变厚度树脂基复合材料构件固化变形数值模拟与影响因素分析

甘建业; 胡伟叶; 张艺澄; 褚奇奕; 郝小忠

doi:10.13801/j.cnki.fhclxb.20220922.001

变厚度树脂基复合材料构件固化变形数值模拟与影响因素分析

doi: 10.13801/j.cnki.fhclxb.20220922.001

1.
南京航空航天大学　机电学院，南京 210016
2.
南京晨光集团有限责任公司，南京 210006

基金项目: 国家自然科学基金重大项目(52090052)

详细信息

通讯作者:
郝小忠，博士，教授，博士生导师，研究方向为先进复合材料构件新原理固化技术与装备　E-mail: xhao@nuaa.edu.cn

中图分类号: TB332
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- 被引次数: 0
出版历程
- 收稿日期: 2022-07-21
- 修回日期: 2022-09-07
- 录用日期: 2022-09-10
- 网络出版日期: 2022-09-26
- 刊出日期: 2023-07-15

Numerical simulation and influence factors analysis of cure-induced distortions in resin matrix composites with variable thickness

1.
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2.
Nanjing Chenguang Group CO., LTD., Nanjing 210006, China

Funds: Major Program of National Natural Science Foundation of China (52090052)

摘要

摘要: 通过层间丢层形成的变厚度树脂基复合材料构件具有减材减重、可刚性裁剪等优点，常应用于机翼结构等重要位置。但层间丢层会导致构件内部的不连续性，并使构件在固化后产生不均匀残余应力，脱模后发生复杂固化变形。针对变厚度复合材料构件的固化变形预测问题，现有研究多采用等效材料性能参数的建模方法，尚未考虑其树脂口袋等结构特点。本文基于分层建模方法，在丢层位置引入树脂口袋结构，建立了变厚度构件固化变形数值仿真模型。通过与传统等效建模方法、传统分层建模方法及实验的结果比较，本文模型最大翘曲变形模拟值的误差与实验值误差仅为1.01×10⁻² mm，且变形趋势一致，验证了模型的有效性和准确性。并分析了不同丢层方式、过渡区斜率、厚薄比对变厚度构件固化变形的影响规律，其中离散丢层的构件变形最小，重叠丢层的构件变形最大，且增加过渡区斜率和降低厚薄比可以有效降低其翘曲变形。
- 复合材料 /
- 变厚度 /
- 固化变形 /
- 残余应力 /
- 数值模拟
Abstract: The carbon fiber reinforced polymer (CFRP) composite parts with variable thickness possessed the advantages of material saving, weight reduction, and elastic tailoring properties, and were often used in important application such as wing structures. However, dropping-off plies between layers caused a discontinuity inside the part. Therefore, uneven residual stress could be generated after the curing, and the complex cure-induced distortion (CID) appeared after demolding. For the prediction of the CID of CFRP parts with variable thickness, the existing research mainly adopted the modeling method of equivalent material parameters, without considering the structural characteristics of the resin pocket. In this paper, based on the laminated modeling method, the resin pocket structure was introduced at the dropping-off plies position, and the numerical simulation model of the CID was established. Compared with the results of the traditional equivalent modeling method, the traditional laminated modeling method and experiment, it is proved that the proposed model has the preferable accuracy, the error of the simulated CID is only 1.01×10⁻² mm compared with the experimental result, and the deformation trend is consistent. The influence of different ply drop-off patterns, taper section slopes, and thickness-to-thin ratios on the CID was analyzed. The part with a dispersed ply drop-off pattern presents the smallest CID, and the part with the overlapped ply drop-off pattern has the largest CID. Increasing the taper section slope and reducing the thickness ratio can effectively reduce the warpage.
- composite /
- variable thickness /
- cure-induced deformation /
- residual stress /
- numerical simulation

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图 1 典型变厚度构件丢层结构示意图

Figure 1. Schematic of typical tapered part with dropped plies

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图 2 丢层方式示意图

Figure 2. Schematic of ply drop-off patterns

nD—Number of piles dropped

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图 3 模型有限元网格示意图

Figure 3. Schematic of finite element mesh in the model

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图 4 模型边界条件示意图

Figure 4. Schematic of model boundary conditions

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图 5 变厚度T800 HB/3900-2复合材料构件代表性体积单元(RVE)的有限元模型

Figure 5. Finite element model of representative volume element (RVE) of tapered T800 HB/3900-2 composite part

H—Hight of the RVE; L—Lenght of the RVE; W—Width of the RVE

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图 6 变厚度T800 HB/3900-2复合材料构件厚度方向和不同区域温度和固化度的发展

Figure 6. Development of temperature and curing degree in thickness direction and different regions of tapered T800 HB/3900-2 composite part

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图 7 变厚度T800 HB/3900-2复合材料构件过渡区(X=100 mm)厚度方向上的残余应力σ_X分布

Figure 7. Residual stress σ_X distribution of tapered T800 HB/3900-2 composite part in the thickness direction of taper section (X=100 mm)

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图 8 传统等效建模方法、传统分层建模方法和本文方法所建变厚度T800 HB/3900-2复合材料构件模型在过渡区(X=100 mm)厚度方向上的残余应力σ_X分布

Figure 8. Residual stress σ_X distribution of tapered T800 HB/3900-2 composite part of traditional equivalent model , traditional laminated model and the proposed model on the thickness of taper section (X=100 mm)

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图 9 传统分层建模、传统等效建模和本文方法所建变厚度T800 HB/3900-2复合材料构件模型的位移云图

Figure 9. Displacement contours of the models of tapered T800 HB/3900-2 composite part built by traditional equivalent model, traditional laminated model and the proposed model

U—Total displacement (mm); U₂—Y directional displacement

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图 10 预浸料铺层和装袋流程^[24]

Figure 10. Lay-up and bagging procedure for tapered prepreg^[24]

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图 11 变厚度T800 HB/3900-2复合材料构件变形测量

Figure 11. Deformation measurement of tapered T800 HB/3900-2 composite part

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图 12 变厚度T800 HB/3900-2复合材料构件底面变形模拟结果与扫描结果对比

Figure 12. Comparison of simulation and scanning results of warping deformation on the bottom surface of tapered T800 HB/3900-2 composite part

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图 13 构件A、B、C、D、E、F固化后过渡区(X=200 mm)厚度方向上σ_X分布

Figure 13. σ_X distribution in the thickness direction of taper section (X=200 mm) after curing of part A, B, C, D, E and F

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图 14 构件A、B、C、D、E、F变形云图

Figure 14. Deformation cloud maps of part A, B, C, D, E and F

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图 15 构件A、B、C、D、E、F最大变形量

Figure 15. Maximum deformation of part A, B, C, D, E and F

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图 16 不同过渡区斜率变厚度T800 HB/3900-2复合材料构件的最大变形量

Figure 16. Maximum deformation of tapered T800 HB/3900-2 composite parts with different taper section slopes

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图 17 不同厚薄比变厚度T800 HB/3900-2复合材料构件的最大变形量

Figure 17. Maximum deformation of tapered T800 HB/3900-2 composite parts with different thickness-to-thin ratios

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表 1 T800 HB碳纤维/3900-2环氧树脂复合材料的热学性能^[16]

Table 1. Thermal properties of T800 HB carbon fiber/3900-2 epoxy composite^[16]

Constant	Value
ρ/(kg·m⁻³)	1600
ρ_r/(kg·m⁻³)	1380
C/(J·kg⁻¹·K⁻¹)	925
k_x/(W·m⁻¹·K⁻¹)	7·61
k_y=k_z/(W·m⁻¹·K⁻¹)	0.90
V_f/vol%	62.5
H_R/(kJ·kg⁻¹)	246
Notes: ρ—Composite density; ρ_r—Resin density; C—Specific heat capacity; k_x, k_y and k_z—Longitudinal , normal and transverse thermal conductivity coefficient, respectively; H_R—Total amount of heat; V_f—Average fiber volume fraction.

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表 2 3900-2树脂的固化动力学参数^[16]

Table 2. Cure kinetics constants of 3900-2 resin^[16]

Constant	Value
A/s^–1	1.933×10⁵
∆E/(J∙mol^–1)	7.25×10⁴
m	0.1781
n	1.2323
R/(J∙mol^–1∙K^–1)	8.314
Notes: A—Frequency factor of autocatalytic model; ∆E— Activation energy of autocatalytic model; m, n—Reaction constant; R—Perfect gas constant.

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表 3 T800 HB/3900-2单向复合材料的材料参数^[16]

Table 3. Material parameters of T800 HB/3900-2 unidirectional composites^[16]

Parameter	Viscous	Rubbery	Glassy
E₁/MPa	169000	169000	169000
E₂=E₃/MPa	0.272	272.133	8620
G₁₂=G₁₃/MPa	0.068	68.033	5000
G₂₃/MPa	0.068	68.033	1220
ν₁₂=ν₁₃	0.5	0.5	0.355
ν₂₃	0.995	0.995	0.41
β₁/(10⁻⁶ ℃⁻¹)	—	—	0
β₂=β₃/(10⁻⁶ ℃⁻¹)	—	—	29.5
γ₁/%	0	0	—
γ₂=γ₃/%	-0.19	−0.18	—
Notes: E₁, E₂, E₃—Elastic modulus of composite; G₁₂, G₁₃, G₂₃—Shear modulus of composite; ν₁₂ , ν₁₃, ν₂₃—Poisson's ratio of composite; β₁, β₂, β₃—Coefficient of thermal expansion (CTE) of composite; γ₁, γ₂, γ₃—Chemical shrinkage coefficient of composite.

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表 4 3900-2树脂的材料参数

Table 4. Material parameters of 3900-2 resin

Parameter	Value
E_r/MPa	0.0471 (Viscous)^[16]
	47.1 (Rubbery)^[16]
	4710 (Glassy)^[16]
G_r/MPa	0.0157 (Viscous)
	15.7 (Rubbery)
	1744.4 (Glassy)
ν_r	0.5 (Viscous & Rubbery)^[16,33]
ν_r	0.35 (Glassy)^[35]
β_re/(10⁻⁶ ℃⁻¹)	80^[36]
γ_re/%	−0.99^[36]
Notes: E_r—Elastic modulus of the resin; β_re—CTE of the resin; γ_re—Chemical shrinkage coefficient of the resin.

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表 5 边界条件(BC)^[21]

Table 5. Boundary conditions (BC)^[21]

Plane	BC1	BC2	BC3	BC4	BC5
X=0	S	S	S	R_X/R_Y	S
X =L	D_X	S	S	R_X/D_Y	T_X
Y=0	S	S	S	F	S
Y=W	S	D_Y	S	F	T_Y
Z=0	S	S	S	S	S
Z=H	S	S	D_Z	S	T_Z
Notes: D denotes to apply a uniform displacement to the plane; S denotes to apply a symmetrical constraint to the plane; R denotes to limit the displacement of the plane; F denotes that no constraints are imposed; T denotes that the plane is coupled to the other parallel plane, ensuring that all nodes in these two planes move in the same direction.

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表 6 [45/−45/90/0]_nS铺层T800 HB/3900-2复合材料等效性能

Table 6. Equivalent material properties of T800 HB/3900-2 composites with [45/−45/90/0]_nS layup

Parameter	Viscous	Rubbery	Glassy
E₁=E₂/MPa	44896	45906	60408
E₃/MPa	18.44	12557	10116
G₁₂/MPa	2730.4	4887.5	18347.8
G₁₃=G₂₃/MPa	0.068	68.033	2157.1
ν₁₂	5.92×10⁻⁵	0.029	0.195
ν₁₃=ν₂₃	0.995	0.968	0.362
β₁=β₂/(10⁻⁶ ℃⁻¹)	—	—	0.773
β₃/(10⁻⁶ ℃⁻¹)	—	—	11.765
γ₁=γ₂/%	−0.00013	−0.133	—
γ₃/%	−0.37	−0.36	—

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表 7 变厚度T800 HB/3900-2复合材料构件编号和丢层方式

Table 7. IDs and ply drop-off patterns of tapered T800 HB/3900-2 composite part

Part ID	Ply drop-off pattern
A	Staircased (nD=1)
B	Overlapped (nD=1)
C	Staircased (nD=2)
D	Overlapped (nD=2)
E	Dispersed I (nD=1)
F	Dispersed II (nD=1)

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