RVE Size Εffect and Homogenizing Response of Directional Modulus in Stochastic Multi-scale Chopped Carbon Fiber Composite Structure Model

doi:10.12382/bgxb.2021.0835

Abstract

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

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.

Figures/Tables 17

Fig. 1 Coordinate transformation of length differential of CCF

Fig. 2 Fiber orientation

Fig. 3 Discrete angle of single cell fiber in RVE

Fig. 4 Unit cell with single wavy CCF

Fig. 5 Random arrangement angle of RVE space variation

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

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

Fig. 7 Composite structure test samples and their mesoscopic images

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

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

Fig. 10 Surface boundary conditions of RVE

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

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

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

Fig. 14 Average directional modulus varying with rotation angle β

Fig. 15 Average directional modulus varying with rotation angle α

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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