考虑界面相的复合材料宏—细观渐进损伤解析模型研究
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摘要
碳纤维增强树脂基复合材料的刚度、强度等宏观力学性能均是由其细观组分结构与性能决定的，为了充分发挥复合材料的可设计性优势，从细观材料组分层面来揭示宏观力学性能的本质是十分必要的。在此需求下，宏-细观协同分析力学模型的研究成为了热点。人们不断地深入了解复合材料细观结构与性能的同时，那些能够和宏观力学分析方法很好相结合的细观力学模型也在迅速地发展，其中通用单胞方法（GMC）就是颇具代表性，有限容积直接平均细观力学方法（FVDAM）则是目前处于发展阶段并且颇具潜力的细观力学方法。这两种方法都是半解析的形式，所以比较容易同现有的商业有限元软件相结合来构建宏-细观分析模型。
本文分别以GMC和FVDAM这两种细观力学方法为基础，面向复合材料的不同层面提出了具有普适性的宏-细观渐进损伤解析模型。本文模型突破了传统宏-细观模型计算效率的瓶颈，并且可以更加细致地考虑细观组分的结构、缺陷及损伤。利用本文提出的模型，研究了单向板的材料常数、单向板横向拉伸/压缩性能、层合板强度和层合板钉连结构的挤压性能，从细观纤维、基体和界面相组分的层面揭示了细观组分性能与结构对宏观力学性能的影响规律。本文主要工作内容如下：
（1）基于GMC和FVDAM细观力学方法，考虑不同的纤维分布，构建了包含细观组分（纤维、界面和基体）的代表性体积单元解析模型。研究了纤维分布和界面相性能对宏观弹性常数预报的影响，通过与实验数据对比，验证了本文模型的合理性与高精度；从细观组分应力和损伤的角度（例如基体、界面相的应力状态）揭示了单向板横向拉伸/压缩的破坏机理及损伤模式，最终指出GMC和FVDAM这两种细观力学方法在预报单向板横向拉伸/压缩的失效行为方面的优势与不足。
（2）将本文提出解析模型与经典层合板理论相结合，进一步提出了宏-细观层合板强度预报解析模型，研究了不同基体组分失效准则（Max-strain、Max-stress、Tsai-Hill和Tsai-Wu）对双轴载荷下层合板（含单向板）强度谱预报的影响。应用本文的预报模型分析了“World-Wide Failure Exercise (WWFE)”中层合板强度预报的全部算例，包括四种材料体系、五种铺层类型、指定载荷下应力-应变曲线等方面。通过与实验数据对比发现本文的强度预报模型有着较广的适用范围和较高的预测精度。
（3）将本文的宏-细观解析模型通过Abaqus用户自定义子程序USDFLD与有限元相结合，构建了基于细观组分失效判断的宏-细观强度预报模型。应用该模型对层合板连接结构的单钉双剪挤压破坏行为进行了研究，预报了三种典型的破坏模式（净拉伸、剪出和挤压破坏），同实验现象吻合很好，并分析了损伤形成的原因。然后研究了连接件的几何尺寸对其极限挤压强度的影响，并同实验对比验证了该模型的预测精度较高。
The stiffness, strength and macroscopic mechanical response of compositematerials are determined by the microscopic components and structures of them. It isnecessary to analyze the macroscopic mechanical response based on the microscopiccomponents and structures of composite materials in order to take full advantage ofthe designability for composte materials. The macro-micro multiscale model isbecoming a hot spot of research interest under this demand. These micromechanicalmethods are developed with high speed with in-depth understandings of mesoscopicstructures and performances of the composite materials. The Generalized Method ofCells (GMC) is a representative homogenized method and the Finite Volume DirectAveraging Miromechanics (FVDAM) is an emerging and promising micromechanicsmethod which is currently under-way to be developed. It is very easy to develop amacro/micro multiscale modle coubled with Finite Element Methods (FEM) due toboth of them are semi-analytical micromechanics methods.
The general macro-micro progressive damage analytic models based on GMCand FVDAM are developed according to different structure levels in this paper. Themodels, in which more details such as structure, defects and damage can beconsidered, broke through the bottleneck of efficiency in traditional macro-micromodel. The material constants of unidirectional laminate, behavior of unidirectionallaminate under tensile/compressive loading, failure envelopes of composite laminatesand bearing strength of bolted laminates are studied by the analytic model presentedin this paper. The influence of micro-mechanical properties and structure ofcomponents such as fiber, matrix and interphase on the macro-mechanical propertiesare revealed. The main body of this paper is as follows,
1. Four types of Representative Volume Element, including fiber, matrix andinterface, are constructed according to different fiber arrays, these models are used topredict the effective elastic properties of unidirectional composite laminate, then theeffects of micro-structure and properties of interface on the effective elasticproperties pridition of unidirectional composite laminate are studied. The accuracy ofthese models is anylized and verified by comparing the simulative value withexperimental data. Furthermore, the tensile/compressive failure behaviors arepredicted, and the predictive strengths with different RVEs are compared. Thedamage mechanism and failure modes are illustrated from micro-component levelsuch as stress of matrix and interface. Finally, the advantage and disadvantage inGMC model and FVDAM model are evaluated.
2. Macro/micro multi-scale analysis models based on the GMC and FVDAMseparately coupled with classical lamination theory were conducted to predict biaxialfailure envelopes of composite laminates, applying failure criteria such as Max-strain,Max-stress, Tsai-Hill and Tsai-Wu failure criteria at the constituent level. And thenthese multi-scale models were used to analyze the all of the examples in the WorldWide Failure Exercise (WWFE), including foure material systems, five layups andthe stress-strain curves under applied loadings. It is focused to compare the accuracyand applicability of GMC and FVDAM model separately and finally thehigh-performaces of these models are indicated.
3. A specimen-level multiscale methodology based on GMC which isimplemented in ABAQUS through the user subroutine USDFLD has been developedto predict the progressive damage of composite bolted joint laminates. The three maintypes of failure modes (net-tension, shear-out and bearing failure) are simulated, andthe accuracy was verified through comparing the simulative results with experimentalfailure modes. Finally, the effect of geometry of specimen on the limit strength ofcomposite bolted joint laminates was studied, and the accuracy was demonstrated bybeing compared with experimental data.
本文分别以GMC和FVDAM这两种细观力学方法为基础，面向复合材料的不同层面提出了具有普适性的宏-细观渐进损伤解析模型。本文模型突破了传统宏-细观模型计算效率的瓶颈，并且可以更加细致地考虑细观组分的结构、缺陷及损伤。利用本文提出的模型，研究了单向板的材料常数、单向板横向拉伸/压缩性能、层合板强度和层合板钉连结构的挤压性能，从细观纤维、基体和界面相组分的层面揭示了细观组分性能与结构对宏观力学性能的影响规律。本文主要工作内容如下：
（1）基于GMC和FVDAM细观力学方法，考虑不同的纤维分布，构建了包含细观组分（纤维、界面和基体）的代表性体积单元解析模型。研究了纤维分布和界面相性能对宏观弹性常数预报的影响，通过与实验数据对比，验证了本文模型的合理性与高精度；从细观组分应力和损伤的角度（例如基体、界面相的应力状态）揭示了单向板横向拉伸/压缩的破坏机理及损伤模式，最终指出GMC和FVDAM这两种细观力学方法在预报单向板横向拉伸/压缩的失效行为方面的优势与不足。
（2）将本文提出解析模型与经典层合板理论相结合，进一步提出了宏-细观层合板强度预报解析模型，研究了不同基体组分失效准则（Max-strain、Max-stress、Tsai-Hill和Tsai-Wu）对双轴载荷下层合板（含单向板）强度谱预报的影响。应用本文的预报模型分析了“World-Wide Failure Exercise (WWFE)”中层合板强度预报的全部算例，包括四种材料体系、五种铺层类型、指定载荷下应力-应变曲线等方面。通过与实验数据对比发现本文的强度预报模型有着较广的适用范围和较高的预测精度。
（3）将本文的宏-细观解析模型通过Abaqus用户自定义子程序USDFLD与有限元相结合，构建了基于细观组分失效判断的宏-细观强度预报模型。应用该模型对层合板连接结构的单钉双剪挤压破坏行为进行了研究，预报了三种典型的破坏模式（净拉伸、剪出和挤压破坏），同实验现象吻合很好，并分析了损伤形成的原因。然后研究了连接件的几何尺寸对其极限挤压强度的影响，并同实验对比验证了该模型的预测精度较高。
The stiffness, strength and macroscopic mechanical response of compositematerials are determined by the microscopic components and structures of them. It isnecessary to analyze the macroscopic mechanical response based on the microscopiccomponents and structures of composite materials in order to take full advantage ofthe designability for composte materials. The macro-micro multiscale model isbecoming a hot spot of research interest under this demand. These micromechanicalmethods are developed with high speed with in-depth understandings of mesoscopicstructures and performances of the composite materials. The Generalized Method ofCells (GMC) is a representative homogenized method and the Finite Volume DirectAveraging Miromechanics (FVDAM) is an emerging and promising micromechanicsmethod which is currently under-way to be developed. It is very easy to develop amacro/micro multiscale modle coubled with Finite Element Methods (FEM) due toboth of them are semi-analytical micromechanics methods.
The general macro-micro progressive damage analytic models based on GMCand FVDAM are developed according to different structure levels in this paper. Themodels, in which more details such as structure, defects and damage can beconsidered, broke through the bottleneck of efficiency in traditional macro-micromodel. The material constants of unidirectional laminate, behavior of unidirectionallaminate under tensile/compressive loading, failure envelopes of composite laminatesand bearing strength of bolted laminates are studied by the analytic model presentedin this paper. The influence of micro-mechanical properties and structure ofcomponents such as fiber, matrix and interphase on the macro-mechanical propertiesare revealed. The main body of this paper is as follows,
1. Four types of Representative Volume Element, including fiber, matrix andinterface, are constructed according to different fiber arrays, these models are used topredict the effective elastic properties of unidirectional composite laminate, then theeffects of micro-structure and properties of interface on the effective elasticproperties pridition of unidirectional composite laminate are studied. The accuracy ofthese models is anylized and verified by comparing the simulative value withexperimental data. Furthermore, the tensile/compressive failure behaviors arepredicted, and the predictive strengths with different RVEs are compared. Thedamage mechanism and failure modes are illustrated from micro-component levelsuch as stress of matrix and interface. Finally, the advantage and disadvantage inGMC model and FVDAM model are evaluated.
2. Macro/micro multi-scale analysis models based on the GMC and FVDAMseparately coupled with classical lamination theory were conducted to predict biaxialfailure envelopes of composite laminates, applying failure criteria such as Max-strain,Max-stress, Tsai-Hill and Tsai-Wu failure criteria at the constituent level. And thenthese multi-scale models were used to analyze the all of the examples in the WorldWide Failure Exercise (WWFE), including foure material systems, five layups andthe stress-strain curves under applied loadings. It is focused to compare the accuracyand applicability of GMC and FVDAM model separately and finally thehigh-performaces of these models are indicated.
3. A specimen-level multiscale methodology based on GMC which isimplemented in ABAQUS through the user subroutine USDFLD has been developedto predict the progressive damage of composite bolted joint laminates. The three maintypes of failure modes (net-tension, shear-out and bearing failure) are simulated, andthe accuracy was verified through comparing the simulative results with experimentalfailure modes. Finally, the effect of geometry of specimen on the limit strength ofcomposite bolted joint laminates was studied, and the accuracy was demonstrated bybeing compared with experimental data.
引文
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