三维编织复合材料几何建模及界面损伤力学研究
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摘要
三维编织复合材料性能优良其最大优势是具有高的可设计性,在航空航天、国防、医疗、民用设施等高科技领域被广泛应用。因此,对这种高性能材料的力学性能及损伤情况的研究就变得尤为重要。目前,对三维编织复合材料力学行为的研究取得了一定的成果,但仍然有许多问题需要进一步研究分析。本文针对三维编织复合材料,从弹性常数预测、纤维及纤维基体界面受力、纤维损伤三个方面进行了研究。
第一章介绍了三维编织复合材料的产生和发展过程,综述了从几何建模、力学性能数值仿真、界面力学分析等方面对三维编织复合材料取得的成果和研究现状,并说明了本文的选题目的和研究意义。
第二章通过采用内部单胞纤维弯曲模型、表面单胞和角单胞折线模型的三单胞模型来预报三维编织复合材料的有效弹性模量。首先,建立周期性的三单胞模型,根据纤维在模型中的几何分布,分别计算出各个模型中纤维和基体的体积百分比。然后,通过刚度平均得到各单胞模型的刚度矩阵。最后,通过体积平均法得出了三维编织复合材料预制件的有效弹性模量。
第三章研究了单根直纤维及界面的受力分析。首先,弯曲的纤维可以表示为一系列直纤维微元通过坐标变换组合而成,通过对纤维拔出模型理论方面的分析得到纤维轴向应力和剪切应力。然后,通过有限元软件对纤维拔出模型进行模拟,得到纤维和基体的应力云图和数据。最后,对结果进行了分析,并对材料可能发生损坏进行了阐述。
第四章探讨了带有缺陷的编织复合材料界面的应力场分布。首先,通过轴对称界面端奇异应力场的特征值法、界面力学和断裂力学的理论对三维编织复合材料在两种缺陷下的应力场分布和断裂准则进行了理论分析。然后,通过有限元软件对两种缺陷进行了数值模拟,得到了奇异点处的应力场和应力强度因子。最后还模拟分析了裂纹尺度对材料应力场的影响。
3-D braided composites is widely used in aerospace, defense, medical, civilian facilities and other high-tech areas by its excellent performance and outstanding designability. The research of 3-D braided composites mechanical property and damage is a very important problem. At present, though the research of mechanics behavior of 3-D braided composites has some progress, there are many problems need to be further investigated. This paper studies 3-D braided composites by predicting elastic constants, analysing stress and damage of fiber and fiber matrix interface using theory and numerical analysis.
In the first chapter, the development of 3-D braided composites is introduced, the recent research progress of 3-D braided composites on geometry modeling, process, numerical simulation of mechanical property, analysis of interfacial mechanics are reviewed, and the writer expounds the purpose of this topic and significance of research.
In the second chapter, effective modulus of the 3-D braided composites is predicted by using internal cell curved fiber model, surface cell and angle cell polyline flber model. First, according to the geometric distribution of fiber in model, periodic three cell models is established, and fiber and matrix volume percentage of each model is separately calculated. Then, the stiffness matrix of each single cell model is get through averaging stiffness. Finally, the effective elastic modulus of 3D braided composites preform are obtained by the method of averaging volume.
In the third chapter, the writer researches a single straight fiber and analyses stress of interface. First, curved fibre can be expressed as a combination of a series of infinitesimal straight fiber through coordinate transformation, fiber axial stress and the shear stress are get by the theoretical analysis of fiber drawing model. Then, the stress nephogram and data of fiber and matrix are obtained through simulating fiber drawing model using the finite element software. Finally, the numerical results are analysed.
In the fourth chapter, the writer discusses the stress distribution of defective braided composites. First, through using the eigenvalue method of axisymmetric interface singular stress field, interface mechanics and fracture mechanics theory, the stress distribution and fracture criterion of defective 3-D braided composites are analysed. Then, through the numerical simulation for two defect of 3-D braided composites by the finite element software, the singular point of the stress distribution and the stress intensity factor are obtained. Finally, the crack scale effect for material stress distribution is simulated and analysed.
第一章介绍了三维编织复合材料的产生和发展过程,综述了从几何建模、力学性能数值仿真、界面力学分析等方面对三维编织复合材料取得的成果和研究现状,并说明了本文的选题目的和研究意义。
第二章通过采用内部单胞纤维弯曲模型、表面单胞和角单胞折线模型的三单胞模型来预报三维编织复合材料的有效弹性模量。首先,建立周期性的三单胞模型,根据纤维在模型中的几何分布,分别计算出各个模型中纤维和基体的体积百分比。然后,通过刚度平均得到各单胞模型的刚度矩阵。最后,通过体积平均法得出了三维编织复合材料预制件的有效弹性模量。
第三章研究了单根直纤维及界面的受力分析。首先,弯曲的纤维可以表示为一系列直纤维微元通过坐标变换组合而成,通过对纤维拔出模型理论方面的分析得到纤维轴向应力和剪切应力。然后,通过有限元软件对纤维拔出模型进行模拟,得到纤维和基体的应力云图和数据。最后,对结果进行了分析,并对材料可能发生损坏进行了阐述。
第四章探讨了带有缺陷的编织复合材料界面的应力场分布。首先,通过轴对称界面端奇异应力场的特征值法、界面力学和断裂力学的理论对三维编织复合材料在两种缺陷下的应力场分布和断裂准则进行了理论分析。然后,通过有限元软件对两种缺陷进行了数值模拟,得到了奇异点处的应力场和应力强度因子。最后还模拟分析了裂纹尺度对材料应力场的影响。
3-D braided composites is widely used in aerospace, defense, medical, civilian facilities and other high-tech areas by its excellent performance and outstanding designability. The research of 3-D braided composites mechanical property and damage is a very important problem. At present, though the research of mechanics behavior of 3-D braided composites has some progress, there are many problems need to be further investigated. This paper studies 3-D braided composites by predicting elastic constants, analysing stress and damage of fiber and fiber matrix interface using theory and numerical analysis.
In the first chapter, the development of 3-D braided composites is introduced, the recent research progress of 3-D braided composites on geometry modeling, process, numerical simulation of mechanical property, analysis of interfacial mechanics are reviewed, and the writer expounds the purpose of this topic and significance of research.
In the second chapter, effective modulus of the 3-D braided composites is predicted by using internal cell curved fiber model, surface cell and angle cell polyline flber model. First, according to the geometric distribution of fiber in model, periodic three cell models is established, and fiber and matrix volume percentage of each model is separately calculated. Then, the stiffness matrix of each single cell model is get through averaging stiffness. Finally, the effective elastic modulus of 3D braided composites preform are obtained by the method of averaging volume.
In the third chapter, the writer researches a single straight fiber and analyses stress of interface. First, curved fibre can be expressed as a combination of a series of infinitesimal straight fiber through coordinate transformation, fiber axial stress and the shear stress are get by the theoretical analysis of fiber drawing model. Then, the stress nephogram and data of fiber and matrix are obtained through simulating fiber drawing model using the finite element software. Finally, the numerical results are analysed.
In the fourth chapter, the writer discusses the stress distribution of defective braided composites. First, through using the eigenvalue method of axisymmetric interface singular stress field, interface mechanics and fracture mechanics theory, the stress distribution and fracture criterion of defective 3-D braided composites are analysed. Then, through the numerical simulation for two defect of 3-D braided composites by the finite element software, the singular point of the stress distribution and the stress intensity factor are obtained. Finally, the crack scale effect for material stress distribution is simulated and analysed.
引文
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