基于变分原理的机织复合材料细观力学模型
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摘要
纺织复合材料本身具有明显的结构特性，是一种多相体材料。其力学性能及损伤破坏机理不仅取决于各组分材料的性能，同时也取决于细观结构特征。采用细观力学分析建立材料宏观力学性能与材料各组分性能以及细观结构参数之间的内在联系是材料科学发展的新趋势。本课题较系统地阐述了一般机织复合材料的细观结构划分，以及机织复合材料细观结构的参数表征方法，并建立了一般机织复合材料的细观结构模型。在此基础上，首次引入有限元约束变分原理和拉格朗日乘子法，建立了一个概念清晰、结果准确、通用性强的机织复合材料细观分析模型，该模型可用于有效预测机织复合材料在多向受载情况下的局部应力。该模型考虑了织物几何参数，纱线相互作用以及基体分布等因素。第一步，通过从上到下逐层分解的方法，将机织复合材料单胞从几何上分解成基体和纱线胞元；第二步，按照从下到上的均匀化方法，建立材料外部载荷和内部应力之间的联系。模型的关键在于使用拉格朗日乘子法来计算“应力集中因子”。最后，借助“应力集中因子”求出复合材料的三维刚度矩阵，进而可以求出实验材料的弹性常数。通过将材料的预测弹性常数与试验测出的弹性性能进行对比，验证了该预测模型的准确性。
As a multiphase material, woven fabric composites have a significant structural mechanism. The mechanical behavior and failure mechanism of woven fabric composites depend significantly on its micro-structure and the properties of each constituent. It is a new trend to study the relationship between the macro-mechanical behavior and the properties of the constituents as well as the micro-structural parameters. In this paper, the general rules are illustrated to characterize the micro-structure of woven composites by some design parameters. A geometrical structure model of general woven composites is put forward. Based on the above studies, a simple variational principle and a method of Lagrangian multipliers are introduced for the first time to construct the mesomechanic model. Then a new mesomechanic model is presented to predict the mechanical properties of woven composites. The model accounts for fabric geometry, yarn interactions and yarn crisp. First, by constructing a multi-level decomposition scheme, the composites unit cell is split up into matrix and yarn cells. Then, by a multi-step homogenization procedure, a link is established between the external loading and the internal stresses. The principle idea lies in the interpretation that the "stress concentration factors" can be computed at each step by applying the complementary variational principle. In addition to modeling the stress and strain fields, the compliance matrix is computed in this paper using "stress concentration factors". Samples of woven preform and composites are made in the laboratory. At the end, the theoretical predictions of numerical stiffness are compared with the testing results and a good agreement is reported.
As a multiphase material, woven fabric composites have a significant structural mechanism. The mechanical behavior and failure mechanism of woven fabric composites depend significantly on its micro-structure and the properties of each constituent. It is a new trend to study the relationship between the macro-mechanical behavior and the properties of the constituents as well as the micro-structural parameters. In this paper, the general rules are illustrated to characterize the micro-structure of woven composites by some design parameters. A geometrical structure model of general woven composites is put forward. Based on the above studies, a simple variational principle and a method of Lagrangian multipliers are introduced for the first time to construct the mesomechanic model. Then a new mesomechanic model is presented to predict the mechanical properties of woven composites. The model accounts for fabric geometry, yarn interactions and yarn crisp. First, by constructing a multi-level decomposition scheme, the composites unit cell is split up into matrix and yarn cells. Then, by a multi-step homogenization procedure, a link is established between the external loading and the internal stresses. The principle idea lies in the interpretation that the "stress concentration factors" can be computed at each step by applying the complementary variational principle. In addition to modeling the stress and strain fields, the compliance matrix is computed in this paper using "stress concentration factors". Samples of woven preform and composites are made in the laboratory. At the end, the theoretical predictions of numerical stiffness are compared with the testing results and a good agreement is reported.
引文
[1] 黄争鸣编，复合材料细观力学引论，科学出版社，2004。p6
[2] Peirce F T. The geometry of cloth structure. Journal of the Textile Institute, 1937. 28(3): T45～96.
[3] Ishikawa T, Chou T.W. 'Stiffness and strength behaviour of woven fabric composites', J. Mater. Sci., 1982.17, 3211-3220.
[4] Naik,R.A.,' Failure analysis of woven and braided fabric reinforced composites', J. Composite Mater., 1995.29,2334-2363.
[5] Naik,N.K.and Shembekar,P.S. Elastic behavi0r of woven fabric composites! Ⅰ Lamina analysis, J. Composite Mater. 1992, 26,2196-2225.
[6] Vandeurzen, Ph., Ivens,J. and Verpoest, I.,A three-dimensional micro me cha-nical analysis of woven fabric composites I. Geometric analysis, Composites Science and Technology, 1996. 56(11),1303-1315.
[7] Whitney T J, Chou T W. Modeling of 3D angle-interlock textile structural composite. Journal of Composite Materials, 1989,23(9):890-911.
[8] Byun J H, Chou T W. Elastic properties of three-dimensional angle-interlock fabric per-forms. Journal of the Textile institute,1990,81(4):538-548.
[9] 丁辛，易洪雷。论多层机织物接结组织结构的表征，全国第十二届玻璃钢／复合材料年会论文集，青岛，1997年10月，21-24
[10] 丁辛，易洪雷，正交接结组织结构特征及其对纤维体积含量的影响，天津纺织工学院学报，1998，17(4)：15-19
[11] 易洪雷，丁辛。三维机织复合材料的弹性性能预报模型。力学学报，2003，35(5)：569-577
[12] 燕瑛，成传贤．基于细观结构的三维机织复合材料弹性性能的分析．航空学报．1999，20(4)：289-293
[13] 郭兴峰，黄故。三维正交机织物结构的几何模型，复合材料学报，2005，22(4)：183-187．
[14] 周储伟，三维机织复合材料的一种梁单元细观力学模型，复合材料学报，2004，21(6)：155-160
[15] Naik,N,K. Azad,SK.N.M. "Stress and failure analysis of 3D 0rthogonal interlock woven composites". Journal of Reinforced Plastics and Composites, 2001, Vol.20, No.17, p1485-1523
[16] Vandeurzen, Ph., Ivens,J. and Verpoest, I., Micro-Stress Analysis of woven fabric Composites by Multilevel Decomposition, Journal of Composite Materials, 1998,32(7),623:651
[17] 王勖成，有限单元法，清华大学出版社，2003，p1
[18] Paumelle., "Microstress analysis in woven composites structures", La recherche aerospatiale, 1990,6,47-72
[19] 易洪雷，丁辛。三维机织复合材料力学性能研究进展，力学进展，2001，31(2)：161-171
[20] Chang Sung Lee, Virtual material characterization of 3D orthogonal woven composite materials by large-scale computing, Journal of Composite Materials, 2005,v 39, n 10, p 851-863
[21] Feirce, ET. "A 'handle' of cloth as a measurable quantity." J. Text. Inst., 1930, 20:T377-T417
[22] Hoffman, R. M. "Some relations of fibre properties to fabric hand" 1954, Text. Res. J., 21:66-77
[23] Lomov S.V., Compression of reinforcements: A mathematical model, Journal of Reinforced Plastics and Composites, 2000,v1, n16, p1329-1350
[24] Naik,N.K, An analytical model for compressive strength of plain weave fabric composites, Composites Science and Technology, v63, nS, April, 2003, p609-625
[25] Witcomb, J., Kyeongsik, W., Enhanced direct stiffness method for finite element analysis of textile composites, Composite structures, 1994,28: 385-390
[26] 杨彩云．机织复合材料纤维体积含量计算机图像测定．复合材料学报．2005，22(4)142-148
[27] 赵渠森、赵攀峰．真空辅助成型工艺(VARI)研究．纤维复合材料2002，19(1)．42-46
[28] 吴智深．FRP复合材料在基础工程设施增强和加固方面的现状与发展[A]中国首届纤维增强塑料(FRP)混凝土结构学术交流会论文[C]．2000．6．5-20．
[29] Peirce F T. The geometry of cloth structure. Journal of the Textile Institute, 1937, 28(3): T45～96
[30] Chen, D. and S. Cheng. "Analysis of Composite Materials: A Micro-Mechanical Approach," Journal of Reinforcement Plastics and Composites, 1993,12:1323-1338
[31] Benveniste, Y. "A New Approach to the Application of Mori-Tanaka's Theory in Composite Materials," Mechanics of Materials, 1987, 6:147-153
[32] Chamis, C. C. "Mechanical of Composites Materials: Past, Present, and Future." Journal Composites Technology and Research, 1989, 11:3-14
[33] Chen, D. and S. Cheng. "Analysis on Composite Materials: A micro-mechanical Approach," Journal of Reinforced Plastics and Composites, 1993,12:1323-1338
[2] Peirce F T. The geometry of cloth structure. Journal of the Textile Institute, 1937. 28(3): T45～96.
[3] Ishikawa T, Chou T.W. 'Stiffness and strength behaviour of woven fabric composites', J. Mater. Sci., 1982.17, 3211-3220.
[4] Naik,R.A.,' Failure analysis of woven and braided fabric reinforced composites', J. Composite Mater., 1995.29,2334-2363.
[5] Naik,N.K.and Shembekar,P.S. Elastic behavi0r of woven fabric composites! Ⅰ Lamina analysis, J. Composite Mater. 1992, 26,2196-2225.
[6] Vandeurzen, Ph., Ivens,J. and Verpoest, I.,A three-dimensional micro me cha-nical analysis of woven fabric composites I. Geometric analysis, Composites Science and Technology, 1996. 56(11),1303-1315.
[7] Whitney T J, Chou T W. Modeling of 3D angle-interlock textile structural composite. Journal of Composite Materials, 1989,23(9):890-911.
[8] Byun J H, Chou T W. Elastic properties of three-dimensional angle-interlock fabric per-forms. Journal of the Textile institute,1990,81(4):538-548.
[9] 丁辛，易洪雷。论多层机织物接结组织结构的表征，全国第十二届玻璃钢／复合材料年会论文集，青岛，1997年10月，21-24
[10] 丁辛，易洪雷，正交接结组织结构特征及其对纤维体积含量的影响，天津纺织工学院学报，1998，17(4)：15-19
[11] 易洪雷，丁辛。三维机织复合材料的弹性性能预报模型。力学学报，2003，35(5)：569-577
[12] 燕瑛，成传贤．基于细观结构的三维机织复合材料弹性性能的分析．航空学报．1999，20(4)：289-293
[13] 郭兴峰，黄故。三维正交机织物结构的几何模型，复合材料学报，2005，22(4)：183-187．
[14] 周储伟，三维机织复合材料的一种梁单元细观力学模型，复合材料学报，2004，21(6)：155-160
[15] Naik,N,K. Azad,SK.N.M. "Stress and failure analysis of 3D 0rthogonal interlock woven composites". Journal of Reinforced Plastics and Composites, 2001, Vol.20, No.17, p1485-1523
[16] Vandeurzen, Ph., Ivens,J. and Verpoest, I., Micro-Stress Analysis of woven fabric Composites by Multilevel Decomposition, Journal of Composite Materials, 1998,32(7),623:651
[17] 王勖成，有限单元法，清华大学出版社，2003，p1
[18] Paumelle., "Microstress analysis in woven composites structures", La recherche aerospatiale, 1990,6,47-72
[19] 易洪雷，丁辛。三维机织复合材料力学性能研究进展，力学进展，2001，31(2)：161-171
[20] Chang Sung Lee, Virtual material characterization of 3D orthogonal woven composite materials by large-scale computing, Journal of Composite Materials, 2005,v 39, n 10, p 851-863
[21] Feirce, ET. "A 'handle' of cloth as a measurable quantity." J. Text. Inst., 1930, 20:T377-T417
[22] Hoffman, R. M. "Some relations of fibre properties to fabric hand" 1954, Text. Res. J., 21:66-77
[23] Lomov S.V., Compression of reinforcements: A mathematical model, Journal of Reinforced Plastics and Composites, 2000,v1, n16, p1329-1350
[24] Naik,N.K, An analytical model for compressive strength of plain weave fabric composites, Composites Science and Technology, v63, nS, April, 2003, p609-625
[25] Witcomb, J., Kyeongsik, W., Enhanced direct stiffness method for finite element analysis of textile composites, Composite structures, 1994,28: 385-390
[26] 杨彩云．机织复合材料纤维体积含量计算机图像测定．复合材料学报．2005，22(4)142-148
[27] 赵渠森、赵攀峰．真空辅助成型工艺(VARI)研究．纤维复合材料2002，19(1)．42-46
[28] 吴智深．FRP复合材料在基础工程设施增强和加固方面的现状与发展[A]中国首届纤维增强塑料(FRP)混凝土结构学术交流会论文[C]．2000．6．5-20．
[29] Peirce F T. The geometry of cloth structure. Journal of the Textile Institute, 1937, 28(3): T45～96
[30] Chen, D. and S. Cheng. "Analysis of Composite Materials: A Micro-Mechanical Approach," Journal of Reinforcement Plastics and Composites, 1993,12:1323-1338
[31] Benveniste, Y. "A New Approach to the Application of Mori-Tanaka's Theory in Composite Materials," Mechanics of Materials, 1987, 6:147-153
[32] Chamis, C. C. "Mechanical of Composites Materials: Past, Present, and Future." Journal Composites Technology and Research, 1989, 11:3-14
[33] Chen, D. and S. Cheng. "Analysis on Composite Materials: A micro-mechanical Approach," Journal of Reinforced Plastics and Composites, 1993,12:1323-1338
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