基于均匀化理论的4D轴编C/C复合材料的细观力学性能预测
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摘要
为实现4D轴编C/C复合材料细观力学性能的预测,首先针对4D轴编C/C复合材料的结构特点,建立了其代表性体积单元;然后利用均匀化理论和周期性边界条件为理论基础,编写了一般周期性边界条件子程序作为位移边界条件,分析讨论了代表性体积单元的变形特征、应变分布特征,获得了等效刚度矩阵;同时与编写的周期性边界条件子程序作为位移边界条件情况下的计算结果和已有实验结果分别进行了对比。研究结果表明,随着界面强度的增加,一般周期性边界条件预测的材料力学性能相比周期性边界条件预测情况下的误差小,更接近实验数值,从而验证了编写的一般周期性边界条件子程序的有效性和正确性,并进一步得出了代表性体积单元参数对材料力学性能的影响规律,得到了一些有一定指导意义的结果。
In order to get a prediction method about micromechanical properties of four directional(4 D) in-plane carbon/carbon composites,representative volume element is firstly given according structure of 4D in-plane carbon/carbon composites.The subprogram of the aperiodic boundary conditions is realized as a displacement boundary condition using the homogenization method and periodic boundary conditions as a theory basis.The deformation feature and strain distribution feature are discussed,and then the equivalent stiffness matrix is computed.The results have been compared with the results of subprogram of the periodic boundary conditions and experiments values.With the increase of interface strength,the mechanical properties of materials predicted by the aperiodic boundary conditions are with less error than those under the periodic boundary conditions,which is closer to the experimental values.The validity and applicability of the aperiodic boundary conditions has been verified.At the same time,the effect of material parameters on mechanical properties has been further obtained and some valuable result is acquired.
In order to get a prediction method about micromechanical properties of four directional(4 D) in-plane carbon/carbon composites,representative volume element is firstly given according structure of 4D in-plane carbon/carbon composites.The subprogram of the aperiodic boundary conditions is realized as a displacement boundary condition using the homogenization method and periodic boundary conditions as a theory basis.The deformation feature and strain distribution feature are discussed,and then the equivalent stiffness matrix is computed.The results have been compared with the results of subprogram of the periodic boundary conditions and experiments values.With the increase of interface strength,the mechanical properties of materials predicted by the aperiodic boundary conditions are with less error than those under the periodic boundary conditions,which is closer to the experimental values.The validity and applicability of the aperiodic boundary conditions has been verified.At the same time,the effect of material parameters on mechanical properties has been further obtained and some valuable result is acquired.
引文
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[12]廖英强,刘勇琼.轴棒法炭/炭复合材料力学性能预测研究[J].功能材料,2013,44(6):878-881LIAO Yingqiang,LIU Yongqiong.Forecast research on mechanical properties of carbon/carbon composites made by axial rod method[J].Journal of Functional materials,2013,44(6):878-882
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[14]宋广兴,齐乐华,李贺军.均匀化方法在C/C复合材料中的应用研究[J].科学技术与工程,2007,13(7):3081-3083SONG Guangxing,QI Lehua,LI Hejun.Computational homogenization analysis in simulation of carbon/carbon composites[J].Science Technology and Engineering,2007,13(7):3081-3083
[15]Wajed Zaman,Li Kezhi,Li Wei,et al.Flexural strength and thermal expansion of 4D in-planecarbon/Carbon composites after flexural fatigue loading[J].New Carbon Materials,2014,29(3):169-175
[16]廖英强,刘勇琼.应用纳米压痕技术测试沥青炭的力学性能[J].材料导报,2012,26(3):85-88.LIAO Yingqiang,LIU Yongqiong.Testing on mechanical property of pitch-derived carbon based on nano-indentation techniques[J].Materials Review,2012,26(3):85-88
[17]廖英强,刘勇琼,嵇阿琳.轴棒法C/C复合材料界面刚度性能的研究[J].材料导报,2011,25(10):143-145.LIAO Yingqiang,LIU Yongqiong,JI Alin.Interface stiffness research of C/C composite made by axial rod method[J].Material Review,2011,25(10):143-145
[18]Guedes J M,Kikuchi N.Preprocessing and Post processing for materials based on the homogenization method with adaptive finite element methods[J].Computer Methods in Applied Mechanics and Engineering,1990,83:98-143.
[19]Mahmood M Shokrieh,Mohammad S Mazloomi.A new analytical model for calculation of stiffness of three-dimensional four-directional braided composites[J].Composite Structure,2012,94(3):1005-1015.
[20]Xia Z H,Zhang Y F,Fernand E.A unified periodical boundary conditions for representative volume elements of composites and applications[J].International Journal of Solids and Structures,2003,40:1907-1921
[21]张超,许希武,严雪.纺织复合材料细观力学分析的一般性周期性边界条件及其有限元实现[J].航空学报,2013,34(7):1636-1645ZHANG Chao,XU Xiwu,YAN Xue.General periodic boundary conditions and their application to micromechanical finite element analysis of textile composites[J].Acta Aeronautica Et Astronautica Sinica,2013,34(7):1636-1645
[22]卢子兴.复合材料界面的内聚力模型及其应用[J].固体力学学报,2015,36(10):85-94LU Zixing.A simple review for cohesive zone models of composite interface their applications[D].Chinese Journal of Solid Mechanics,2015,36(10):85-94
[23]于飞,陈向明,张阿盈,等.一种改进的内聚力模型在复合材料层合板低速冲击损伤模拟中的应用[J].复合材料学报,2015,32(6):1745-1753YU Fei,CHENG Xiangming,ZHANG Ayin,et al.Application of modified cohesive zone damage model in damage simulation of composite laminates subject to low-velocity impact[J].Acta Materiae Composites Sinica,2015,32(6):1745-1753
[24]宋广兴.基于均匀化理论非编织碳碳复合材料力学性能数值模拟研究[D].西北工业大学,2007:35-40.SONG Guangxing.Simulate study of effective mechanics properties for nonwoven carbon/carbon composites based on homo-genization theory[D].Northwestern Polytehnical University,2007:35-40.
[25]John D B,Dan D E.Carbon-carbon materials and composite[M].Park Ridge Noyes Publications,1993:169-195
[2]宋桂明,周玉,王玉金,等.固体火箭发动机喉衬材料[J].固体火箭技术,1998,21(2):51-55SONG Guiming,ZHOU Yu,WANG Yujin,et al.Throat materials for solid rocket motors[J].Journal of Solid Rocket Technology,1998,21(2):51-55
[3]Kalidinli S R,Franco E.Numerical evaluation of isostrain and weighted-average models for elastic moduli of three-dimensional composites[J].Composites Science and Technology,1997,57:293-305
[4]Peter W Chung,Kumar K Tamma,Raju R Namburu.Asymptotic expansion homo-genization for heterogeneous media:Computational issues and applications[J].Composites,2001,32:1291-1301
[5]刘书田,程耿东.复合材料应力分析的均匀化方法[J].力学学报,1997,29(3):306-313LIU Shutian,CHENG Gengdong.Homogeniza-tion method of stress analysis of composite structures[J].Acta Mechanica Sinica,1997,29(3):306-313
[6]谢先海,廖道训.均匀化理论中等效弹性模量的计算[J].华中科技大学学报,2001,29(4):44-46XIE Xianhai,LIAO Daoxun.Computation method of equivalent elastic tensor in homogenization method[J].Journal of Huazhong University of Science and Technology,2001,29(4):44-46
[7]刘书田,程耿东.基于均匀化理论的复合材料热膨胀系数预测方法[J].大连理工大学学报,1995,35(5):451-457LIU Shutian,CHENG Gengdong.Homogeniza-tion-based method for predicting thermal expansion coefficients of composite materials[J].Journal of Dalian University of Technology,1995,35(5):451-457
[8]董纪伟.基于均匀化理论的三维编织复合材料宏细观力学性能的数值模拟[D].南京航空航天大学,2007:24-25Dong Jiwei.Homogenization-based method for simulating macro and micro mechanical properties of 3D braided composites[D].Nanjing University of Aeronautics and Astronautics the Graduate School,2007:24-25
[9]Hassani B,Hinton E.A Review of homogenization and topology optimi-zation I-Homogenization theory for media with periodic structures[J].Computers and Structures,1998,69:707-717.
[10]Hassani B,Hinton E.A Review of homogenization and topology optimi-zation II-Homogenization theory for media with periodic structures[J].Computers and Structures,1998,69:719-738.
[11]唐敏,高波,杨月城,等.基于均匀化方法的4D轴编C/C复合材料的性能预测[J].固体火箭技术,2011,34(1):109-118TANG Min,GAO Bo,YANG Yuecheng,et al.Mechanical properties predfiction of 4D-inplain carbon/carbon composites based on homogenization method[J].Journal of Solid Rocket Technology,2011,34(1):109-118
[12]廖英强,刘勇琼.轴棒法炭/炭复合材料力学性能预测研究[J].功能材料,2013,44(6):878-881LIAO Yingqiang,LIU Yongqiong.Forecast research on mechanical properties of carbon/carbon composites made by axial rod method[J].Journal of Functional materials,2013,44(6):878-882
[13]单忠德,康怀镕,藏勇,等.三维织造层间增强的纤维棒复合材料细观结构模型及力学性能有限元模拟[J].复合材料学报,2015,32(1):138-149SHAN Zhongde,KANG Huairong,ZANG Yong,et al.Microscopic structure model and finite element simulation of mechanical properties of fiber-bar composites reinforced by three dimensional weaving[J].Acta Materiae Composite Sinica,2015,32(1):138-149
[14]宋广兴,齐乐华,李贺军.均匀化方法在C/C复合材料中的应用研究[J].科学技术与工程,2007,13(7):3081-3083SONG Guangxing,QI Lehua,LI Hejun.Computational homogenization analysis in simulation of carbon/carbon composites[J].Science Technology and Engineering,2007,13(7):3081-3083
[15]Wajed Zaman,Li Kezhi,Li Wei,et al.Flexural strength and thermal expansion of 4D in-planecarbon/Carbon composites after flexural fatigue loading[J].New Carbon Materials,2014,29(3):169-175
[16]廖英强,刘勇琼.应用纳米压痕技术测试沥青炭的力学性能[J].材料导报,2012,26(3):85-88.LIAO Yingqiang,LIU Yongqiong.Testing on mechanical property of pitch-derived carbon based on nano-indentation techniques[J].Materials Review,2012,26(3):85-88
[17]廖英强,刘勇琼,嵇阿琳.轴棒法C/C复合材料界面刚度性能的研究[J].材料导报,2011,25(10):143-145.LIAO Yingqiang,LIU Yongqiong,JI Alin.Interface stiffness research of C/C composite made by axial rod method[J].Material Review,2011,25(10):143-145
[18]Guedes J M,Kikuchi N.Preprocessing and Post processing for materials based on the homogenization method with adaptive finite element methods[J].Computer Methods in Applied Mechanics and Engineering,1990,83:98-143.
[19]Mahmood M Shokrieh,Mohammad S Mazloomi.A new analytical model for calculation of stiffness of three-dimensional four-directional braided composites[J].Composite Structure,2012,94(3):1005-1015.
[20]Xia Z H,Zhang Y F,Fernand E.A unified periodical boundary conditions for representative volume elements of composites and applications[J].International Journal of Solids and Structures,2003,40:1907-1921
[21]张超,许希武,严雪.纺织复合材料细观力学分析的一般性周期性边界条件及其有限元实现[J].航空学报,2013,34(7):1636-1645ZHANG Chao,XU Xiwu,YAN Xue.General periodic boundary conditions and their application to micromechanical finite element analysis of textile composites[J].Acta Aeronautica Et Astronautica Sinica,2013,34(7):1636-1645
[22]卢子兴.复合材料界面的内聚力模型及其应用[J].固体力学学报,2015,36(10):85-94LU Zixing.A simple review for cohesive zone models of composite interface their applications[D].Chinese Journal of Solid Mechanics,2015,36(10):85-94
[23]于飞,陈向明,张阿盈,等.一种改进的内聚力模型在复合材料层合板低速冲击损伤模拟中的应用[J].复合材料学报,2015,32(6):1745-1753YU Fei,CHENG Xiangming,ZHANG Ayin,et al.Application of modified cohesive zone damage model in damage simulation of composite laminates subject to low-velocity impact[J].Acta Materiae Composites Sinica,2015,32(6):1745-1753
[24]宋广兴.基于均匀化理论非编织碳碳复合材料力学性能数值模拟研究[D].西北工业大学,2007:35-40.SONG Guangxing.Simulate study of effective mechanics properties for nonwoven carbon/carbon composites based on homo-genization theory[D].Northwestern Polytehnical University,2007:35-40.
[25]John D B,Dan D E.Carbon-carbon materials and composite[M].Park Ridge Noyes Publications,1993:169-195
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