复合材料热/力学性能的双尺度渐近分析
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摘要
随着航天技术的迅猛发展,对复合材料及其结构在热力耦合条件下的性能表征和损毁机理的研究需求日趋迫切。对复合材料进行多尺度建模与计算与物质世界的基本性质相符合,可以更加准确地表征材料的性能以及预报材料在一定工况下的响应规律;而且,它为依赖于微结构的材料性能的优化提供了有利的支持,我们可以基于多尺度计算,在材料制备前进行加工工艺与微结构的设计。
在众多跨尺度计算方法中,双尺度渐近分析方法是一种适用于周期性构造复合材料性能表征与结构分析的通用、高效、精确的方法。其基本思想是:材料性能的计算和预测沿着从细观到宏观这一过程,采用双尺度均匀化方法,由细观尺度下的单胞计算出宏观尺度下材料的均匀化性能参数;而结构物理、力学行为的计算与预测则是从宏观平均场方程出发,从宏观到细观,利用双尺度渐近展开技术,计算出细观尺度下物理、力学量的局部涨落。本文主要基于双尺度渐近分析方法对复合材料的热/力学有效性能与响应规律进行了多尺度表征与计算。
首先,从热力耦合问题的基本方程出发,建立了复合材料温度场和力学场的双尺度渐近表达式;得到了复合材料宏观均匀化热传导系数、刚度系数和热膨胀系数的表达式;并且将该方法与有限元方法相结合,给出了数值实现双尺度计算的计算步骤。
其次,通过数值试验验证了双尺度分析方法预报复合材料宏观性能的有效性,进而研究了夹杂百分含量、夹杂形状和夹杂之间的相互作用对复合材料宏观性能的影响;并且通过数值试验验证了双尺度分析方法描述结构场函数的有效性和高效性。
接下来,将双尺度渐近分析方法应用于ZrB2-SiC超高温陶瓷材料体系,进行了跨越微观-细观-宏观的多尺度表征与模拟的尝试,计算了ZrB2-SiC超高温陶瓷的热响应规律,分析了SiC夹杂颗粒的尺寸和分布位置对细观结构的影响;并且建立了碳纤维增韧超高温陶瓷基复合材料的单胞模型,计算了碳纤维增韧超高温陶瓷基复合材料结构在一定工况下的响应,确定了结构内的最大应力值及其所在位置。
然后,考虑到界面相的小尺寸对计算规模的影响,提出了二重双尺度方法。将二重双尺度方法与有限元方法相结合,计算了宏观轴向均匀拉伸载荷、横向均匀拉伸载荷和横向均匀剪切载荷条件下含界面相单向纤维增强复合材料的三维应力场分布,确定了各种载荷条件下复合材料结构内的最大应力值及其所在位置;讨论了界面相性能对应力场分布的影响,结果显示纤维—界面相—基体力学性能的等差过渡有利于缓解轴向拉伸载荷下复合材料内纤维在界面附近的应力集中。
最后,针对单向复合材料直杆,按照组分材料的不同性质引入不同的破坏准则,提出预报单向纤维增强复合材料轴向强度的双尺度方法。在预报轴向拉伸强度时,通过引入纤维等效拉伸强度的概念,将拉伸载荷下的渐近损伤与双尺度方法联系起来。结果显示采用双尺度方法预报的复合材料宏观强度值与实验值吻合较好,说明了该方法的有效性。
With the rapid development of space technology, the investigations on macroscopic properties’characterization and broken-down mechanism of composite material structures under thermo-elasticity coupling condition are extremely desired. The multi-scale modeling and computation for composite materials is coincident with the intrinsic nature of physical world, so it can more exactly characterize properties of composites and predict the response of composites under certain loading (or working) condition. Moreover, it supplies a method to optimize microstructure of composites for the best properties. That is, based on multi-scale modeling and computation, we can design the microstructure of composites and determine the processing before preparation of composites.
Among many multi-scale methods known, two-scale asymptotic analysis method is a general, efficient and accurate method which is suitable for properties’characterization and response analysis of composites with periodic configuration. Its main idea is that the computation for properties of composites is presented with two-scale homogenization in the process from mesoscopic to macroscopic, and then the local fluctuations of physical and mechanical fields are described with two-scale asymptotic technique in the process from macroscopic to mesoscopic. In this paper, based on two-scale asymptotic method principally, the effective thermal/mechanical properties of composites are characterized as well as the responses of composite structures in multiple scales under certain loading (or working) condition are computed.
Firstly, two-scale asymptotic formulae of the temperature and the mechanical fields are derived on the base of the basic equations of thermo-elasticity coupling problem, and then the expressions of effective thermal conductivities, stiffness and thermal expansion coefficients of composites are deduced. Whereafter, combining with finite element method, the numerical computing procedure of two-scale method is established.
Secondly, the validity of two-scale method for characterizing the effective properties of composites is evaluated by numerical experiments. The changes of the effective properties of composites resulting from the variations of the volume fraction and shape of inclusion and the interaction of the inclusions are analyzed. After that, the validity and efficiency of two-scale method for describing the temperature and mechanical fields of composite structure are validated by numerical experiments.
Thirdly, two-scale asymptotic method is employed in the field of ZrB2-SiC ultra high temperature ceramics (UHTCs) to implement multi-scale characterization and simulation which links micro-, meso- and macro-scale. The thermal response of ZrB2-SiC is computed and the influences of the size and the location of SiC inclusion on microstructure of ZrB2-SiC are analyzed. Furthermore, the unit cell of carbon fibre toughened UHTCs matrix composite is modeled, the response of the composite under certain working condition is computed, and the maximal stress in the composite and its location are determined.
Fourthly, considering the influence of the tiny size of interphase on the computation, a dual two-scale method is proposed. 3-D stress distributions of unidirectional-fibre reinforced composites with interphase under macroscopic axial uniform tension, transversal uniform tension and transversal uniform shear are respectively calculated and the maximal stress and their locations are determined. The influence of different interphases on the distributions of stress fields is discussed. The results show that arithmetical transition of the properties of fibre, interphase and matrix is beneficial to abate stress concentration of fibre which occurs near the interphase under macroscopic axial uniform tension.
Finally, different failure criteria are introduced according to different attributes of components of unidirectional composite to establish a two-scale method for predicting the axial strength of unidirectional-fibre reinforced composites. When applying the method to predict the axial tensile strength, the concept of fibrous effective tensile strength is defined to relate the progressive damage with the method. The calculated values have a good agreement with the experiment results which verifies the validity of this method.
在众多跨尺度计算方法中,双尺度渐近分析方法是一种适用于周期性构造复合材料性能表征与结构分析的通用、高效、精确的方法。其基本思想是:材料性能的计算和预测沿着从细观到宏观这一过程,采用双尺度均匀化方法,由细观尺度下的单胞计算出宏观尺度下材料的均匀化性能参数;而结构物理、力学行为的计算与预测则是从宏观平均场方程出发,从宏观到细观,利用双尺度渐近展开技术,计算出细观尺度下物理、力学量的局部涨落。本文主要基于双尺度渐近分析方法对复合材料的热/力学有效性能与响应规律进行了多尺度表征与计算。
首先,从热力耦合问题的基本方程出发,建立了复合材料温度场和力学场的双尺度渐近表达式;得到了复合材料宏观均匀化热传导系数、刚度系数和热膨胀系数的表达式;并且将该方法与有限元方法相结合,给出了数值实现双尺度计算的计算步骤。
其次,通过数值试验验证了双尺度分析方法预报复合材料宏观性能的有效性,进而研究了夹杂百分含量、夹杂形状和夹杂之间的相互作用对复合材料宏观性能的影响;并且通过数值试验验证了双尺度分析方法描述结构场函数的有效性和高效性。
接下来,将双尺度渐近分析方法应用于ZrB2-SiC超高温陶瓷材料体系,进行了跨越微观-细观-宏观的多尺度表征与模拟的尝试,计算了ZrB2-SiC超高温陶瓷的热响应规律,分析了SiC夹杂颗粒的尺寸和分布位置对细观结构的影响;并且建立了碳纤维增韧超高温陶瓷基复合材料的单胞模型,计算了碳纤维增韧超高温陶瓷基复合材料结构在一定工况下的响应,确定了结构内的最大应力值及其所在位置。
然后,考虑到界面相的小尺寸对计算规模的影响,提出了二重双尺度方法。将二重双尺度方法与有限元方法相结合,计算了宏观轴向均匀拉伸载荷、横向均匀拉伸载荷和横向均匀剪切载荷条件下含界面相单向纤维增强复合材料的三维应力场分布,确定了各种载荷条件下复合材料结构内的最大应力值及其所在位置;讨论了界面相性能对应力场分布的影响,结果显示纤维—界面相—基体力学性能的等差过渡有利于缓解轴向拉伸载荷下复合材料内纤维在界面附近的应力集中。
最后,针对单向复合材料直杆,按照组分材料的不同性质引入不同的破坏准则,提出预报单向纤维增强复合材料轴向强度的双尺度方法。在预报轴向拉伸强度时,通过引入纤维等效拉伸强度的概念,将拉伸载荷下的渐近损伤与双尺度方法联系起来。结果显示采用双尺度方法预报的复合材料宏观强度值与实验值吻合较好,说明了该方法的有效性。
With the rapid development of space technology, the investigations on macroscopic properties’characterization and broken-down mechanism of composite material structures under thermo-elasticity coupling condition are extremely desired. The multi-scale modeling and computation for composite materials is coincident with the intrinsic nature of physical world, so it can more exactly characterize properties of composites and predict the response of composites under certain loading (or working) condition. Moreover, it supplies a method to optimize microstructure of composites for the best properties. That is, based on multi-scale modeling and computation, we can design the microstructure of composites and determine the processing before preparation of composites.
Among many multi-scale methods known, two-scale asymptotic analysis method is a general, efficient and accurate method which is suitable for properties’characterization and response analysis of composites with periodic configuration. Its main idea is that the computation for properties of composites is presented with two-scale homogenization in the process from mesoscopic to macroscopic, and then the local fluctuations of physical and mechanical fields are described with two-scale asymptotic technique in the process from macroscopic to mesoscopic. In this paper, based on two-scale asymptotic method principally, the effective thermal/mechanical properties of composites are characterized as well as the responses of composite structures in multiple scales under certain loading (or working) condition are computed.
Firstly, two-scale asymptotic formulae of the temperature and the mechanical fields are derived on the base of the basic equations of thermo-elasticity coupling problem, and then the expressions of effective thermal conductivities, stiffness and thermal expansion coefficients of composites are deduced. Whereafter, combining with finite element method, the numerical computing procedure of two-scale method is established.
Secondly, the validity of two-scale method for characterizing the effective properties of composites is evaluated by numerical experiments. The changes of the effective properties of composites resulting from the variations of the volume fraction and shape of inclusion and the interaction of the inclusions are analyzed. After that, the validity and efficiency of two-scale method for describing the temperature and mechanical fields of composite structure are validated by numerical experiments.
Thirdly, two-scale asymptotic method is employed in the field of ZrB2-SiC ultra high temperature ceramics (UHTCs) to implement multi-scale characterization and simulation which links micro-, meso- and macro-scale. The thermal response of ZrB2-SiC is computed and the influences of the size and the location of SiC inclusion on microstructure of ZrB2-SiC are analyzed. Furthermore, the unit cell of carbon fibre toughened UHTCs matrix composite is modeled, the response of the composite under certain working condition is computed, and the maximal stress in the composite and its location are determined.
Fourthly, considering the influence of the tiny size of interphase on the computation, a dual two-scale method is proposed. 3-D stress distributions of unidirectional-fibre reinforced composites with interphase under macroscopic axial uniform tension, transversal uniform tension and transversal uniform shear are respectively calculated and the maximal stress and their locations are determined. The influence of different interphases on the distributions of stress fields is discussed. The results show that arithmetical transition of the properties of fibre, interphase and matrix is beneficial to abate stress concentration of fibre which occurs near the interphase under macroscopic axial uniform tension.
Finally, different failure criteria are introduced according to different attributes of components of unidirectional composite to establish a two-scale method for predicting the axial strength of unidirectional-fibre reinforced composites. When applying the method to predict the axial tensile strength, the concept of fibrous effective tensile strength is defined to relate the progressive damage with the method. The calculated values have a good agreement with the experiment results which verifies the validity of this method.
引文
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