三维编织复合材料细观结构平均刚度及其压缩性能的研究
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摘要
本文以三维编织复合材料的细观结构，平均刚度及其压缩力学性能为主要研究对象。分析了三维四步编织过程中纱线的运动路径及交织方式，以三维实体纱线和单胞的几何模型为基础，对三维编织预制件的内部结构进行了细观结构分析并建立了相关结构参数的模型。对复合固化后的三维编织复合材料的内部单胞、表面单胞和角单胞进行了结构分析并建立了模型。采用局部剖切法建立了编织预制件和编织复合材料的模型，该模型能较好地表现内部结构的复杂性，可以较好地反映纱线的走向，单元体中的纱线计算长度可以较精确地算出。解决了表面单胞和角单胞中的纱线不能与内部单胞中纱线有效连接的问题；
与预制件相比，复合材料内部的纱线结构发生了变化，这种变化也体现在纤维体积分数以及其它结构参数上。提出了不同的主体纱排数m和列数n组合的三维编织预制件可以作出不同的单胞体划分结构，建议通过作图法进行单胞分布的设计。推导出了纤维体积分数公式，提出了对编织复合材料工艺和结构参数进行优化设计的思路。
在紧密结构状态下，1×1编织预型件正模型的纱线体积分数和45°模型的内部单胞的纱线体积分相同，但与表面单胞和角单胞的纱线体积分数不同。内部单胞的紧密度最大，角单胞的紧密度最小，表面单胞紧密度介于以上两值之间。在最大编织角γ=54.7°时，1×1四向编织预制件正单胞模型和45°模型内部单胞的最大纱线体积分数相等，都是：V_(ymax)=67.96％。对45°模型，编织复合材料内部、表面和角单胞的纱线体积分数不同，分别为：V_(ymax)~i=67.96％；V_(ymax)~s=58.23％；V_(ymax)~c=37.31％。内部、表面和角单胞区域的紧度呈逐渐递减的趋势。提出了经压模后编织复合材料中纱线编织角发生变化的概念，并将这一变化应用到了所建模型及刚度计算当中。另外还给出了编织预制件到编织复合材料变形前后单胞模型的单胞尺寸算式。
运用所建立的代表性体积单元(RVE)模型对整体编织复合材料(四向)的平均刚度进行了预测。预测出的三维编织复合材料的有效弹性性能结果和实验结果吻合较好。将三维编织复合材料看成是由纤维束组成的倾斜纤维束空间结构，采用三单胞力学模型，用体积平均法和单胞刚度加权法，对编织复合材料整体弹性刚度进行的预测，结果能够较准确地预测出三维编织复合材料的弹性性能。另外，进行了拉伸和压缩性能试验，从拉伸和压缩试验结果来看，编织复合材料的弹性模量主要受编织角和纤维体积分数的影响。
本文提出了差别纤维体积分数的假设，各个纤维束的纤维体积分数与单胞的纤维体积分数并不相等，需要分别进行计算，并分别给出了各纤维束的纤维体积分数计算式；还提出了三单胞弹性模量按比例叠加的思想，并给出了比例计算式，计算出了结果。结果与试验数据以及与其它文献数据吻合的较好。
对三维编织复合材料压缩破坏进行了试验研究，从应力-应变响应图中观察到几个明显的缓冲区的存在，并认为这是由于内部交错单层板的逐“层”失效引起的。三维编织复合材料纵向压缩的破坏有三种典型的宏观破坏模式：整体松散型破坏、45°角破坏和鼓凸状破坏。通过压缩破坏试验，发现破坏层面出现纤维束之间的树脂粉碎性破坏，而纤维束基本上保持着圆柱状，认为纤维束之间的基体存在着较大的变形，三维编织复合材料内部的应变场在细观上表现为非均匀性。
This paper describe research concerning the microstructure ,mean stiffness and compression properties of three -dimentionally braided composite materials, the braided process and yarn path in 4-step 3-D(lxl) rectangular braided composites are analysed, based on 3-D solid yarn and unit cell geometric model, microstructure inside 3-D braided preforms is analysed and some geometric models are set up. The paper also presents an analytic description of interior, surface and corner unit of 3-D braided composites and establishes several mathematic models.
Models of braided performs and composites have been established with local-cut method. They can easily describe the complexity of braided structure and show the direction of yarns in braided performs and composites, and can accurately calculate the length of yarns. A problem that yarns between inner cell , surface cell and coner cell cannot be connected effectly has been solved in this paper.
The final yarn structures in composites have changed comparing with those in the preforms after which are impregnated with matrix and consolidated into the final shape. This paper proposed that each different combination of row m and column n of main body yarns can scheme two type of section plot of perform and the section of perform can be designed . The expressions of fiber volume fraction are deduced. An optimization design proposal is give to the process of braided composites and structure parameters.
When all yarns of preform in jamming condition, The biggest yarn volume fraction of right face model is equal to that of inner cell of 45° model, but not equal to that of surface cell and coner cell. when we employed the biggest braiding angel r=54.7° ,The biggest yarn volume fraction of inner cell ,surface cell and corner cell of 1x1 braided performs in 45°
model are follows: Vymax = 67.96% , Vsymax= 58.23% and Vcymax = 37.31%. compactness of
Vyaa
inner , surface and the corner area are decrease grudaully. This paper proposed a concept of changed braiding angle in the process from braided preforms to final composites .meanwhile the changed braiding angle has been used in model established and the process of calculation of mean stiffness. Calculations of dimensions of representative unit cell have been given when performs changed to composite materials.
Application of the model established to predict mean stiffness of 3-D braided compoites was conducted in this paper, including four direction and five direction braided composites.
The experimental results show that the RVE mechanical model can reasonably predict the effective elastic constants of 3-D braided composite materials and the results show close agreement with theoretical predictions. We see yarn in braided composites as rod of inclined structures and use the structural model of three cell to predict monolithic stiffness of 3-D braided composites with method of volume average and method of weighted average of three cell's stiffness. In addition, the mechanical experiments of braided composite materials were carried out, such as tensile, compression and experiments. The braiding angle and fiber volume fraction have notable effect on module of elasticity.
In this paper we proposed a hypothesis of difference fiber volume fraction and presented expressions respectively. The fiber volume fraction of unit cell is not equal to that of each lamina ,which need calculate eachly.The paper also advanced conception of weighted average of three cell's stiffness. The results of calculation agree with my experimental data and other documents.
Based upon compression failure experiments of braided composites, some mitigating areas can be seen from the response curve of stress and stain. The phenomenon indicates that it is the failure of fiber bundles(lamina) bring on. three typically macroscopic failure modes of compression of 3-D braided composites have found, they are wholly unfasten failure, 45 degree breaking section failure and drum-like breaking failure. Through the compression experiments of braided
与预制件相比，复合材料内部的纱线结构发生了变化，这种变化也体现在纤维体积分数以及其它结构参数上。提出了不同的主体纱排数m和列数n组合的三维编织预制件可以作出不同的单胞体划分结构，建议通过作图法进行单胞分布的设计。推导出了纤维体积分数公式，提出了对编织复合材料工艺和结构参数进行优化设计的思路。
在紧密结构状态下，1×1编织预型件正模型的纱线体积分数和45°模型的内部单胞的纱线体积分相同，但与表面单胞和角单胞的纱线体积分数不同。内部单胞的紧密度最大，角单胞的紧密度最小，表面单胞紧密度介于以上两值之间。在最大编织角γ=54.7°时，1×1四向编织预制件正单胞模型和45°模型内部单胞的最大纱线体积分数相等，都是：V_(ymax)=67.96％。对45°模型，编织复合材料内部、表面和角单胞的纱线体积分数不同，分别为：V_(ymax)~i=67.96％；V_(ymax)~s=58.23％；V_(ymax)~c=37.31％。内部、表面和角单胞区域的紧度呈逐渐递减的趋势。提出了经压模后编织复合材料中纱线编织角发生变化的概念，并将这一变化应用到了所建模型及刚度计算当中。另外还给出了编织预制件到编织复合材料变形前后单胞模型的单胞尺寸算式。
运用所建立的代表性体积单元(RVE)模型对整体编织复合材料(四向)的平均刚度进行了预测。预测出的三维编织复合材料的有效弹性性能结果和实验结果吻合较好。将三维编织复合材料看成是由纤维束组成的倾斜纤维束空间结构，采用三单胞力学模型，用体积平均法和单胞刚度加权法，对编织复合材料整体弹性刚度进行的预测，结果能够较准确地预测出三维编织复合材料的弹性性能。另外，进行了拉伸和压缩性能试验，从拉伸和压缩试验结果来看，编织复合材料的弹性模量主要受编织角和纤维体积分数的影响。
本文提出了差别纤维体积分数的假设，各个纤维束的纤维体积分数与单胞的纤维体积分数并不相等，需要分别进行计算，并分别给出了各纤维束的纤维体积分数计算式；还提出了三单胞弹性模量按比例叠加的思想，并给出了比例计算式，计算出了结果。结果与试验数据以及与其它文献数据吻合的较好。
对三维编织复合材料压缩破坏进行了试验研究，从应力-应变响应图中观察到几个明显的缓冲区的存在，并认为这是由于内部交错单层板的逐“层”失效引起的。三维编织复合材料纵向压缩的破坏有三种典型的宏观破坏模式：整体松散型破坏、45°角破坏和鼓凸状破坏。通过压缩破坏试验，发现破坏层面出现纤维束之间的树脂粉碎性破坏，而纤维束基本上保持着圆柱状，认为纤维束之间的基体存在着较大的变形，三维编织复合材料内部的应变场在细观上表现为非均匀性。
This paper describe research concerning the microstructure ,mean stiffness and compression properties of three -dimentionally braided composite materials, the braided process and yarn path in 4-step 3-D(lxl) rectangular braided composites are analysed, based on 3-D solid yarn and unit cell geometric model, microstructure inside 3-D braided preforms is analysed and some geometric models are set up. The paper also presents an analytic description of interior, surface and corner unit of 3-D braided composites and establishes several mathematic models.
Models of braided performs and composites have been established with local-cut method. They can easily describe the complexity of braided structure and show the direction of yarns in braided performs and composites, and can accurately calculate the length of yarns. A problem that yarns between inner cell , surface cell and coner cell cannot be connected effectly has been solved in this paper.
The final yarn structures in composites have changed comparing with those in the preforms after which are impregnated with matrix and consolidated into the final shape. This paper proposed that each different combination of row m and column n of main body yarns can scheme two type of section plot of perform and the section of perform can be designed . The expressions of fiber volume fraction are deduced. An optimization design proposal is give to the process of braided composites and structure parameters.
When all yarns of preform in jamming condition, The biggest yarn volume fraction of right face model is equal to that of inner cell of 45° model, but not equal to that of surface cell and coner cell. when we employed the biggest braiding angel r=54.7° ,The biggest yarn volume fraction of inner cell ,surface cell and corner cell of 1x1 braided performs in 45°
model are follows: Vymax = 67.96% , Vsymax= 58.23% and Vcymax = 37.31%. compactness of
Vyaa
inner , surface and the corner area are decrease grudaully. This paper proposed a concept of changed braiding angle in the process from braided preforms to final composites .meanwhile the changed braiding angle has been used in model established and the process of calculation of mean stiffness. Calculations of dimensions of representative unit cell have been given when performs changed to composite materials.
Application of the model established to predict mean stiffness of 3-D braided compoites was conducted in this paper, including four direction and five direction braided composites.
The experimental results show that the RVE mechanical model can reasonably predict the effective elastic constants of 3-D braided composite materials and the results show close agreement with theoretical predictions. We see yarn in braided composites as rod of inclined structures and use the structural model of three cell to predict monolithic stiffness of 3-D braided composites with method of volume average and method of weighted average of three cell's stiffness. In addition, the mechanical experiments of braided composite materials were carried out, such as tensile, compression and experiments. The braiding angle and fiber volume fraction have notable effect on module of elasticity.
In this paper we proposed a hypothesis of difference fiber volume fraction and presented expressions respectively. The fiber volume fraction of unit cell is not equal to that of each lamina ,which need calculate eachly.The paper also advanced conception of weighted average of three cell's stiffness. The results of calculation agree with my experimental data and other documents.
Based upon compression failure experiments of braided composites, some mitigating areas can be seen from the response curve of stress and stain. The phenomenon indicates that it is the failure of fiber bundles(lamina) bring on. three typically macroscopic failure modes of compression of 3-D braided composites have found, they are wholly unfasten failure, 45 degree breaking section failure and drum-like breaking failure. Through the compression experiments of braided
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