聚合物基复合材料粘弹性性能预测
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摘要
聚合物基复合材料作为工程材料,以其比刚度高、比强度高、耐腐蚀和抗疲劳性能好、可设计性强等优异性能广泛应用于航空航天等高科技工业中。由于聚合物以及其它粘弹性基体材料的使用,使得粘弹性成为复合材料的重要特性。粘弹性复合材料的宏观特性和其等效本构关系,虽然可以通过大量材料特征实验手段获取,但是也存在不少困难,对于材料设计也极为不方便。本文基于渐进均匀化理论和有限元法预测聚合物基复合材料的等效粘弹性性能。
本文运用弹性-粘弹性对应原理及Laplace变换简化了粘弹性本构方程和控制方程。在利用均匀化理论求解弹性问题的基础上,推导了基体和夹杂都是各向同性复合材料的等效松弛模量表达式。利用ANSYS软件建立复合材料的细观单胞模型,用FORTRAN语言编写了求解等效松弛模量的应用程序,最后用MATLAB软件对结果后处理。讨论了夹杂的体积分数和松弛参数对各向同性复合材料的等效松弛模量的影响。给出了具体实例,并与其他方法进行比较,说明该方法的有效性。
在各向同性复合材料的研究基础上讨论了单向纤维复合材料的横观各向同性性能,给出了具体的表达式。基于均匀化方法预测了单向纤维复合材料的等效松弛模量,给出了等效松弛模量随纤维体积分数变化的规律。在相同参数条件下讨论了圆形纤维和矩形纤维对复合材料的增强效果。
本文的研究可对粘弹性复合材料的设计和应用起到一定的指导作用。
As a kind of engineering material, polymer matrix composite has been widespread used in aerospace and other high-tech industries due to its high specific stiffness, high specific strength, good corrosion resistance, good fatigue resistance, good designability and other excellent properties. Thanks to the use of polymer and other viscoelastic material, the viscoelastic characteristics become an important property of composite materials. The macroscopic properties and equivalent constitutive relationship of viscoelastic composite materials can be obtained by a large number of material characteristics experimental means, but there are many difficulties and very inconvenient for the material design. In this paper, the effective properties of viscoelastic composite materials are predicted based on the asymptotic homogenization method and finite element theory.
In this paper, the viscoelastic constitutive equation is simplified through elastic- viscoelastic correspondence principle and Laplace transformation. Based on homogenization theory to solve elastic problems, the expression of effective relaxation modulus of composites which both matrix and inclusions are isotropic is discussed. The finite element software ANSYS is used to establish the composite unit cell model. The FORTRAN language is used to write the application program that solves the effective relaxation modulus. Finally, the MATLAB software is used to post-process the results.
The influence of the volume fraction of inclusion and the relaxation parameters on effective relaxation modulus of isotropic composite is studied. Specific examples are given and compared with other methods to show that this method is effective.
The transversely isotropic of unidirectional fiber composite materials is discussed based on the study of isotropic composites, and concrete expression is given. The effective relaxation modulus of unidirectional fiber composite materials is predicted based on the homogenization theory. And the influence of volume fraction on effective relaxation modulus is studied. The effect of circular fibers and rectangular fiber on enhance of the composite material is discussed with the same parameters.
This study can play a guiding role to the viscoelastic composites design and application.
本文运用弹性-粘弹性对应原理及Laplace变换简化了粘弹性本构方程和控制方程。在利用均匀化理论求解弹性问题的基础上,推导了基体和夹杂都是各向同性复合材料的等效松弛模量表达式。利用ANSYS软件建立复合材料的细观单胞模型,用FORTRAN语言编写了求解等效松弛模量的应用程序,最后用MATLAB软件对结果后处理。讨论了夹杂的体积分数和松弛参数对各向同性复合材料的等效松弛模量的影响。给出了具体实例,并与其他方法进行比较,说明该方法的有效性。
在各向同性复合材料的研究基础上讨论了单向纤维复合材料的横观各向同性性能,给出了具体的表达式。基于均匀化方法预测了单向纤维复合材料的等效松弛模量,给出了等效松弛模量随纤维体积分数变化的规律。在相同参数条件下讨论了圆形纤维和矩形纤维对复合材料的增强效果。
本文的研究可对粘弹性复合材料的设计和应用起到一定的指导作用。
As a kind of engineering material, polymer matrix composite has been widespread used in aerospace and other high-tech industries due to its high specific stiffness, high specific strength, good corrosion resistance, good fatigue resistance, good designability and other excellent properties. Thanks to the use of polymer and other viscoelastic material, the viscoelastic characteristics become an important property of composite materials. The macroscopic properties and equivalent constitutive relationship of viscoelastic composite materials can be obtained by a large number of material characteristics experimental means, but there are many difficulties and very inconvenient for the material design. In this paper, the effective properties of viscoelastic composite materials are predicted based on the asymptotic homogenization method and finite element theory.
In this paper, the viscoelastic constitutive equation is simplified through elastic- viscoelastic correspondence principle and Laplace transformation. Based on homogenization theory to solve elastic problems, the expression of effective relaxation modulus of composites which both matrix and inclusions are isotropic is discussed. The finite element software ANSYS is used to establish the composite unit cell model. The FORTRAN language is used to write the application program that solves the effective relaxation modulus. Finally, the MATLAB software is used to post-process the results.
The influence of the volume fraction of inclusion and the relaxation parameters on effective relaxation modulus of isotropic composite is studied. Specific examples are given and compared with other methods to show that this method is effective.
The transversely isotropic of unidirectional fiber composite materials is discussed based on the study of isotropic composites, and concrete expression is given. The effective relaxation modulus of unidirectional fiber composite materials is predicted based on the homogenization theory. And the influence of volume fraction on effective relaxation modulus is studied. The effect of circular fibers and rectangular fiber on enhance of the composite material is discussed with the same parameters.
This study can play a guiding role to the viscoelastic composites design and application.
引文
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[2]周光泉,刘孝敏.粘弹性理论[M].合肥:中国科学技术大学出版社,1996
[3]王震鸣,范赋群.复合材料及其结构力学进展(第二册).广州:华南理工大学出版社,1992:163-177
[4]张恒,王震鸣,李江.复合材料及其结构的粘弹性力学[A].见:王震鸣,范赋群.复合材料及其结构力学进展.武汉工业大学出版社,1992:45-60
[5] Ferry J D. Viscoelastic Properties of Polymers. 3rd ED. New York: John Wiley, 1980
[6]曲艳双等.树脂基复合材料的粘弹性研究进展[J].纤维复合材料.2008:42-44
[7]张义同.热粘弹性理论[M].天津大学出版社,2002:3-34.
[8]郭大智等,层状粘弹性体系力学[M].哈尔滨:哈尔滨工业大学出版社,2001
[9]卢哲安,肖贵泽和杨炳尧.粘弹性界面对复合材料有效性能的影响[J].武汉理工大学学报.2001: 15-18
[10]杨庆生.短纤维复合材料的细观力学模型研究[J].大连理工大学学报.1994:218-221
[11]杨黎明,王礼立.用Eshelby理论研究复合材料线粘弹性本构关系[J].爆炸与冲击.1991: 245-250
[12]陈浩然、袁彪和郑长良.短纤维增强SiC/Al复合材料在高温下粘弹性拉伸性能的细观力学分析[J].玻璃钢/复合材料.1995:3-6
[13] Luciano R, Barbero E J. Analytical expression for the relaxation modus of the linear viscoelastic composites with periodic microstructure[J].Journal of Applied Mechanics, 1995, 62:786
[14] Laws N, Mclaughlin J R. Self-consistent estimates for the viscoelastic creep compliances of composites[J]. Proceedings of the Royal Society, 1978, 39:251-273
[15] Hashin Z. Viscoelastic behavior of heterogeneous media[J]. Journal of Applied Mechanics, 1965, 29:630-636
[16] Brock-enbrough J R, Suresh S, Wienecke. Deformation of metal-matrix Composite continuous fibers: geometrical effect of fiber distribution and shaper[J]. Acta Metal Mater, 1991, 39:735
[17]穆霞英.蠕变力学[M].西安:西安交通大学出版社.1990
[18]过梅丽.高聚物与复合材料的动态力学热分析[M].北京:化学工业出版社,2002
[19] Milios J, Spathis G. Comp. Sci. Tech. 25, 1986, 4:301-309
[20] Suarez S A, Gibson R F, Sun C T, Chaturvedi S K. Bxp. Mech. 26. 1986, 2: 175-184
[21] Doan C, Gerard J F, Merle G, Xie M. Comp. Sci. Tech. 34, 1989, 4: 337-351
[22]李晨,刘勃,周彦豪.复合材料学报.1989,4:79-86
[23]郭兆璞,陈浩然和段滋华.复合材料层合板非线性粘弹性有限元分析[J].大连理工大学学报.1996:252-257
[24]黄百鸣.复合材料细观力学引论[M].北京:科学出版社, 2004:6
[25]杜善义.王彪.复合材料细观力学[M].北京:科学出版社,1998:1-51
[26] J D Eshelby. The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems, Proceedings of the Royal Society, London, Series A, 1957, 240:367-396
[27] R Hill. A Self-consistent Mechanics of Composite Materials, J. Mech. Phys. Solids, 1965, 13:213-222
[28] T Mori, K Tanaka. Average Stress in Matrix and Average Energy of Materials with Misfitting inclusions. Act. Metal, 1973, 21:571-574
[29] R A Roscoe. The Viscosity of Suspensions of Rigid Spheres. Brit. J. Appl. Phys. 1952, 3:267-269
[30] Z. Hashin, S. Shtrikman. A Variational Approach to the Theory of the Elastic Behaviour of Multiphase Materials. J. Mach. Phys. Solids. 1963, 11:127-140
[31] Z. Hashin. The Differential Scheme and Its Application to Cracked Materials. J. Mech. Phys. Solids. 1988, 36:719-764
[32] J. M. Duva and D. Storm. ASME Trans. J. Engng. Mater. Tech.1989,111,368-371
[33] E H Kerner. Proc. Phys. Soc. 1956, B69:801-808
[34] N. Laws, J. R. Brock-enbrough. The Effect of Micro-crack Systems on the Loss of Stiffness of Brittle Solids. Int. J. Solids Structures. 1987,23:1247-1268
[35] T. W. Chou, S.Nomura, M. Taya. J. Comp. Mater. 1980, 14:178-188
[36] T. T. Wu, Int. J. Solids Structures. 1966, 2:1-8
[37] B. Budiansky, R. J. O’Connell, Elastic Moduli of a Cracked Solid. Int. J. Solids Structures. 1976, 12:81-97
[38] M. Taya, T. Mura. On Stiffness and Strength of an Aligned Short-Fiber Reinforced Composite Containing Fiber-End Cracks Under Uniaxial Applied Stress. J. Appl. Mech, 1984, 48:361-367
[39]杜善义,李文芳.含随机分布微裂纹的相变颗粒增强增韧陶瓷材料的强度和刚度预报[J].固体力学学报.1997,15:104-110
[40] R. M. Christensen. A Critical Evaluation for a Class of Micromechanics Models. J. Mech. Phys. Solids. 1990,38:379-404
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