聚合物基复合材料多尺度方法的研究
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摘要
本文旨在研究聚合物基复合材料的力学行为。根据材料内部结构的尺度特征，分别从纳观、细观和宏观不同层次展开了分析研究。假设材料内部结构呈周期性或近似周期性分布，以逐次渐近均匀化方法与有限元方法相结合，建立了细观和纳观单胞分析模型，利用FORTRAN语言编写了多尺度渐近均匀化应用程序，研究了聚合物基复合材料宏观力学性能与微结构间的关系以及细观局部应力分布规律。
本文利用多尺度渐近均匀化理论与有限元分析技术，建立了预测聚合物基复合材料有效性能的计算模型，研究了颗粒和聚合物基体的模量比以及颗粒的泊松比、形状、体积份数等对聚合物基复合材料的宏观有效弹性常数的影响规律；然后利用有限元分析技术模拟了材料的单向拉伸实验，对均匀化方法所得到的聚合物基复合材料的宏观有效弹性常数进行了实验验证，得到的结果显示两者是吻合的。
本文建立了基于多尺度渐近均匀化理论的宏观应力场与细观单胞局部应力场的分析模型，研究了聚合物基复合材料的细观局部应力与模量比、颗粒形状、泊松比和体积组份的关系，定性分析了聚合物基复合材料的细观破坏形式；研究了模量比和体积份数对宏观应力集中处细观局部应力集中影响；针对局部应力集中问题，利用网格自适应分析技术与有限元法相结合，构建了网格层叠技术，并与多尺度渐近均匀化理论相结合研究夹杂对聚合物基复合材料的宏观应力场与细观单胞局部应力场的影响，得到了一些有用的结果。
利用三相球模型与界面位移跳跃假设，建立含非完美界面聚合物基复合材料有效弹性常数的预测模型，推导出其有效体积模量和有效剪切模量的理论预测公式。分析讨论了界面参数对聚合物基复合材料有效弹性常数的影响。本文得到的预测模型具有一般性，在界面参数C=1时，模型简化成完美界面情形；在界面参数C=0时，模型简化成脱粘界面情形。
结晶聚合物—无机纳米复合材料内部结构是一个多尺度复杂结构体系。本文利用多尺度逐次渐近均匀化理论的分析计算模型，在实验分析的基础上，从材料的微观结构特点出发，建立了结晶聚合物—无机纳米复合材料的多尺度分析计算模型。将结晶聚合物—无机纳米复合材料内部结构分别用宏观、细观和纳观三个层次来描述。利用建立的多尺度逐次渐近均匀化理论和有限元法，经两次纳观层次均匀化和一次细观层次均匀化，通过数值计算结果讨论了聚合物结晶度、聚合物结晶相弹性模量、无机纳米颗粒弹性模量和无机纳米颗粒体积份数等参数对聚合物—无机纳米复合材料有效弹性模量的影响，并获得了一些有价值的结果。
本文工作力图为聚合物基复合材料的改性设计提供理论依据。
According to the scale characteristic of material internal structure, the mechanical properties of polymer matrix composites are studied from multilevels (macroscopic, microscopic and nanoscopic levels) in this work. Microscopic structure of polymer matrix composites is assumed to be periodic or approximately periodic. The finite element method is combined with multiscale successive homogenization theory based on asymptotic expansion. Microscopic and nanoscopic base cells analysis models are established. A computational program based on multiscale homogenization method is written by FORTRAN language. The relation between macroscopic mechanical properties of polymer matrix composites and microscopic structure is studied. Local variation rule of microscopic stress is researched.
The computed model for predicting the effective properties of polymer matrix composites is established based on multiscale asymptotic homogenization theory and finite element analysis technology. The influence of ratio of modulus of particle and polymer matrix, particle Poisson's ratio, shape, volume fraction on effective elastic constants of polymer matrix composites is studied. Uniaxial tension experiment is simulated by finite element analysis technology to validate macroscopic effective elastic constants of polymer matrix composites computed by homogenization method. Experiment results show the accordance with computed results.
Based on homogenization theory, the analyzed models of macroscopic stress field and the microscopic unit cell local field are established in this work. The relation between microscopic local stress of polymer matrix composites and ratio of modulus, particle shape, Poisson's ratio and volume fraction is investigated. The microscopic failure modes of polymer matrix composites are qualitatively analyzed. The effect of ratio of modulus and volume fraction on microscopic local stress concentration at macroscopic stress concentration location is analyzed. Mesh adaptive analysis technique is combined with the finite element method to study local stress problem. Mesh superposition technique is constructed and combined with homogenization method to research the effect of heterogeneity on macroscopic stress field and unit cell microscopic local stress field of polymer matrix composites. Some available results are obtained.
The effective elastic constant prediction model of polymer matrix composites with imperfect interface is established by integrating three phase model with interface displacement jump assumption. The theoretical predicting formulae of effective bulk modulus and effective shear modulus have been derived. The effect of interface parameters on the effective elastic constants of polymer matrix composites is discussed. The predicted results in this paper have the generality and universality. The model is simplified as perfect interface case when interface parameter C is equal to 1 and as debonding interface case when interface parameter C is equal to O.
Crystalline polymer-inorganic nanocomposites present a multiscale complex structure system. The model of multiscale successive asymptotic homogenization theory is applied. Based on the experiment analysis of crystalline polymer-inorganic nanocomposites, from a microscopic structure characteristic of material point of view, a multiscale analysis computing model of crystalline polymer-inorganic nanocomposites is established. Internal structure of crystalline polymer-inorganic nanocomposites is described by multilevels(macroscopic, microscopic and nanoscopic levels). The finite element method is combined with multiscale successive homogenization theory based on asymptotic expansion for predicting effective modulus of crystalline polymer-inorganic nanocomposites. Two nanoscopic level homogenizations and one microscopic homogenization are used. The effect of crystal degree of polymer, elastic modulus of crystal inclusion, elastic modulus of nanoparticle and volume fraction of nanoparticle on the effective elastic modulus of polymer-inorganic nanocomposite is discussed respectively. Some valuable results are obtained.
This work may be used to supply guidelines for the modifying design of polymer matrix composites.
本文利用多尺度渐近均匀化理论与有限元分析技术，建立了预测聚合物基复合材料有效性能的计算模型，研究了颗粒和聚合物基体的模量比以及颗粒的泊松比、形状、体积份数等对聚合物基复合材料的宏观有效弹性常数的影响规律；然后利用有限元分析技术模拟了材料的单向拉伸实验，对均匀化方法所得到的聚合物基复合材料的宏观有效弹性常数进行了实验验证，得到的结果显示两者是吻合的。
本文建立了基于多尺度渐近均匀化理论的宏观应力场与细观单胞局部应力场的分析模型，研究了聚合物基复合材料的细观局部应力与模量比、颗粒形状、泊松比和体积组份的关系，定性分析了聚合物基复合材料的细观破坏形式；研究了模量比和体积份数对宏观应力集中处细观局部应力集中影响；针对局部应力集中问题，利用网格自适应分析技术与有限元法相结合，构建了网格层叠技术，并与多尺度渐近均匀化理论相结合研究夹杂对聚合物基复合材料的宏观应力场与细观单胞局部应力场的影响，得到了一些有用的结果。
利用三相球模型与界面位移跳跃假设，建立含非完美界面聚合物基复合材料有效弹性常数的预测模型，推导出其有效体积模量和有效剪切模量的理论预测公式。分析讨论了界面参数对聚合物基复合材料有效弹性常数的影响。本文得到的预测模型具有一般性，在界面参数C=1时，模型简化成完美界面情形；在界面参数C=0时，模型简化成脱粘界面情形。
结晶聚合物—无机纳米复合材料内部结构是一个多尺度复杂结构体系。本文利用多尺度逐次渐近均匀化理论的分析计算模型，在实验分析的基础上，从材料的微观结构特点出发，建立了结晶聚合物—无机纳米复合材料的多尺度分析计算模型。将结晶聚合物—无机纳米复合材料内部结构分别用宏观、细观和纳观三个层次来描述。利用建立的多尺度逐次渐近均匀化理论和有限元法，经两次纳观层次均匀化和一次细观层次均匀化，通过数值计算结果讨论了聚合物结晶度、聚合物结晶相弹性模量、无机纳米颗粒弹性模量和无机纳米颗粒体积份数等参数对聚合物—无机纳米复合材料有效弹性模量的影响，并获得了一些有价值的结果。
本文工作力图为聚合物基复合材料的改性设计提供理论依据。
According to the scale characteristic of material internal structure, the mechanical properties of polymer matrix composites are studied from multilevels (macroscopic, microscopic and nanoscopic levels) in this work. Microscopic structure of polymer matrix composites is assumed to be periodic or approximately periodic. The finite element method is combined with multiscale successive homogenization theory based on asymptotic expansion. Microscopic and nanoscopic base cells analysis models are established. A computational program based on multiscale homogenization method is written by FORTRAN language. The relation between macroscopic mechanical properties of polymer matrix composites and microscopic structure is studied. Local variation rule of microscopic stress is researched.
The computed model for predicting the effective properties of polymer matrix composites is established based on multiscale asymptotic homogenization theory and finite element analysis technology. The influence of ratio of modulus of particle and polymer matrix, particle Poisson's ratio, shape, volume fraction on effective elastic constants of polymer matrix composites is studied. Uniaxial tension experiment is simulated by finite element analysis technology to validate macroscopic effective elastic constants of polymer matrix composites computed by homogenization method. Experiment results show the accordance with computed results.
Based on homogenization theory, the analyzed models of macroscopic stress field and the microscopic unit cell local field are established in this work. The relation between microscopic local stress of polymer matrix composites and ratio of modulus, particle shape, Poisson's ratio and volume fraction is investigated. The microscopic failure modes of polymer matrix composites are qualitatively analyzed. The effect of ratio of modulus and volume fraction on microscopic local stress concentration at macroscopic stress concentration location is analyzed. Mesh adaptive analysis technique is combined with the finite element method to study local stress problem. Mesh superposition technique is constructed and combined with homogenization method to research the effect of heterogeneity on macroscopic stress field and unit cell microscopic local stress field of polymer matrix composites. Some available results are obtained.
The effective elastic constant prediction model of polymer matrix composites with imperfect interface is established by integrating three phase model with interface displacement jump assumption. The theoretical predicting formulae of effective bulk modulus and effective shear modulus have been derived. The effect of interface parameters on the effective elastic constants of polymer matrix composites is discussed. The predicted results in this paper have the generality and universality. The model is simplified as perfect interface case when interface parameter C is equal to 1 and as debonding interface case when interface parameter C is equal to O.
Crystalline polymer-inorganic nanocomposites present a multiscale complex structure system. The model of multiscale successive asymptotic homogenization theory is applied. Based on the experiment analysis of crystalline polymer-inorganic nanocomposites, from a microscopic structure characteristic of material point of view, a multiscale analysis computing model of crystalline polymer-inorganic nanocomposites is established. Internal structure of crystalline polymer-inorganic nanocomposites is described by multilevels(macroscopic, microscopic and nanoscopic levels). The finite element method is combined with multiscale successive homogenization theory based on asymptotic expansion for predicting effective modulus of crystalline polymer-inorganic nanocomposites. Two nanoscopic level homogenizations and one microscopic homogenization are used. The effect of crystal degree of polymer, elastic modulus of crystal inclusion, elastic modulus of nanoparticle and volume fraction of nanoparticle on the effective elastic modulus of polymer-inorganic nanocomposite is discussed respectively. Some valuable results are obtained.
This work may be used to supply guidelines for the modifying design of polymer matrix composites.
引文
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