复合材料高精度宏-细观统一本构模型及其应用研究
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摘要
新一代航空发动机将大量采用新型的复合材料结构。为满足航空科技发展的需要,必须对复合材料结构从宏观尺度与细观尺度上深入系统地研究其力学行为。本文开展了复合材料宏-细观统一本构模型-通用单胞模型的深入研究,发展了复合材料高精度宏-细观统一本构模型以及基于该模型的多尺度有限元分析技术。本文的研究结果具有重要的理论意义和工程应用价值。
本文采用了以应力取代应变作为未知量,对通用单胞模型的算法进行了改进。改进后的模型在保证计算精度不变的前提下,大大提高了计算效率。用改进算法的通用单胞模型对纤维增强复合材料的热膨胀系数进行了计算,结果表明该模型可以考虑纤维复杂截面形状和排列方式对复合材料力学特性的影响。同时,本文把改进算法推广到三维情况,并对颗粒增强复合材料的宏观性能进行了预测,验证了通用单胞模型的合理性。
把通用单胞模型细观位移模式由线性提高到二阶,发展了高精度通用单胞模型,从而可以考虑细观正应力与剪应力之间的耦合。为了提高计算效率,进一步采用界面的平均量代替细观位移函数中的系数作为未知量,提出了改进的高精度通用单胞模型。利用改进的高阶模型对复合材料的宏观弹塑性性能及细观应力场进行了分析,并与细观力学有限元法的结果和试验值进行了对比,结果吻合较好。
本文发展了一种对复合材料结构进行宏细观一体化分析的多尺度有限元法,并将通用单胞模型融入到通用有限元程序系统,实现了复合材料结构的宏-细观一体化分析。该方法既能够考虑细观结构特征对宏观性能的影响,又能够在结构分析中获得宏观应力、应变场的同时,获得细观应力、应变场,为复合材料结构损伤分析打下了良好的基础。利用开发的软件系统对复合材料叶片环结构进行了分析。结果表明,本文发展的方法是有效的,对复合材料结构在新一代航空发动机上的应用具有重要意义。
The composite structures will be broadly used in the next generation aeroengine. A high-fidelity unified macro- and micro-mechanics constitutive model and its applications for composites are studied to satisfy needs of analyzing mechanical behaviors of composites and structures on macroscopic and microscopic scales. A multi-scale finite element stress analysis corresponding to the constitutive model is developed. The method can be applied to engineering practice and possesses great importance in theory.
An efficient implementation of the Generalized Method of Cell(GMC) effectively replaces the subcell strains by the subcell interfacial tractions as the basic unknown micro-variables, which in turn substantially reduces the size of the system of equations for the determination of these micro-variables. This substantial reduction in the size of the system of equations for the unknown micro-variables makes possible the analysis of repeating unit cells containing thousands of subcells, which could not be analyzed previously by the original formulation of GMC. The thermal expansion coefficients of composites have been analyzed in the paper. The results indicate that the influence of fiber shape and packing arrangement can be considered.
The efficient implementation of GMC can be extended to the three dimensional GMC. It is used to predict mechanical behavior of particulate reinforced metal matrix composites. The results indicate that GMC accurately predicts the engineering properties of the particulate reinforced composites studied. The high-fidelity GMC is presented through introducing the higher-order displacement field. The model overcomes shortcomings of the absence of so-called shear coupling. The efficient reformulation of high-fidelity GMC is presented based on the hypothesis of periodicity in composite microstructure. In this approach, surface-averaged quantities are the primary variables that replace the coefficient of the displacement after the mechanical equations are analyzed and answered in microscopic elements. It reduces the number of equations involved and eliminates the
concept of generic cells. The transverse and longitudinal variables are dis-coupled. The effective moduli and local stress fields are analyzed. Numerical results based on this model agree well with the available results from experiments and theoretical analysis.
A unified macro- and micro-mechanics analysis multi-scale finite element method for composite structures is developed. The software for computes have been developed by integrating the model into the general finite element method program. Not only the method can consider micro-structural geometry effects on macro-properties, but also it can obtain both macroscopic and microscopic stress and strain fields, which provide sufficient basis for the damage and fracture analysis of composite structures. The ring is analyzed with the developed software. The validity of the model is verified by the result. It’s significant to applying composite structures in the next generation aeroengine.
本文采用了以应力取代应变作为未知量,对通用单胞模型的算法进行了改进。改进后的模型在保证计算精度不变的前提下,大大提高了计算效率。用改进算法的通用单胞模型对纤维增强复合材料的热膨胀系数进行了计算,结果表明该模型可以考虑纤维复杂截面形状和排列方式对复合材料力学特性的影响。同时,本文把改进算法推广到三维情况,并对颗粒增强复合材料的宏观性能进行了预测,验证了通用单胞模型的合理性。
把通用单胞模型细观位移模式由线性提高到二阶,发展了高精度通用单胞模型,从而可以考虑细观正应力与剪应力之间的耦合。为了提高计算效率,进一步采用界面的平均量代替细观位移函数中的系数作为未知量,提出了改进的高精度通用单胞模型。利用改进的高阶模型对复合材料的宏观弹塑性性能及细观应力场进行了分析,并与细观力学有限元法的结果和试验值进行了对比,结果吻合较好。
本文发展了一种对复合材料结构进行宏细观一体化分析的多尺度有限元法,并将通用单胞模型融入到通用有限元程序系统,实现了复合材料结构的宏-细观一体化分析。该方法既能够考虑细观结构特征对宏观性能的影响,又能够在结构分析中获得宏观应力、应变场的同时,获得细观应力、应变场,为复合材料结构损伤分析打下了良好的基础。利用开发的软件系统对复合材料叶片环结构进行了分析。结果表明,本文发展的方法是有效的,对复合材料结构在新一代航空发动机上的应用具有重要意义。
The composite structures will be broadly used in the next generation aeroengine. A high-fidelity unified macro- and micro-mechanics constitutive model and its applications for composites are studied to satisfy needs of analyzing mechanical behaviors of composites and structures on macroscopic and microscopic scales. A multi-scale finite element stress analysis corresponding to the constitutive model is developed. The method can be applied to engineering practice and possesses great importance in theory.
An efficient implementation of the Generalized Method of Cell(GMC) effectively replaces the subcell strains by the subcell interfacial tractions as the basic unknown micro-variables, which in turn substantially reduces the size of the system of equations for the determination of these micro-variables. This substantial reduction in the size of the system of equations for the unknown micro-variables makes possible the analysis of repeating unit cells containing thousands of subcells, which could not be analyzed previously by the original formulation of GMC. The thermal expansion coefficients of composites have been analyzed in the paper. The results indicate that the influence of fiber shape and packing arrangement can be considered.
The efficient implementation of GMC can be extended to the three dimensional GMC. It is used to predict mechanical behavior of particulate reinforced metal matrix composites. The results indicate that GMC accurately predicts the engineering properties of the particulate reinforced composites studied. The high-fidelity GMC is presented through introducing the higher-order displacement field. The model overcomes shortcomings of the absence of so-called shear coupling. The efficient reformulation of high-fidelity GMC is presented based on the hypothesis of periodicity in composite microstructure. In this approach, surface-averaged quantities are the primary variables that replace the coefficient of the displacement after the mechanical equations are analyzed and answered in microscopic elements. It reduces the number of equations involved and eliminates the
concept of generic cells. The transverse and longitudinal variables are dis-coupled. The effective moduli and local stress fields are analyzed. Numerical results based on this model agree well with the available results from experiments and theoretical analysis.
A unified macro- and micro-mechanics analysis multi-scale finite element method for composite structures is developed. The software for computes have been developed by integrating the model into the general finite element method program. Not only the method can consider micro-structural geometry effects on macro-properties, but also it can obtain both macroscopic and microscopic stress and strain fields, which provide sufficient basis for the damage and fracture analysis of composite structures. The ring is analyzed with the developed software. The validity of the model is verified by the result. It’s significant to applying composite structures in the next generation aeroengine.
引文
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