随机多尺度短切碳纤维复合结构模型中RVE尺寸效应和方向模量的均一化响应

doi:10.12382/bgxb.2021.0835

摘要/Abstract

摘要：

采用一种新型的多尺度短切纤维填充树脂均匀化方法，目的在于探寻随机短切纤维离散角度对复合结构方向模量的均一化响应，同时研究卷曲短切碳纤维(CCF)单元在具有代表体积元(RVE)结构中随机分布所引起的复合材料结构性能变化。在均一化方法中使用一种基于高斯定理的RVE结构子域后处理方案，用于提取三维结构的平均应变和应力。利用X射线计算机断层扫描方法确定2阶张量取向角和剪切纤维长度在测试样品中的概率分布信息，设计比较3种尺寸的RVE模型，通过实验和计算研究CCF多尺度复合模型应力影响区衰减长度的影响因素和该均匀化方法引起的带有旋转角度的RVE方向模量均匀化响应。研究结果表明，复合结构的剪切模量比正轴模量相对旋转角度更为敏感，衰减长度与RVE尺寸、单胞结构和纤维扭曲度等因素相关。因此，研究随机短纤维的离散性对宏观复合结构方向模量的设计，铺层角度的优化等领域具有十分重要的应用。

关键词: 短切碳纤维, 代表体积元, 代表性单胞, 均一化, 树脂基复合材料

Abstract:

A new homogenization method of multi-scale chopped fiber filling resin matrix was adopted with the purpose of exploring the effect of the discrete angle of stochastic chopped fiber on the homogenizing response of directional modulus of the composite structure. We also studied the changes of composite structure performance caused by the random distribution of the crimp chopped carbon fiber (CCF) unit in the representative volume element (RVE) structure. In the homogenization method, a RVE subdomain post-processing scheme based on Gauss theorem was used to extract the average strain and stress of the three-dimensional structure. In addition, X-ray computed tomography (CT) was employed to determine the second-order tensor orientation angle and the probability distribution information of chopped fiber length in the test sample. The RVE models of three dimensions were designed and compared. The influencing factors of attenuation length in stress-affected zone of multi-scale CCF composite model and the homogenizing response of RVE directional modulus with rotation angle caused by this homogenization method were studied by experiments and calculations. The results showed that the shear modulus of the composite structure is more sensitive to rotation angle than the positive axial modulus, and that the attenuation length is related to RVE size, unit cell (UC) structure and fiber tortuosity. Therefore, it is of practical significane to study the discreteness of stochastic chopped carbon fiber for the design of directional modulus of macroscopic composite structures and the optimization of layering angle.

Key words: chopped carbon fiber, representative volume element, representative unite cell, homogenization, resin matrix composite

邱伊健, 郑萍, 程香平, 郭玉松. 随机多尺度短切碳纤维复合结构模型中RVE尺寸效应和方向模量的均一化响应[J]. 兵工学报, 2023, 44(3): 702-717.

QIU Yijian, ZHENG Ping, CHENG Xiangping, GUO Yusong. RVE Size Εffect and Homogenizing Response of Directional Modulus in Stochastic Multi-scale Chopped Carbon Fiber Composite Structure Model[J]. Acta Armamentarii, 2023, 44(3): 702-717.

图/表 17

图1 卷曲短纤维长度微分的坐标变换

Fig. 1 Coordinate transformation of length differential of CCF

图2 纤维取向

Fig. 2 Fiber orientation

图3 单胞纤维在RVE中的离散角度

Fig. 3 Discrete angle of single cell fiber in RVE

图4 包含单根波动碳纤维的单胞结构

Fig. 4 Unit cell with single wavy CCF

图5 RVE空间变化的随机排列角度，

Fig. 5 Random arrangement angle of RVE space variation

图6 HE算法的流程图

Fig. 6 Flowchart of space direction-sensitive hoteling expansion algorithm

表1 RVE结构各相材料属性

Table 1 Material properties of each phase in RVE structure

基体材料		CCF		界面材料
参数	数值	参数	数值	参数	数值
ρ/(t·m^-3)	1.14	ρ(/t·m^-3)	1.86	ρ/(t·m^-3)	1.14
E/GPa	3.0	E/TPa	0.38	E/GPa	5.0
ν	0.37	ν	0.22	ν	0.35
σ_s	20	D_CCF/μm	6.9	d_i/μm	8.3
强化模量/GPa	30	G₁₂，G₁₃/TPa	0.12	强化模量/GPa	32
强化指数	75	G₂₃/TPa	0.255	强化指数	74.5
线性强化模量/GPa	10	横纵比	145	线性强化模量/GPa	11
		L_CCF/mm	1	L_m/mm	0.4
		弯曲度	3
		体积分数/%	0.2~1.24

图7 复合结构实验样本及其细观显微图像

Fig. 7 Composite structure test samples and their mesoscopic images

图8 实验样本中随机取向纤维的长度和方向角的统计分布

Fig. 8 Statistical distribution of length and orientation angle of randomly oriented fibers in experimental samples

图9 3种尺寸RVE的纤维填充过程(纤维横纵比：145DCCF=6.9 μm，纤维扭曲度=0.3)

Fig. 9 Fiber filling process of CCF for RVE of three sizes(Fiber aspect ratio: 145DCCF=6.9 μm, Torsion of fiber= 0.3)

图10 RVE面边界约束方程

Fig. 10 Surface boundary conditions of RVE

图11 衰减长度t对RVE计算精度的影响，VCCF=1.24%

Fig. 11 Influence of attenuation length t on the accuracy of RVE calculation, VCCF=1.24%

图12 RVE体积，纤维扭曲度和UC结构与RVE应力影响区长度关系

Fig. 12 Relationship among RVE volume, fiber tortuosity, UC structure and the length of RVE

图13 VCCF=1.24%以及旋转张量角度α=45°，β=90°时的模量空间随机分布

Fig. 13 Spatial random distribution of modulus with VCCF=1.24% and rotation tensor angle α=45° and β=90°

图14 随角β改变的平均方向模量的变化

Fig. 14 Average directional modulus varying with rotation angle β

图15 随角α改变的平均方向模量的变化

Fig. 15 Average directional modulus varying with rotation angle α

表2 当α=β=45°时，均一化模量与实验对比

Table 2 Comparison of the homogenization modulus with the experiment when α=β=45°

参数/GPa	均一化模量α=β=45°	实验测定模量
E_1’	311	313
E_2'	308	311
E_3'	284	285
G_1'2'	605	612
G_2'3'	610	615
G_3'1'	561	566
v_1'2_'	0.255	0.26
v_2'3'	0.252	0.256
v_3'1'	0.249	0.251

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