler RC, Crochet MJ, Pipes RB. Fiber Orientation Development in Molding of Polymer Composites[J]. J. Compos,1983,17:330
[10]Advani SG, Tucker Ⅲ CL. Rheological Characterization of Fiber-Filled Polymer Composit-es via Constitutive Modeling[J]. Journal of Rheology,1987,31:751-784
[11]Jeffery G B. The motion of ellipsoidal particles immersed in a viscous fluid [J]. Journal of Fluid Mechanics,1922, (14):284-304
[12]Jeffery G B. The motion of ellipsoidal particles immersed in a viscous fluid[J]. Proc R Soc-Lond A,1922,102(715):161-179
[13]Bretherton F P. The motion of rigid particles in a shear flow at low Reynolds number [J]. Journal of Fluid Mechanics,1962,14:284-304
[14]Batchelor G K. Slender body theory for particles of arbitrary cross-section in Stokes flow[J]. Journal of Fluid Mechanics,1970,44:419-440
[15]Batchelor G K. The stress system in a suspension of force-free particles[J]. Journal of Fluid Mechanics,1969,1:545-570
[16]Batchelor G K. The stress system in a suspension of force-free particles[J]. Journal of Fluid Mechanics,1970,41:545
[17]Batchelor G K. The stress generated in a non-dilute suspension of elongated particles by pure straining motion[J]. Journal of Fluid Mechanics,1971,46:813-829
[18]Dihn S M R C, Armstrong A. Rheological equation state for semi-concentrated fiber suspensions[J]. Journal of Rheology,1984,8(3):207-279
[19]Ausias G., Agassant JF, Vincent M, et al. Rheology of short glass fiber reinforced polypropylene[J]. Journal of Rheology,1992,36(4):525-542
[20]Batchelor G K. The stress system in a suspension of force-free particles[J]. Journal of Fluid Mechanics,1969,1:545-570
[21]Tucker C L. Flow regimes for fiber suspensions in narrow gaps [J]. Journal of Non- newtoni an Fluid Mechanic,1991,39:239-268
[22]Folgar F, Tucker C L. Orientation behavior of fibers in concentrated suspensions[J]. Journal of Reinforced Plastics and Composites,1984,3:98-119
[23]Advani S G, Tucker Ⅲ C L. The use of tensors to describe and predict fiber orientation in short fiber composites[J]. Journal of Rheology,1987,31(8):751-784
[24]Advani S G, Tucker Ⅲ C L. Rheological characterization of fiber-filled polymer composites via constitutive modeling[J]. Journal of Rheology,1987,31:751-784
[25]Cintra J S, Tucker Ⅲ C L. Orthotropic closure approximation for flow-induced fiber orientation[J]. Journal of Rheology,1995,39:1095-1122
[26]Advani S G, Tucker Ⅲ C L. Closure approximation for three-dimensional structure tensors[J]. Journal of Rheology,1990,34(3):367-386
[27]Shaqfeh ESG, Koch D L. Orientational dispersion of fibers in extensional flows[J]. Physics Fluids A:Fluids Dynamics,1990,2(7):1077-1093
[28]Fischer G, Eyerer P. Measuring spatial orientation of short fiber-reinforced thermoplastics by image analysis[J]. Polymer Composites,1988,9:253-265
[29]Kim E G, Park J K, Jo S H. A study on fiber orientation during the injection molding of fiber-reinforced polymeric composites[J]. Journal of Materials Processing Technology, 2001,111:225-232
[30]Stover C A, Koch D L, Cohen C. Observations of fiber orientation in simple shear flow of semi-dilute suspensions[J]. Journal of Fluid Mechanics,1992,238:277-296
[31]Altan M C, Rao B N. Closed-form solution for the orientation field in a centre-gated disk[J]. Journal of Rheology,1995,39(3):581-599
[32]Tang L, Altan M C. Entry flow of fibers suspension in a straight channel[J]. Journal of Non-Fluid Mechanics,1995,6:183-216
[33]Jay H. Phelps, Charles L. Tucker Ⅲ. An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics[J]. Journal of Non- newtonian Fluid Mechanic,2009,156:165-176
[34]Marko Hyensjo, Anders Dahlkild. Study of the rotational diffusivity coefficient of fibers in planar contraction flows with varying tubule levels[J]. International Journal of Multiphase Flow,2008,34:894-903
[35]Mina Djalili-Moghaddam, Staffan Toll. A model for short-range interactions in fiber suspensions[J]. Journal of Non- newtoni an Fluid Mechanic,2005,132,73-83
[36]叶红宁,周持兴,张勇.高浓度纤维悬浮体系中纤维取向的模拟及测定[J].上海交 通大学学报,1994,28：114-119
[37]叶红宇,周持兴.纤维增强塑料在挤出过程中纤维取向的模拟[J].高分子材料科学与工程,1994,10(1)：73-78
[38]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[J].上海交通大学学报,1999,33(2)
[39]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[J].化工学报,1999,50(4).443-448
[40]林兰芬,董金祥.纤维增强塑料注塑成型集成仿真建模[J].复合材料学报,1999,16(3)：103-109
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