基于螺旋几何模型的三维编织复合材料热机械性能研究
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摘要
三维编织复合材料是将古老的编织技术与现代复合材料成型技术有机地融于一体而形成的一种具有独特结构的复合材料，它从根本上克服了单向增强的复合材料层板易分层、开裂等缺点，具有比强度高、比刚度高、优良的抗冲击损伤性能、抗疲劳断裂性能、耐烧蚀性能、结构整体性和可设计性等，因此倍受工程界的普遍关注，在航空、航天、国防、体育用品和生物医疗等领域得到了广泛应用。为了更好地开发和利用三维编织复合材料，国内外研究者在近20余年中对三维编织复合材料的细微观结构与宏观力学性能之间的关系进行了大量的研究和探索，取得了许多突出成就，并逐渐发展成力学领域的一个热门研究方向。本文综述和分析了三维编织复合材料的国内外研究现状，针对三维四向碳/环氧编织复合材料，从细观结构几何模型、刚度和强度预报、热物理性能以及热力耦合行为四个方面进行了理论计算和数值分析。
由于三维四向编织复合材料内部空间纤维束的相互挤压和扭结，将造成纤维束弯曲和截面形状变化，本文对现有的米字型单胞模型进行了改进，用空间抛物线来模拟单胞内纤维束路径，建立了三维四向编织复合材料螺旋型单胞几何模型。螺旋型单胞几何模型避免了内部空间纤维束在单胞中心的交叉，能够更加精确地反映三维四向编织复合材料内部的细观结构。该几何模型虽然以三维四向编织复合材料为对象，但所得结果具有普遍意义，研究方法可以推广到三维多向编织复合材料，为三维多向编织复合材料力学性能分析与材料优化设计提供参考。
基于螺旋型单胞几何模型，本文对三维四向碳/环氧编织复合材料的刚度和强度进行了数值预报与理论计算。应用多相有限元法，把单胞模型划分为三种子单胞，结合高斯积分法对三维四向碳/环氧编织复合材料的有效工程弹性常数进行了数值预报；对三维四向编织复合材料单胞内的应力场分布和单向拉伸应力应变关系曲线进行了数值模拟；分别采用蔡-吴准则和米赛斯准则数值预报了三维四向编织复合材料的强度，研究了三维编织复合材料拉伸损伤机理；基于螺旋型单胞几何模型，对三维四向碳/环氧编织复合材料的有效工程弹性常数和强度进行了理论推导，并将理论推导结果与相应的数值预报进行了对比分析。
为了研究三维四向编织复合材料的热机械性能，本文基于螺旋型单胞几何模型，推导了三维四向编织复合材料热弹性问题的稳态热分析有限元方程，建立了三维四向编织复合材料热物理性能分析的力学模型，数值预报了等效热传导系数和热膨胀系数，并讨论了编织角度、纤维体积含量等因素对三维四向编织复合材料热物理性能的影响。结合热传导问题的有限元理论，对三维四向编织复合材料进行了稳态热传导分析，数值预报了第一类边界条件（已知边界温度）和第二类边界条件（已知边界热流）的三维四向编织复合材料的温度场分布。在稳态热传导分析的基础上，建立了三维四向编织复合材料热力耦合行为分析的有限元方法。通过对三维四向编织复合材料单胞模型施加相同的机械载荷与不同的热载荷条件（稳态温度场、已知边界温度和已知边界热流），对三维四向编织复合材料在热力耦合作用下的强度进行预报，讨论了编织角度、纤维体积含量等因素对三维四向编织复合材料热力耦合强度的影响。
The ancient braiding technology and the processing technique for moderncomposites are combined organically to make the composites with unique structure,which fundamentally overcomes the shortcomings of the unidirectional compositelaminates, such as delamination and cracking etc. The3D braided composites hasbeen paid much more attention by engineering for its excellent mechanical properties,such as high specific strength, high specific stiffness, impact toughness,fatigue-fracture, ablative resistance, structural integrity and designability etc. So the3D braided composites is widely used in the fields of high technology such asaeronautics, astronautics, marine, sports, and biomedical etc. In order to make betteruse of3D braided composites, the scholars at home and abroad have carried out a lotof exploration and research on the relationships between microscopic and macromechanical properties in past20years. Some outstanding achievement has beenmade and the3D braided composites have been gradually developed into a popularresearch direction of mechanics. The development and research on3D braidedcomposites at home and abroad are reviewed and analyzed. The geometric model,stiffness and strength, thermo-physical properties and thermo-mechanical couplingbehaviors of3D four-directional carbon/epoxy braided composites are investigatedby using numerical and theoretical methods in this dissertation.
Owing to the squeezing and twisting of braid yarns each other within the3Dfour-directional braided composites, the braid yarns exhibit the bending andvariational cross-section. A helix geometry model for3D four-directional braidedcomposites is established based on the fiber hexprism diagonal brick cell in thispaper. The spatial parabolic is used to simulate the yarn axis of the unit cell. Fourbraiding yarns in the unit cell are curved to avoid the collision at the center of theunit cell. The helix geometry model reflects more accurately the microstructure of3D four-directional braided composites. Though the microscopic geometric model isestablished to the case of3D four-directional braided composites, but the results havegeneral significance and the research methods can be extended to3Dmulti-directional braided composites. These will provide reference for furtheranalyzing the mechanical properties and optimization design of3D multi-directional braided composites.
The stiffness and strength of3D four-directional carbon/epoxy braided compositesare predicted based on the helix geometry model by numerical simulation andtheoretical derivation. The RVE is divided into three kinds of elements according tothe finite multiphase element method: matrix element, yarn element and mixedelement and the gauss quadrature has been proposed to predict the effective elasticconstants. The unit cell stress fields and longitudinal tensile stress-strain relationshipsof3D braided composites are presented through the finite element theory of spaceproblem. The Tsai–Wu and Von Mises criterion are used to predict the failure in theyarn and matrix, respectively, and the longitudinal tensile strength of3D braidedcomposites is calculated and the damage mechanisms of the composites are analyzed.The effective elastic constants and longitudinal tensile strength of3D braidedcomposites are theoretically calculated based on the helix geometry model andcompared with the simulation results.
In order to investigate the thermal mechanical properties of3D four-directionalbraided composites, the finite element equations of steady state thermal analysis ofthermoelastic problem for3D four-directional braided composites are derived and themechanical model of thermo-physical properties analysis for3D four-directionalbraided composites are developed based on the based on the helix geometry model.By numerical computing, the effective thermal conductivity coefficients and thermalexpansion coefficients of3D four-directional braided composites are obtained. Theinfluences of the braid angle and fiber volume fraction on the thermo-physicalproperties of three-dimensional four-directional braided composites are discussed.The steady state thermal conductivity analysis is presented by using the finiteelement theory of thermal conductivity problem. The distribution of temperature of3D braided composites with the first class boundary condition (the distribution oftemperature on the surface is known) and the second class boundary condition (thedistribution of heat flux on the surface is known) are determined. The finite elementmethods of thermo-mechanical coupling behaviors analysis for3D four-directionalbraided composites are developed on the basis of the steady state thermalconductivity analyses. By applying the same mechanical loads and the differentthermal loads (the temperature on the unit cell remains constant, the distribution oftemperature on the surface is known, the distribution of heat flux on the surface is known), the strength of3D braided four-directional composites are analyzed. Theeffects of the braiding angle and fiber volume fraction on the thermo-mechanicalcoupling behaviors of3D braided composites are discussed.
由于三维四向编织复合材料内部空间纤维束的相互挤压和扭结，将造成纤维束弯曲和截面形状变化，本文对现有的米字型单胞模型进行了改进，用空间抛物线来模拟单胞内纤维束路径，建立了三维四向编织复合材料螺旋型单胞几何模型。螺旋型单胞几何模型避免了内部空间纤维束在单胞中心的交叉，能够更加精确地反映三维四向编织复合材料内部的细观结构。该几何模型虽然以三维四向编织复合材料为对象，但所得结果具有普遍意义，研究方法可以推广到三维多向编织复合材料，为三维多向编织复合材料力学性能分析与材料优化设计提供参考。
基于螺旋型单胞几何模型，本文对三维四向碳/环氧编织复合材料的刚度和强度进行了数值预报与理论计算。应用多相有限元法，把单胞模型划分为三种子单胞，结合高斯积分法对三维四向碳/环氧编织复合材料的有效工程弹性常数进行了数值预报；对三维四向编织复合材料单胞内的应力场分布和单向拉伸应力应变关系曲线进行了数值模拟；分别采用蔡-吴准则和米赛斯准则数值预报了三维四向编织复合材料的强度，研究了三维编织复合材料拉伸损伤机理；基于螺旋型单胞几何模型，对三维四向碳/环氧编织复合材料的有效工程弹性常数和强度进行了理论推导，并将理论推导结果与相应的数值预报进行了对比分析。
为了研究三维四向编织复合材料的热机械性能，本文基于螺旋型单胞几何模型，推导了三维四向编织复合材料热弹性问题的稳态热分析有限元方程，建立了三维四向编织复合材料热物理性能分析的力学模型，数值预报了等效热传导系数和热膨胀系数，并讨论了编织角度、纤维体积含量等因素对三维四向编织复合材料热物理性能的影响。结合热传导问题的有限元理论，对三维四向编织复合材料进行了稳态热传导分析，数值预报了第一类边界条件（已知边界温度）和第二类边界条件（已知边界热流）的三维四向编织复合材料的温度场分布。在稳态热传导分析的基础上，建立了三维四向编织复合材料热力耦合行为分析的有限元方法。通过对三维四向编织复合材料单胞模型施加相同的机械载荷与不同的热载荷条件（稳态温度场、已知边界温度和已知边界热流），对三维四向编织复合材料在热力耦合作用下的强度进行预报，讨论了编织角度、纤维体积含量等因素对三维四向编织复合材料热力耦合强度的影响。
The ancient braiding technology and the processing technique for moderncomposites are combined organically to make the composites with unique structure,which fundamentally overcomes the shortcomings of the unidirectional compositelaminates, such as delamination and cracking etc. The3D braided composites hasbeen paid much more attention by engineering for its excellent mechanical properties,such as high specific strength, high specific stiffness, impact toughness,fatigue-fracture, ablative resistance, structural integrity and designability etc. So the3D braided composites is widely used in the fields of high technology such asaeronautics, astronautics, marine, sports, and biomedical etc. In order to make betteruse of3D braided composites, the scholars at home and abroad have carried out a lotof exploration and research on the relationships between microscopic and macromechanical properties in past20years. Some outstanding achievement has beenmade and the3D braided composites have been gradually developed into a popularresearch direction of mechanics. The development and research on3D braidedcomposites at home and abroad are reviewed and analyzed. The geometric model,stiffness and strength, thermo-physical properties and thermo-mechanical couplingbehaviors of3D four-directional carbon/epoxy braided composites are investigatedby using numerical and theoretical methods in this dissertation.
Owing to the squeezing and twisting of braid yarns each other within the3Dfour-directional braided composites, the braid yarns exhibit the bending andvariational cross-section. A helix geometry model for3D four-directional braidedcomposites is established based on the fiber hexprism diagonal brick cell in thispaper. The spatial parabolic is used to simulate the yarn axis of the unit cell. Fourbraiding yarns in the unit cell are curved to avoid the collision at the center of theunit cell. The helix geometry model reflects more accurately the microstructure of3D four-directional braided composites. Though the microscopic geometric model isestablished to the case of3D four-directional braided composites, but the results havegeneral significance and the research methods can be extended to3Dmulti-directional braided composites. These will provide reference for furtheranalyzing the mechanical properties and optimization design of3D multi-directional braided composites.
The stiffness and strength of3D four-directional carbon/epoxy braided compositesare predicted based on the helix geometry model by numerical simulation andtheoretical derivation. The RVE is divided into three kinds of elements according tothe finite multiphase element method: matrix element, yarn element and mixedelement and the gauss quadrature has been proposed to predict the effective elasticconstants. The unit cell stress fields and longitudinal tensile stress-strain relationshipsof3D braided composites are presented through the finite element theory of spaceproblem. The Tsai–Wu and Von Mises criterion are used to predict the failure in theyarn and matrix, respectively, and the longitudinal tensile strength of3D braidedcomposites is calculated and the damage mechanisms of the composites are analyzed.The effective elastic constants and longitudinal tensile strength of3D braidedcomposites are theoretically calculated based on the helix geometry model andcompared with the simulation results.
In order to investigate the thermal mechanical properties of3D four-directionalbraided composites, the finite element equations of steady state thermal analysis ofthermoelastic problem for3D four-directional braided composites are derived and themechanical model of thermo-physical properties analysis for3D four-directionalbraided composites are developed based on the based on the helix geometry model.By numerical computing, the effective thermal conductivity coefficients and thermalexpansion coefficients of3D four-directional braided composites are obtained. Theinfluences of the braid angle and fiber volume fraction on the thermo-physicalproperties of three-dimensional four-directional braided composites are discussed.The steady state thermal conductivity analysis is presented by using the finiteelement theory of thermal conductivity problem. The distribution of temperature of3D braided composites with the first class boundary condition (the distribution oftemperature on the surface is known) and the second class boundary condition (thedistribution of heat flux on the surface is known) are determined. The finite elementmethods of thermo-mechanical coupling behaviors analysis for3D four-directionalbraided composites are developed on the basis of the steady state thermalconductivity analyses. By applying the same mechanical loads and the differentthermal loads (the temperature on the unit cell remains constant, the distribution oftemperature on the surface is known, the distribution of heat flux on the surface is known), the strength of3D braided four-directional composites are analyzed. Theeffects of the braiding angle and fiber volume fraction on the thermo-mechanicalcoupling behaviors of3D braided composites are discussed.
引文
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