三维四向编织复合材料改进模型的细观分析

三维编织复合材料现有的成型方法将导致编织物单胞模型发生变化,据此提出了一种改进的具有矩形截面的单元内胞模型,假设编织纱线具有平行六边形横截面,分析了不同区域胞体内部纤维束的空间构型,建立了三维四向编织复合材料内部单胞三维实体模型。通过分析编织物内纱线间的空间接触关系,采取合理的假设,推导了编织工艺参数和模型结构参数的关系,并计算了三维四向编织复合材料的纤维体积含量,为该种材料后续力学性能分析奠定了基础。该模型适用于部分不规则成型工艺,并有可能应用于其他形式的编织工艺研究。     

三维五向编织复合材料的力学性能分析Ⅱ: 细观应力数值模拟

在实验观察的基础上, 考虑轴纱的挤压变形及纱线填充因子变化, 修正了现有的细观结构模型, 建立了更加真实反映三维五向编织复合材料内部编织结构的单胞模型。利用该模型采用3D 有限元法计算了材料的轴向弹性模量, 数值预测与实验数据吻合较好。分析了单胞在拉伸载荷作用下的细观应力分布, 为材料进一步的强度预测奠定了基础。      

四步法矩形组合截面三维编织物的细观结构

采用控制体积法研究了以四步法编织矩形组合截面三维编织物的特殊细观结构。根据三维编织原理,得到编织物内各区域携纱器的运动规律。从中看出, 除了常规矩形截面三维编织物所具有的内部、棱(外) 角和表面区域外, 矩形交接区域的内部、内角和表面具有特殊的细观结构。分析了矩形组合截面三维编织物所特有的矩形交接区域以及交接内部、交接内角和交接表面的细观结构, 建立了这三个区域的单胞模型。结果表明, 交接区域的内部单胞外形为立方体, 交接区域的内角单胞外形为七棱柱体, 交接区域的表面单胞为五棱柱体。与常规矩形截面的单胞相比, 矩形组合截面在交接区域中, 纱线的空间形态和编织角均存在明显不同。      

三维六向编织复合材料渐进损伤模拟及强度预测

基于三维六向编织复合材料的细观结构,假设第六向纱线的截面形状为菱形,建立了三维六向编织复合材料的渐进损伤有限元模型。采用Linde等提出的失效准则,引入周期性位移边界条件,对三维六向编织复合材料的纵向拉伸应力-应变行为进行了渐进损伤数值模拟,讨论了单胞模型在纵向拉伸载荷作用下的细观损伤起始、扩展和最终失效的演化过程,并预测了材料的拉伸强度。在此基础上,进一步研究了编织角、纤维体积分数和编织纱水平取向角等参数对材料纵向拉伸力学性能的影响规律。研究结果表明,三维六向编织复合材料的轴向纱线拉伸断裂是导致其破坏的最主要因素。所得数值结果与现有试验值吻合较好,验证了该模型的有效性,为更深入研究此类材料的力学性能奠定了基础。     

二维二轴1×1编织复合材料细观结构模型及力学性能有限元分析

考虑纤维束相互挤压及横截面形状变化, 采用纤维束截面六边形假设, 建立了二维二轴1×1编织复合材料的参数化单胞结构模型。通过引入周期性位移边界条件, 基于细观有限元方法, 对编织材料的弹性性能进行预测, 讨论了编织角及纤维体积含量对面内弹性常数的影响, 并分析了典型载荷下单胞细观应力场分布。研究表明: 单胞结构模型有效反映了纤维束的空间构型和交织特征, 实现了不同编织工艺参数下模型的快速建立; 基于单胞有限元模型的弹性性能预测结果与试验结果较为吻合; 模型给出了单胞合理的应力场分布, 为二维编织复合材料的结构优化和损伤预测奠定基础。      

三维编织中纱线的运动规律分析

三维编织通过携纱器的间歇运动,使编织纱线彼此相互交织。编织纱线趋向于沿携纱器运动的方向运动。本文作者采用最小二乘法拟合携纱器的运动趋势线,系统地分析了编织过程中纱线的空间运动规律。在此基础上,获得的预制件结构单胞模型包含内部单胞和表面单胞。单胞的取向平行于预制件的表面,有利于材料的力学性能分析。     

三维全五向编织复合材料的细观结构分析

针对三维全五向编织复合材料,研究了其四步法编织工艺的实现过程,并详细描述了编织复合材料各控制区域内纱线的空间走向及运动规律,在此基础上建立了能反映三维全五向编织复合材料基本结构的几何单胞模型。通过分析编织物内纱线间的空间挤压关系,设定合理的假设,计算了全五向编织复合材料的纤维体积含量,并分析了纤维体积含量与编织工艺参数之间的关系,为进一步研究该材料的力学性能奠定了基础。     

圆管状立体机织复合材料的多尺度分析

采用多尺度耦合的数值模型研究了圆管状立体机织复合材料的力学性能。建立了反映纤维束中纤维/基体二相材料的微观尺度单胞和反映周期性编织结构的细观尺度扇形单胞,并重点讨论了扇形单胞的周期性边界条件。通过逐级计算微观单胞、细观单胞的平均弹性常数,得到了圆管状立体机织复合材料的刚度参数,实现了由组分材料性能及编织参数预测圆管的宏观弹性性能,模型预测刚度与试验结果吻合。另一方面,研究了从大到小各尺度耦合的应力分析,对于圆管环向应力非周期分布的情况,建立了嵌入细观单胞的环状模型,进行了复杂荷载下从宏观圆管结构、到细观纤维束尺度、再到微观纤维尺度之间的逐级应力分析。     

三维编织复合材料制件的细观单胞元分析

讨论了实现三维编织复合材料细观结构与宏观响应直接相关连的计算方法——细观单胞元法。该方法采用细观结构单胞作为离散单元对三维编织复合材料制件进行宏观网格剖分,在细观结构分析的基础上,将微结构上的物理量转换为细观单胞元的宏观节点变量,建立了细观单胞元刚度矩阵的求解方法。数值结果表明,该方法能反映细观结构参数的变化对材料宏观物理量的影响。     

三维五向编织复合材料的力学性能分析Ⅰ:细观结构模型

通过观察CCD显微摄像仪获取的三维五向编织复合材料的截面图像,分析了纱线的排列规律及其截面形状的变化,建立了三维实体单胞模型,该模型合理地反映了纱线的交织状态和截面形状。基于该模型建立了编织工艺参数之间的几何关系。将预制件的外型尺寸和体积含量的计算值与实测值进行比较,吻合较好,为材料进一步的有限元分析奠定了基础。     

含纤维束截面形状变化的三维编织复合材料细观模型及刚度预报

基于实验观察和理论研究, 重点分析了材料内部区域纤维束的空间构型, 建立了一个新的三维实体细观结构模型, 并指出了编织工艺参数和模型细观结构参数之间的关系。该模型较真实地反映了纤维束之间的相互挤压变形方式, 纤维束横截面积沿纤维束轴向不断变化, 更符合三维四向编织复合材料的实际结构。基于刚度体积平均及柔度体积平均混合思想, 建立了相应的刚度预报模型。用该模型计算编织复合材料几何特性及工程弹性常数的数值结果与试件实测数据吻合, 表明了该模型的合理有效性, 为进一步研究三维编织复合材料的拉伸强度及破坏机制提供了基础。     

The effect of yarn distortion on the mechanical properties of 3D four-directional braided composites

A representative volume cell (RVC) is chosen to analyze the mechanical properties of 3D (3 dimensions) four-directional braided composites. Owing to braid yarns (an assembly of fibers) squeezing against each other in the braided composites, the braid yarns are distorted. Based on geometrical characteristics of the braided composites, cross-section of each braid yarn is supposed to be an octagon and divided into seven regions in the RVC. The distortion characteristics of yarns are considered in each region. Elastic properties of each region obtained by stochastic function theory are introduced into finite element model to calculate the mechanical properties of the RVC. The influences of yarn distortion on the stiffness and strength of the braided composites are obtained and discussed.     

三维四向编织复合材料界面损伤机理数值分析

考虑界面脱粘表面压应力下摩擦力对材料界面力学性能的影响,建立损伤-摩擦相结合的界面本构模型,编写用户材料子程序VUMAT,实现其在有限元软件ABAQUS中的嵌入。基于周期性胞元分析思想,在单胞模型中纤维束/基体、纤维束/纤维束分界面引入界面单元,结合损伤-摩擦相结合的界面本构模型,建立含界面相三维四向编织复合材料的细观有限元模型。模拟典型载荷下界面损伤的起始和扩展过程,分析界面应力传递和界面破坏机理,研究界面性能对复合材料宏细观力学性能的影响规律,为实现三维四向编织复合材料界面性能优化设计和控制提供参考。      

基于面-内胞模型的三维四向编织复合材料渐进损伤数值模拟

为了准确预测三维四向编织复合材料的纵向拉伸力学性能,对编织复合材料的面胞和内胞细观实体模型进行参数化建模,面胞模型考虑了纱线空间轨迹的偏移和横截面的挤压变形。用体素网格离散模型并施加合适的边界条件,将各组分材料的损伤模型编入到有限元分析软件ABAQUS用户定义材料子程序UMAT中。分别对内编织角为30°和45°的三维四向碳纤维/环氧树脂编织复合材料的面-内胞模型进行数值分析,经体积加权平均获得不同厚度编织复合材料试件的纵向拉伸模量和强度,通过统计具有相同破坏模式的积分点数量研究复合材料的渐进损伤过程。结果表明:基于面-内胞模型预测三维四向编织复合材料的纵向拉伸力学性能与试验值吻合良好,损伤分析结果合理地反映了面胞和内胞的渐进损伤过程。      

A new analytical model for calculation of stiffness of three-dimensional four-directional braided composites

The present paper represents a new analytical method for calculation of the stiffness of three-dimensional four-directional braided composites. In most previous works, the analytical approach had been largely neglected in the favor of the finite element model. Among those who have used the analytical model, the braided preform has been considered as made of one, or three, types of representative unit cells, while microscopic evidence of the microstructure of preforms reveals different configurations of the yarns in the interior, surface and corner regions of a braided preform. This paper presents a Multi-Unit Cell Model in which four kinds of unit cells, namely interior, interior surface, exterior surface and corner unit cells have been introduced as representative cells. Each type of unit cell in a braided composite possesses unique mechanical properties and has been considered as a uni-directional composite. Using rotation matrices, the angle between yarns and longitudinal direction has been incorporated in general coordinates of the model. Finally, using a volume averaging method, the total stiffness of the braided composite is calculated. The results are in good agreement with the available experimental data. The effect of braiding angle on the stiffness of braided composites is also examined.     

Finite Element Analysis of Mechanical Properties of 3D Four-directional Rectangular Braided Composites—Part 2: Validation of the 3D Finite Element Model

In the first part of the work, we have established a new parameterized three-dimensional (3D) finite element model (FEM) which precisely simulated the spatial configuration of the braiding yarns and considered the cross-section deformation as well as the surface contact relationship between the yarns. This paper presents a prediction of the effective elastic properties and the meso-scale mechanical response of 3D braided composites to verify the validation of the FEM. The effects of the braiding parameters on the mechanical properties are investigated in detail. By analyzing the deformation and stress nephogram of the model, a reasonable overall stress field is provided and the results well support the strength prediction. The results indicate it is convenient to predict all the elastic constants of 3D braided composites with different parameters simultaneously using the FEM. Moreover, the FEM can successfully predict the meso-scale mechanical response of 3D braided composites containing periodical structures.     

三维四向编织陶瓷基复合材料改进模型及刚度预报

基于对三维四向编织陶瓷基复合材料CT扫描结果的观察和理论分析, 参考现有交织模型, 建立了改进的胞元三维实体模型, 较为真实地反映了材料内部的细观结构。模型内部纤维束横截面沿纤维束轴向不断发生形状和面积的周期性变化, 纤维束横截面呈平行四边形、五边形交替变化, 不同纤维束轴线间呈交织关系, 接近材料内部纤维束间打紧后的挤压变形规律。通过测算平均纱线填充因子并配合有限元法获得了纤维束及材料的弹性性能, 与试验结果符合较好。有限元仿真显示在材料单胞内, 纤维束承担主要载荷, 纤维束与基体的某些交界处往往会出现应力集中现象, 可能是发生裂纹扩展及局部破坏的主要区域。该细观应力场的获得也为分析材料破坏机理和强度提供了基础。      

Finite Element Analysis of Mechanical Properties of 3D Four-Directional Rectangular Braided Composites Part 1: Microgeometry and 3D Finite Element Model

Based on the microstructure of three-dimensional (3D) four-directional rectangular braided composites, a new parameterized 3D finite element model (FEM) is established. This model precisely simulates the spatial configuration of the braiding yarns and considers the cross-section deformation as well as the surface contact due to the mutual squeezing in the braiding process. Moreover, it is oriented in the same reference frame as the composites, which coincides with the actual configuration of 3D braided composites and facilitates the analysis of mechanical properties. In addition, the model investigates the relationships among the structural parameters, particularly the braiding angle and the interior braiding angle, which were not taken into account in the previous models. Based on the parameterized FEM, the structural geometry of the composites is analyzed and some conclusions are drawn herein. Good agreement has been obtained between the calculated and measured values of the geometric characteristics of braided composite samples.