碳纳米管复合材料界面应力传递及石墨烯弹性性能研究
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摘要
碳纳米管和石墨烯由于其优异的物理和力学性能而被认为是复合材料的理想增强相，它们和复合材料基体的界面力学行为是影响复合材料宏观力学性能的重要因素，近年来已经成为复合材料研究的重点。本论文针对碳纳米管增强复合材料的界面应力传递以及石墨烯的弹性性能开展了理论研究。
建立了一个三维轴对称两圆柱壳模型，并在模型中考虑了碳纳米管与基体的泊松效应、双壁碳纳米管管壁间范德华力以及由于碳纳米管和基体热膨胀系数失配而引起的残余应力的影响，分别研究了双壁碳纳米管和基体在完全粘接和脱粘情况下的界面应力分布和传递机制。根据平衡关系及界面上的位移与应力连续条件，推导出了碳纳米管轴向应力的微分方程，从而得到了碳纳米管轴向应力、基体的轴向平均应力以及碳纳米管与基体界面上切应力的解析表达式，并对这些表达式进行了无量纲化处理。通过数值计算，分析了碳纳米管的细长比、体积分数、基体与碳纳米管的弹性模量比、温度变化、界面摩擦系数以及范德华力对应力分布情况的影响。在此基础上，进一步利用有限单元法对单壁碳纳米管增强聚合物复合材料的界面脱粘、应力传递及拔出载荷进行了数值模拟。建立一个轴对称三圆柱壳模型，引入ABAQUS中的Cohesive单元模拟碳纳米管和聚合物基体之间的界面层，分析了单壁碳纳米管的细长比、界面强度以及热残余应力等因素对单壁碳纳米管与聚合物基体间的界面切应力、碳纳米管的轴向应力以及拔出载荷的影响。
另外，本文提出了一个基于原子间作用势和连续介质力学的理论模型来预测单层石墨烯纳米带的弹性性能。采用弹性拉伸与扭转弹簧模型分别模拟碳-碳键的伸长与键角的变化。利用能量方法得到石墨烯的应变能密度，进而导出单层石墨烯的本构方程，并得到了五个非零弹性常数的解析表达式。利用从Morse势函数与AMBER力场中得到的力常数，分别数值计算了单层石墨烯的等效杨氏模量、泊松比以及剪切弹性模量，证明石墨烯纳米带的弹性模量是各向异性且手性相关的。
Carbon nanotubes and graphene are regarded as the promising reinforcingphase in the advanced composites, due to their superior physical and mechanicalproperties. The interfacial mechanical behavior between the CNTs/graphene andmatrix has great influence on the mechanical properties of composites, and hasattracted much attention of researchers in recent years. In the thesis, theoreticalresearches on the interfacial stress transfer in the carbon nanotubes reinforcedcomposites and elastic properties of a graphene nanosheet have been made.
A three-dimensional axisymmetric two-cylinder model is presented toinvestigate interfacial stress transfer in the double-walled carbon nanotube (DWCNT)reinforced composites when the interface between the DWCNT and the matrix isperfect bonding and debonding, respectively. In the model, the Poisson’s effects ofDWCNT and matrix as well as the effects of the van der Waals (vdW) interactionbetween two layers of DWCNT and the residual stress induced by thermal expansioncoefficient (TEC) mismatch of DWCNT and matrix are taken into account. Based onthe equilibrium relation and the interfacial continuous condition of displacement andstress, the differential equations of DWCNT axial stress are derived, and theanalytical expressions of the interfacial shear stress and the axial stresses of DWCNTand matrix are obtained and nondimensionalized, respectively. Then via numericalcalculation, the influence of DWCNT aspect ratio, DWCNT volume fraction, relativemodulus between the DWCNT and the matrix, temperature variation, interfacialfriction coefficient and vdW force are analyzed, respectively. Furthermore, numericalsimulations based on finite element methods are presented to in the thesis toinvestigate the interfacial debonding as well as stress transfer and pullout force in thesingle-walled carbon nanotubes (SWCNTs) reinforced polymer composites. Anaxisymmetric three-cylinder model is presented, and a cohesive element in theABAQUS code is applied to simulate the interfacial layer between the SWCNTs andpolymer matrix. The influence aspect ratio of SWCNTs, interfacial strength andthermal residual stress on the interfacial shear stress as well as axial stress ofSWCNTs and pullout force are analyzed and discussed.
In addition, an analytical approach is presented in the thesis to predict the elasticproperties of a monolayer graphene nanosheet based on interatomic potential energy and continuum mechanics. The elastic extension and torsional springs are utilized tosimulate the stretching and angle variation of carbon-carbon bond, respectively. Theconstitutive equation of the graphene nanosheet is derived by using the strain energydensity, and the analytical expressions of five nonzero elastic constants are obtained.The in-plane elastic properties of the monolayer graphene nanosheet are proved to beanisotropic. The effective Young’s moduli, Poisson’s ratios and shear modulus of themonolayer graphene nanosheet are calculated according to the force constants derivedfrom Morse potential and AMBER force field, respectively, and they were proved tobe chirality-dependent.
建立了一个三维轴对称两圆柱壳模型，并在模型中考虑了碳纳米管与基体的泊松效应、双壁碳纳米管管壁间范德华力以及由于碳纳米管和基体热膨胀系数失配而引起的残余应力的影响，分别研究了双壁碳纳米管和基体在完全粘接和脱粘情况下的界面应力分布和传递机制。根据平衡关系及界面上的位移与应力连续条件，推导出了碳纳米管轴向应力的微分方程，从而得到了碳纳米管轴向应力、基体的轴向平均应力以及碳纳米管与基体界面上切应力的解析表达式，并对这些表达式进行了无量纲化处理。通过数值计算，分析了碳纳米管的细长比、体积分数、基体与碳纳米管的弹性模量比、温度变化、界面摩擦系数以及范德华力对应力分布情况的影响。在此基础上，进一步利用有限单元法对单壁碳纳米管增强聚合物复合材料的界面脱粘、应力传递及拔出载荷进行了数值模拟。建立一个轴对称三圆柱壳模型，引入ABAQUS中的Cohesive单元模拟碳纳米管和聚合物基体之间的界面层，分析了单壁碳纳米管的细长比、界面强度以及热残余应力等因素对单壁碳纳米管与聚合物基体间的界面切应力、碳纳米管的轴向应力以及拔出载荷的影响。
另外，本文提出了一个基于原子间作用势和连续介质力学的理论模型来预测单层石墨烯纳米带的弹性性能。采用弹性拉伸与扭转弹簧模型分别模拟碳-碳键的伸长与键角的变化。利用能量方法得到石墨烯的应变能密度，进而导出单层石墨烯的本构方程，并得到了五个非零弹性常数的解析表达式。利用从Morse势函数与AMBER力场中得到的力常数，分别数值计算了单层石墨烯的等效杨氏模量、泊松比以及剪切弹性模量，证明石墨烯纳米带的弹性模量是各向异性且手性相关的。
Carbon nanotubes and graphene are regarded as the promising reinforcingphase in the advanced composites, due to their superior physical and mechanicalproperties. The interfacial mechanical behavior between the CNTs/graphene andmatrix has great influence on the mechanical properties of composites, and hasattracted much attention of researchers in recent years. In the thesis, theoreticalresearches on the interfacial stress transfer in the carbon nanotubes reinforcedcomposites and elastic properties of a graphene nanosheet have been made.
A three-dimensional axisymmetric two-cylinder model is presented toinvestigate interfacial stress transfer in the double-walled carbon nanotube (DWCNT)reinforced composites when the interface between the DWCNT and the matrix isperfect bonding and debonding, respectively. In the model, the Poisson’s effects ofDWCNT and matrix as well as the effects of the van der Waals (vdW) interactionbetween two layers of DWCNT and the residual stress induced by thermal expansioncoefficient (TEC) mismatch of DWCNT and matrix are taken into account. Based onthe equilibrium relation and the interfacial continuous condition of displacement andstress, the differential equations of DWCNT axial stress are derived, and theanalytical expressions of the interfacial shear stress and the axial stresses of DWCNTand matrix are obtained and nondimensionalized, respectively. Then via numericalcalculation, the influence of DWCNT aspect ratio, DWCNT volume fraction, relativemodulus between the DWCNT and the matrix, temperature variation, interfacialfriction coefficient and vdW force are analyzed, respectively. Furthermore, numericalsimulations based on finite element methods are presented to in the thesis toinvestigate the interfacial debonding as well as stress transfer and pullout force in thesingle-walled carbon nanotubes (SWCNTs) reinforced polymer composites. Anaxisymmetric three-cylinder model is presented, and a cohesive element in theABAQUS code is applied to simulate the interfacial layer between the SWCNTs andpolymer matrix. The influence aspect ratio of SWCNTs, interfacial strength andthermal residual stress on the interfacial shear stress as well as axial stress ofSWCNTs and pullout force are analyzed and discussed.
In addition, an analytical approach is presented in the thesis to predict the elasticproperties of a monolayer graphene nanosheet based on interatomic potential energy and continuum mechanics. The elastic extension and torsional springs are utilized tosimulate the stretching and angle variation of carbon-carbon bond, respectively. Theconstitutive equation of the graphene nanosheet is derived by using the strain energydensity, and the analytical expressions of five nonzero elastic constants are obtained.The in-plane elastic properties of the monolayer graphene nanosheet are proved to beanisotropic. The effective Young’s moduli, Poisson’s ratios and shear modulus of themonolayer graphene nanosheet are calculated according to the force constants derivedfrom Morse potential and AMBER force field, respectively, and they were proved tobe chirality-dependent.
引文
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