注塑成型纤维增强热塑性树脂复合材料刚度预测方法

黄达勇; 赵先琼

doi:10.13801/j.cnki.fhclxb.20200811.001

注塑成型纤维增强热塑性树脂复合材料刚度预测方法

doi: 10.13801/j.cnki.fhclxb.20200811.001

黄达勇,
赵先琼^,

中南大学　机电工程学院，长沙 410083

基金项目: 国家自然科学基金(51374241)

详细信息

通讯作者:
赵先琼，博士，教授，博士生导师，研究方向为现代机械强度理论及复合材料力学　E-mail：csuzxq@csu.edu.cn

中图分类号: TB332
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出版历程
- 收稿日期: 2020-07-23
- 录用日期: 2020-07-29
- 网络出版日期: 2020-08-11
- 刊出日期: 2021-07-15

Stiffness prediction for injection molded fiber reinforced thermoplastics composite

HUANG Dayong,
ZHAO Xianqiong^,

College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China

摘要

摘要: 基于Hsueh模型的应力场分布，采用代表性体积单元(RVE)平均近似方法，推导出可以退化成Halpin-Tsai模型的泊松比ν₁₂的显性表达式，与桥联模型基本重合。结合Fu模型和Giner模型，引入与纤维长径比(l/a)相关的指数衰减函数得到横向模量E₂₂修正的Halpin-Tsai模型，与自洽模型重合。基于泊松比各向同性假设而推导出的泊松比ν₂₃与有限元结果逼近，远优于Halpin-Tsai模型；基于逆向工程，修正了被Halpin-Tsai模型低估的剪切模量G₂₃。基于经典的层合板分析方法(LAA)，引入纤维长度分布(FLD)及纤维取向广义分布函数，对两种注塑成型短玻璃纤维增强热塑性树脂(FRT)复合材料的弹性常数进行预测。结果表明：4个微观力学组合模型均很好地预测了复合材料的弹性常数，但纤维长度质量分布的预测结果比纤维长度数量分布的结果更为合理，特别是对于纵向杨氏模量E_L的改进效果大于5%。
- 刚度预测 /
- 微观力学 /
- 层合板分析方法(LAA) /
- 纤维增强热塑性复合材料 /
- 纤维长度分布(FLD) /
- 纤维取向分布(FOD)
Abstract: Based on the stress distribution in representative volume element (RVE) for Hsueh model, the explicit expression of Poisson’s ratio ν_12, which can be reduced to the Halpin-Tsai model, was derived from average approximation method, and it basically coincides with the Bridging model. The modified Halpin-Tsai model for transverse modulus E₂₂ was developed by introducing an exponential decay function of l/a related to the Fu and Giner models, and coincides with the self-consistent model. Based on the assumption of Poisson’s ratio properties, the deduced results better than the Halpin-Tsai model are close to the finite element results for Poisson’s ratio ν₂₃, and then the underestimation of shear modulus G₂₃ was corrected by the modified Halpin-Tsai model for ν₂₃ based on reverse engineering. Based on the laminate analogy approach (LAA) in conjunction with fiber length distribution (FLD) and generalized fiber orientation distribution (FOD) functions, the elastic moduli for two kinds of injection molded short glass fiber reinforced thermoplastics (FRT) composite were predicted. The results show that the four combined micromechanical models all predict the elastic moduli of the composites well, but the prediction results of weight distribution of fiber lengths are more reasonable than that of number distribution of fiber lengths, especially more than 5% in the improvement effect of longitudinal Young’s modulus E_L.
- stiffness prediction /
- micromechanics /
- laminate analogy approach (LAA) /
- fiber reinforced thermoplastics (FRT) composite /
- fiber length distribution (FLD) /
- fiber orientation distribution (FOD)

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图 1 Hsueh模型示意图^[38]

Figure 1. Schematic for the Hsueh model^[38]

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图 2 代表性体积单元(RVE)中的应力场分布

Figure 2. Stress field distribution in representative volume element (RVE)

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图 3 理论预测和Tucker的有限元(FE)结果

Figure 3. Theoretical predictions and Tucker’s finite element (FE) results

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图 4 理论预测和Huang^[29]的FE结果

Figure 4. Theoretical predictions and Huang’s FE results^[29]

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图 5 理论预测和Pickering的实验结果

Figure 5. Theoretical predictions and Pickering’s experiments

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图 6 理论预测和Piggott的实验结果

Figure 6. Theoretical predictions and Piggott’s experiments

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表 1 FE分析中组分材料的物理和力学性能

Table 1. Physical and mechanical properties of materials used in FE

E_f	E_m	V_f	ν_f	ν_m	l/a	Ref.
30	1	0.2	0.2	0.38	1, 2, 4, 8, 16, 24, 48	[27]
74	3.35	0.2	0.2	0.35	2, 4, 16, 64, 128, 500	[29]
Notes: E_f—Young’s modulus of fibers; ν_f—Poisson’s ratio of fibers; E_m—Young’s modulus of matrix; ν_m—Poisson’s ratio of matrix; V_f—Volume occupied by fibers; l/a—Fiber aspect ratio.

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表 2 层合板分析方法(LAA)中组分材料的物理和力学性能^[50]

Table 2. Mechanical and physical properties of materials used in laminate analogy approach (LAA)^[50]

Property	Short glass fiber/polyamide-6		Short glass fiber/polybutylene terephthalate
Property	S-glass fiber	Polyamide-6	S-glass fiber	Polybutylene terephthalate
Mass fraction/wt%	35	65	30	70
Volume fraction/vol%	18	82	19	81
Tensile strength/MPa	3620	52.7	3620	64
Elastic modulus/GPa	72.4	1.92	72.4	3.0
Poisson’s ratio	0.22	0.4	0.22	0.4

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表 3 注塑成型短玻璃纤维/(PBT)和短玻璃纤维/(PA6)复合材料的拉伸性能^[50]

Table 3. Tensile properties of injection molded short glass fiber/polybutylene terephthalate (PBT) and short glass fiber/ polyamide-6 (PA6) composites^[50]

Composite	Longitudinal modulus E_L/MPa	Transverse modulus E_T/MPa	Shear modulus G_LT/MPa	Poisson’s ratio ν_LT	Core thickness ratio h_c/%
Short glass fiber/PA6	7816 (s=743)	4507 (s=678)	1641	0.3676^a	13
Short glass fiber/PBT	9739 (s=916)	5846 (s=702)	2051	0.3658^a	16
Notes: ^a—Rule of mixtures; s—Standard deviation.

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表 4 短玻璃纤维/PBT和短玻璃纤维/PA6复合材料的弹性模量预测值与实验值的对比

Table 4. Comparisons of elastic moduli predictions with experiments for short glass fiber/PBT and short glass fiber/PA6 composites

Elastic modulus	PA6-SGF35					PBT-SGF30
Elastic modulus	H-T*	H-T	G-H-T	mH-T-H	F-L	H-T*	H-T	G-H-T	mH-T-H	F-L
E_L/MPa	7250 e=−7.2%	7818 e= 0.0%	7798 e=−0.3%	8239 e=5.4%	7949 e=1.7%	9424 e=−3.2%	9943 e=2.1%	9906 e=1.7%	10239 e=5.1%	9770 e=0.3%
E_T/MPa	3844 e=−14.7%	3960 e=−12.1%	3838 e=−14.9%	3952 e=−12.3%	3991 e=−11.4%	5822 e=−0.4%	5949 e=1.8%	5771 e=1.3%	5885 e=0.7%	5910 e=1.1%
G_LT/MPa	1463 e=−10.8%	1522 e=−7.3%	1516 e=−7.6%	1561 e=−4.9%	1.536 e=−6.4%	2111 e=2.9%	2165 e=5.6%	2156 e=5.2%	2190 e=6.8%	2146 e=4.6%
ν_LT	0.3991 e=8.6%	0.4009 e=9.1%	0.3971 e=8.0%	0.4050 e=10.2%	0.4016 e=9.2%	0.3820 e=4.4%	0.3820 e=4.4%	0.3771 e=3.1%	0.3828 e=4.6%	0.3820 e=4.4%
Notes: *—Eq.(34); e—Relative error; H-T—Halpin-Tsai model; G-H-T—Giner and Halpin-Tsai models; mH-T-H—Modified Halpin-Tsai and Hsueh models; F-L—Fu-Lauke model.

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