纤维增强聚合物复合材料力学性能的数值预测
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摘要
纤维增强塑料复合材料以其质量轻、强度高、易于成型加工等特点被广泛应用于汽车、建筑等行业。对于此类材料的力学性能的预测多采用层合板理论,结合纤维按照单一方向取向时的力学性能进行计算。对单向取向的纤维增强塑料复合材料力学性能进行预测时,通常使用Tandon-Weng模型,一般认为,此模型的计算过程更加简便,结果也相对准确。
但是,纤维单一取向的注塑制品在实际中是不存在的,因此Tandon-Weng模型无法得到实验的验证,其实用性也打了折扣。本文以单一取向的纤维增强塑料复合材料为研究对象,在二维情况下通过有限元数值方法对Tandon-Weng模型的正确性进行了初步的验证。
首先,本文根据三维情况下Tandon-Weng模型的推导过程,推导了Eshelby张量在二维情况下的表达式并对Tandon-Weng模型的计算进行了必要的简化。然后,在纤维周期性均匀分布的情况下,对复合材料建立二维平面模型、采用四节点四边形单元进行网络划分并编写了有限元数值计算程序。最后,在不同的纤维长径比、体积含量和纤维分布形态下,对比了Tandon-Weng模型和有限元数值方法的计算结果。
通过本文的研究初步证明了Tandon-Weng模型的局限性：在对单向取向的纤维增强复合材料力学性能进行预测时,此模型并不适用于所有情况；对于纤维周期性均匀排列的情况,此模型无法反映纤维的分布形态对复合材料力学性能的影响。对Tandon-Weng模型的修正以及在纤维非周期性排列时其正确性的验证有待进一步深入的研究。
Fiber Reinforced Polymer (FRP) is a type of composite, which is widely used in flight, car manufacturing and architecture for its light weight, high modules and covenant processing. Usually, Tandon-Weng model is used to predict the mechanical properties of the composite in which fibers are oriented in a single direction. Generally, Tandon-Weng model is relatively accurate and its calculation is simpler compared with other models.
However, Tandon-Weng model cannot be proved by experiments because samples produced by injection, in which fibers are single-direction oriented, cannot exist. The practicability of this model reduced therefore. The object of this thesis is the single direction oriented FRP, and the verification of the Tandon-Weng model is carried out using the Finite Element Method at the 2D condition.
First of all, the expression of the Eshelby tensor at 2D condition is deduced and the Tandon-Weng model is simplified for 2D problems, according to the deduction with 3D problems. Then, a 2D plane model is created for the composite, in which the distribution of fibers is regular and uniform, that is meshed using 2-nodes rectangular element. A Finite Element Method program is coded and compiled. At last, when the mechanical properties of the composite are calculated using the two methods with different fiber volume percentages, fiber length-radius-ratios and fiber distribution states, the results are compared as well.
The study of this thesis proved that, the Tandon-Weng model has a defect. It is not precise for every problem in prediction of single direction oriented FRP composite. When fibers in the composite are regularly distributed, the Tandon-Weng model cannot indicate the effect of fibers'distribution state on the mechanical properties of the composite. More studies should be carried out to revise the Tandon-Weng model and prove its correctness at the condition that fibers are randomly distributed.
但是,纤维单一取向的注塑制品在实际中是不存在的,因此Tandon-Weng模型无法得到实验的验证,其实用性也打了折扣。本文以单一取向的纤维增强塑料复合材料为研究对象,在二维情况下通过有限元数值方法对Tandon-Weng模型的正确性进行了初步的验证。
首先,本文根据三维情况下Tandon-Weng模型的推导过程,推导了Eshelby张量在二维情况下的表达式并对Tandon-Weng模型的计算进行了必要的简化。然后,在纤维周期性均匀分布的情况下,对复合材料建立二维平面模型、采用四节点四边形单元进行网络划分并编写了有限元数值计算程序。最后,在不同的纤维长径比、体积含量和纤维分布形态下,对比了Tandon-Weng模型和有限元数值方法的计算结果。
通过本文的研究初步证明了Tandon-Weng模型的局限性：在对单向取向的纤维增强复合材料力学性能进行预测时,此模型并不适用于所有情况；对于纤维周期性均匀排列的情况,此模型无法反映纤维的分布形态对复合材料力学性能的影响。对Tandon-Weng模型的修正以及在纤维非周期性排列时其正确性的验证有待进一步深入的研究。
Fiber Reinforced Polymer (FRP) is a type of composite, which is widely used in flight, car manufacturing and architecture for its light weight, high modules and covenant processing. Usually, Tandon-Weng model is used to predict the mechanical properties of the composite in which fibers are oriented in a single direction. Generally, Tandon-Weng model is relatively accurate and its calculation is simpler compared with other models.
However, Tandon-Weng model cannot be proved by experiments because samples produced by injection, in which fibers are single-direction oriented, cannot exist. The practicability of this model reduced therefore. The object of this thesis is the single direction oriented FRP, and the verification of the Tandon-Weng model is carried out using the Finite Element Method at the 2D condition.
First of all, the expression of the Eshelby tensor at 2D condition is deduced and the Tandon-Weng model is simplified for 2D problems, according to the deduction with 3D problems. Then, a 2D plane model is created for the composite, in which the distribution of fibers is regular and uniform, that is meshed using 2-nodes rectangular element. A Finite Element Method program is coded and compiled. At last, when the mechanical properties of the composite are calculated using the two methods with different fiber volume percentages, fiber length-radius-ratios and fiber distribution states, the results are compared as well.
The study of this thesis proved that, the Tandon-Weng model has a defect. It is not precise for every problem in prediction of single direction oriented FRP composite. When fibers in the composite are regularly distributed, the Tandon-Weng model cannot indicate the effect of fibers'distribution state on the mechanical properties of the composite. More studies should be carried out to revise the Tandon-Weng model and prove its correctness at the condition that fibers are randomly distributed.
引文
[1]益小苏,范欣愉.大飞机复合材料技术引领纤维产业发展的思考[J].高科技纤维与应用,2009,34(4)：1-8
[2]陈祥宝,张宝艳,邢丽英.先进树脂基复合材料技术发展及应用现状[J].中国材料进展,2009,28(6)：2-11
[3]常冬艳,王春红.纤维增强塑料在汽车领域的应用[J].非织造布,2006,14(3)：20-32
[4]王建国,郭建龙,屈泽华.碳纳米管的氨基化对环氧树脂力学性能的影响[J].工程塑料应用,2006,34(12)：8-11
[5]Andrews, Wiesenberger MC. Carbon Nanotube Polymer Composites[J]. Current Opinion in Solid State and Materials Science,2004.08.1:31
[6]欧育湘,辛菲,赵毅等.聚合物/碳纳米管纳米复合材料的制备[J].中国塑料,2006,08：1-6
[7]计国庆.玻璃钢复合材料应用于道路护栏的可行性研究[J].城市道桥与防洪,2006,04：49-51
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[13]陈浩.复合材料性能设计的细观力学原理与计算机辅助系统[D].[硕士学位论文].北京工业大学,2004
[14]S. Harish, D. Peter Michael, A. Bensely, D. MohanLal, A. Rajadurai. Mechanical Property Evaluation Of Natural Fiber Coir Composite[J]. Materials Characterization,2009,60:44～ 49
[15]T.W. Chou, S. Nomura. Fiber orientation effects on the thermoelastic properties of short fiber composites[J]. Fiber Science and Technology,1980,14:279～291
[16]林郁彦,冼杏娟.纤维取向性对短纤维增强复合材料力学性能的影响[J].机械工程材料,1980,6：58～62
[17]Yi Pan, Lucian Iorga, Assimina A. Pelegri. Analysis Of 3D Random Chopped Fiber Reinforced Composites Using Fern And Random Sequential Adsorption[J]. Computational Materials Science,2008,43:450～461
[18]ChaoHsun Chen, ChiangHo Cheng. Effective Elastic Moduli Of Misoriented Short Fiber Composites[J]. Int. J. Solids Structures,1996,33 (17):2519～2539
[19]张亚芳,齐雷,张春梅.增强短纤维长径比对复合材料力学性能的影响[J].广州大学学报(自然科学版),2008,7(4)：32～34
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[21]Hill R. Theory of Mechanical Properties of Fiber Strengthened Materials[J]. Journal of the Mechanics and Physics of Solids,1964,12 (12):199～212
[22]Christensen R M, Lo K H. Solutions for Effective Shear Properties in the Phase Sphere and Cylinder Models[J]. Journal of the Mechanics and Physics of Solids,1979,27:315～330
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[27]Hashin Z, Rosen BW. The Elastic Moduli Of Fiber-Reinforced Materials[J]. Journal of Applied. Mechanics,1964, (13):223～232
[28]Hashin Z. On Elastic Behavior Of Fiber Reinforced Materials Of Arbitrary Transverse Phase Geometry[J]. Journal of Mechanics and Physics of Solids,1965, (13):119～134
[29]王连生.细观力学有限元法预测微米短纤维复合材料的有效弹性性能[D].[硕士学位论文].太原：中北大学,2009.06
[30]孙爱芳,刘敏珊,董其伍.短切纤维增强复合材料拉伸强度的预测[J].材料研究学报,2008,22(3)：333-336
[31]K.Zhu, S.Schmauder. Prediction Of The Failure Properties Of Short Fiber Reinforced Composites With Metal And Polymer Matrix[J]. Computational Materials Sicence,2003, 28:743～748
[32]李宁,龚旭.纤维增加复合材料的有效模量预测[J].辽宁省交通高等专科学校学报,2006,8(4)：29-31
[33]张华山,黄争鸣.纤维增强复合材料弹塑性性能的细观研究[J].复合材料学报,2008,25(5)：157～162
[34]方岱宁,刘铁旗.纤维增强高分子聚合物基复合材料有效性能的三维数值分析[J].复合材料学报,1997,14(3)：81-86
[35]赵延军.短纤维增强复合材料力学通性的预测研究.[硕士学位论文].郑州：郑州大学,2004.05
[36]董燕妮.短纤维增强注塑制品力学性能预测.[硕士学位论文].郑州：郑州大学,2007.04
[37]J.D. Eshelby. The Elastic Determination Of The Elastic Field Of An Ellipsoidal Inclusion And Related Problems[J]. Proceedings Of Royal Society Of London, A241:376～396
[38]J.D. Eshelby. The Elastic Field Outside An Ellipsoidal Inclusion[J]. Proceedings of Royal Society of London,1959,252:561～566
[39]Shaofan Li. Micromechanics Graduate Course Notes (CE236) [M].87
[40]G.P. Tandon, G.J. Weng. Effect of Aspect Ration of Inclusions on Elastic Properties of Unidirectionally Aligned Composites[J]. Polymer Composites,1984,5 (4):327～333
[41]Y Takaoand, M.Taya, J.Appl.Mech.,1985,10 (7):80
[42]沈观林,胡更开.复合材料力学[M].北京：清华大学出版社,2006.86～87
[43]荣先成.有限元法[M].成都：西南交通大学出版社,2007.76-82
[44]王连生.细观力学有限元法预测微米短纤维复合材料的有效弹性性能[D].[硕士学位论文].太原：中北大学,2009.06
[45]Vahid Nassehi. Practical Aspects Of Finite Element Modeling Of Polymer Processing[M]. London:John Wiley & Sons LTD.,2002.23
[46]荣先成.有限元法[M].成都：西南交通大学出版社,2007.11
[47]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京：清华大学出版社,2002
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[2]陈祥宝,张宝艳,邢丽英.先进树脂基复合材料技术发展及应用现状[J].中国材料进展,2009,28(6)：2-11
[3]常冬艳,王春红.纤维增强塑料在汽车领域的应用[J].非织造布,2006,14(3)：20-32
[4]王建国,郭建龙,屈泽华.碳纳米管的氨基化对环氧树脂力学性能的影响[J].工程塑料应用,2006,34(12)：8-11
[5]Andrews, Wiesenberger MC. Carbon Nanotube Polymer Composites[J]. Current Opinion in Solid State and Materials Science,2004.08.1:31
[6]欧育湘,辛菲,赵毅等.聚合物/碳纳米管纳米复合材料的制备[J].中国塑料,2006,08：1-6
[7]计国庆.玻璃钢复合材料应用于道路护栏的可行性研究[J].城市道桥与防洪,2006,04：49-51
[8]薛忠民,陈淳.复合材料的应用与回顾[M].硅酸盐通报,2005,05：84-88
[9]潘文琴.玻璃钢复合材料基体树脂的发展现状[M].纤维复合材料,2006,04：55～58
[10]张先知.合成树脂和塑料手册[M].北京：化学工业出版社,2006
[11]杨瑞成,丁旭,陈奎.材料科学与材料世界[M].北京：化学工业出版社,2005
[12]贾少栋.基于复合材料产业分析研究[J].化学工程与装备,2009,(3)：87～88
[13]陈浩.复合材料性能设计的细观力学原理与计算机辅助系统[D].[硕士学位论文].北京工业大学,2004
[14]S. Harish, D. Peter Michael, A. Bensely, D. MohanLal, A. Rajadurai. Mechanical Property Evaluation Of Natural Fiber Coir Composite[J]. Materials Characterization,2009,60:44～ 49
[15]T.W. Chou, S. Nomura. Fiber orientation effects on the thermoelastic properties of short fiber composites[J]. Fiber Science and Technology,1980,14:279～291
[16]林郁彦,冼杏娟.纤维取向性对短纤维增强复合材料力学性能的影响[J].机械工程材料,1980,6：58～62
[17]Yi Pan, Lucian Iorga, Assimina A. Pelegri. Analysis Of 3D Random Chopped Fiber Reinforced Composites Using Fern And Random Sequential Adsorption[J]. Computational Materials Science,2008,43:450～461
[18]ChaoHsun Chen, ChiangHo Cheng. Effective Elastic Moduli Of Misoriented Short Fiber Composites[J]. Int. J. Solids Structures,1996,33 (17):2519～2539
[19]张亚芳,齐雷,张春梅.增强短纤维长径比对复合材料力学性能的影响[J].广州大学学报(自然科学版),2008,7(4)：32～34
[20]Hill R. A selfconsistent mechanics of composite materials[J]. Journal of the Mechanics and Physics of Sol ids,1965,12 (3):213-222
[21]Hill R. Theory of Mechanical Properties of Fiber Strengthened Materials[J]. Journal of the Mechanics and Physics of Solids,1964,12 (12):199～212
[22]Christensen R M, Lo K H. Solutions for Effective Shear Properties in the Phase Sphere and Cylinder Models[J]. Journal of the Mechanics and Physics of Solids,1979,27:315～330
[23]Mori T, Tanaka K. Average Stress in Matrix and Average Elastic Energymaterials with Misfitting Inclusions[J].Acta Metall,1973,21:571～574
[24]Taya M, Chou T W.On Two Kinds Of Ellipsoidal Inhomogeneities In An Infiniteelastic Body:An Application To A Hybrid Composite[J].International JournalSolids and Structures, 1981,17:553-563
[25]Y. Benveniste. A New Approach To The Application Of Mori-Tanaka's Theory In Composite Materials[J]. Mechanical Material,1987,6:147～157
[26]Tsai S W, Hahn H T. Introduction to composites[M]. Lancaster:Technomic Publishing Co. Inc.,1980
[27]Hashin Z, Rosen BW. The Elastic Moduli Of Fiber-Reinforced Materials[J]. Journal of Applied. Mechanics,1964, (13):223～232
[28]Hashin Z. On Elastic Behavior Of Fiber Reinforced Materials Of Arbitrary Transverse Phase Geometry[J]. Journal of Mechanics and Physics of Solids,1965, (13):119～134
[29]王连生.细观力学有限元法预测微米短纤维复合材料的有效弹性性能[D].[硕士学位论文].太原：中北大学,2009.06
[30]孙爱芳,刘敏珊,董其伍.短切纤维增强复合材料拉伸强度的预测[J].材料研究学报,2008,22(3)：333-336
[31]K.Zhu, S.Schmauder. Prediction Of The Failure Properties Of Short Fiber Reinforced Composites With Metal And Polymer Matrix[J]. Computational Materials Sicence,2003, 28:743～748
[32]李宁,龚旭.纤维增加复合材料的有效模量预测[J].辽宁省交通高等专科学校学报,2006,8(4)：29-31
[33]张华山,黄争鸣.纤维增强复合材料弹塑性性能的细观研究[J].复合材料学报,2008,25(5)：157～162
[34]方岱宁,刘铁旗.纤维增强高分子聚合物基复合材料有效性能的三维数值分析[J].复合材料学报,1997,14(3)：81-86
[35]赵延军.短纤维增强复合材料力学通性的预测研究.[硕士学位论文].郑州：郑州大学,2004.05
[36]董燕妮.短纤维增强注塑制品力学性能预测.[硕士学位论文].郑州：郑州大学,2007.04
[37]J.D. Eshelby. The Elastic Determination Of The Elastic Field Of An Ellipsoidal Inclusion And Related Problems[J]. Proceedings Of Royal Society Of London, A241:376～396
[38]J.D. Eshelby. The Elastic Field Outside An Ellipsoidal Inclusion[J]. Proceedings of Royal Society of London,1959,252:561～566
[39]Shaofan Li. Micromechanics Graduate Course Notes (CE236) [M].87
[40]G.P. Tandon, G.J. Weng. Effect of Aspect Ration of Inclusions on Elastic Properties of Unidirectionally Aligned Composites[J]. Polymer Composites,1984,5 (4):327～333
[41]Y Takaoand, M.Taya, J.Appl.Mech.,1985,10 (7):80
[42]沈观林,胡更开.复合材料力学[M].北京：清华大学出版社,2006.86～87
[43]荣先成.有限元法[M].成都：西南交通大学出版社,2007.76-82
[44]王连生.细观力学有限元法预测微米短纤维复合材料的有效弹性性能[D].[硕士学位论文].太原：中北大学,2009.06
[45]Vahid Nassehi. Practical Aspects Of Finite Element Modeling Of Polymer Processing[M]. London:John Wiley & Sons LTD.,2002.23
[46]荣先成.有限元法[M].成都：西南交通大学出版社,2007.11
[47]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京：清华大学出版社,2002
[48]程昌钧,朱媛媛.弹性力学(修订版)[M].上海：上海大学出版社,2005.60
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