Simulation of manufacture of the hat-stiffened composite plate based on multidisciplinary coupling
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摘要: 民机复合材料帽型壁板自动化制造包含自动铺丝(AFP)和热压罐固化过程，工艺复杂，故有必要对其进行理论研究和建模。分别建立粘弹性力学和多孔渗流耦合模型对铺丝过程进行仿真；建立复合材料热传导、化学交联反应、固化动力学、多孔介质渗流和材料性能时变性耦合模型对固化过程进行仿真。应用所建立的耦合模型对AS4/3051-6系列碳纤维/环氧树脂(CFRP)预浸料热压罐固化制备复合材料平板工艺进行仿真，并将其结果与实验结果对比，验证了此方法的有效性。随后，将此方法应用于大型复合材料帽型壁板制造过程仿真，仿真结果表明：(1) AFP头在经过帽型腔体时存在下陷，下陷量与硅橡胶气囊支撑性能相关，应用本文设计芯模下陷量仿真值为原先的38%，铺丝头对蒙皮的影响面积仿真值为原先的30%；(2) 帽型加筋板内部温度与工艺温度不同，其最高温度出现在保温过程结束后升温阶段初期，预测值为工艺温度的106%，且接合处内外层温度差别明显；(3) 帽型加筋壁板内部黏度随时间先减小后急剧上升，内层黏度较外层黏度变化速率更大；(4) 帽型加筋板蒙皮平均厚度预测值由成型前的4.5 mm减少至4 mm，测量厚度为3.88 mm，仿真误差为3.1%。
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关键词:
- 多学科耦合 /
- CFRP复合材料帽型加筋板 /
- 过程仿真 /
- 自动化制造 /
- 芯模
Abstract: The carbon fiber reinforced polymer (CFRP) hat-stiffened plate which is fabricated in wide-bodied airplane is concluded in line with manufacturing crafts of automatic fiber placement (AFP) and autoclave forming that is very complex, so it is necessary to make theoretical research and modeling. Viscoelastic mechanics and percolation model were used to simulate the AFP process, while the composite material heat conduction, curing crosslinking chemical reaction, curing dynamics and porous media percolation model were employed in the simulation of the autoclave process, every multidisciplinary model sharing coupling relationship. On this base, numerical simulation of curing process of manufacturing simple carbon fiber reinforced epoxy resin multilayer under the AS4/3501-6 resin system was carried out. The consequences of simulation were verified when compared with the experimental results. Applying this approach of simulation in CFRP hat-stiffened plate, the results manifest that: (1) The operating head of the AFP equipment can generate a sag whose extend is related to the mandrel’s supporting property, after adding the supporting structure, the simulated sag value and the affecting area value decreases to 38% and 30% compared with the original mandrel; (2) The internal temperature of the hat-stiffened plate is different from the setting process temperature, and the maximum temperature appears in the early heating stage after the end of the insulation process, the predicted value is 106% of the process temperature, and the temperature difference between the inner and outer layers at the joint is obvious; (3) The internal viscosity of the hat-stiffened panels decreases first and then increases sharply, and the change rate of the inner layer viscosity is greater than that of the outer layer; (4) The predicted average skin thickness of the hat-stiffened plate reduces from 4.5 mm before forming to 4 mm, the measured thickness is 3.88 mm, the simulation error is 3.1%. -
图 1 弹性麦克斯韦方程原理
Figure 1. Schematic diagram of Maxwell’s equation of viscoelasticity
σ—Stress in viscoelastic process; ε1—Strain of the spring; ε2—Strain of the damper; η—Viscosity coefficient; E—Elasticity modulus
图 2 复合材料板制造过程仿真原理
Figure 2. Composite plate manufacturing process simulation schematic diagram
图 4 CFRP复合材料板网格划分与边界条件
Figure 4. Mesh generation and condition attachment of CFRP plate
图 8 CFRP板制造内部各点仿真温度
Figure 8. Temperature of internal point of CFRP plate in curing process
图 9 CFRP平板热压罐加热第一阶段温度变化
Figure 9. Temperature inclination of CFRP plate of the first stage in autoclave process
图 10 CFRP平板热压罐加热第二阶段温度变化
Figure 10. Temperature inclination of CFRP plate of the second stage in plate curing process
图 11 CFRP平板热压罐加热第三阶段温度变化
Figure 11. Temperature inclination of CFRP plate of the third stage in plate curing process
图 14 帽型加筋板蒙皮自动铺丝(AFP)过程
Figure 14. Automatic fiber placement (AFP) process of skin of the hat stiffened plate
图 16 多场耦合自动铺丝不同芯模下陷量仿真对比
Figure 16. Sinking quantity comparison with multi-disciplinary simulation in two different mandrel
图 15 增加芯模内部结构的帽型加筋板自动化制造工艺
Figure 15. Automatic manufacturing process of hat-stiffened plate with internal structure
图 18 帽型加筋板内部各点温度仿真
Figure 18. Simulation of internal point temperature of hat-stiffened plate
图 19 帽型加筋板制造过程固化度仿真
Figure 19. Simulation ofcuring degree of hat-stiffened plate manufacture process
图 20 帽型加筋板制造过程黏度仿真
Figure 20. Simulation of process viscosity of hat-stiffened plate manufacture process
图 21 帽型加筋板蒙皮厚度预测
Figure 21. Prediction of the thickness of the skin of hat-stiffened plate
表 1 AS4/3501-6碳纤维/环氧树脂复合材料时变性性能
Table 1. Time-dependent property of AS4/3501-6 carbon fiber/epoxy composites
Parameter Linear time-varying description ${\rho _{\rm{r}}}$/(${\rm{kg}} \cdot {{\rm{m}}^{ - 3}}$) ${\rho _{\rm{r} } } = \left\{ \begin{array}{l}90\alpha + 1\;232\quad \alpha \leqslant0.45\\1\;272\qquad \quad \;\;\alpha \geqslant0.45\end{array} \right.$ ${C_{\rm{r}}}$/(${\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{ - 1}} \cdot {{\rm{K}}^{ - 1}}$) ${C_{\rm{r} } } = 4\;184\left( {0.47 + 6 \times { {10}^{ - 4} }T - 0.14\alpha } \right)$ ${C_{\rm{f}}}$/(${\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{ - 1}} \cdot {{\rm{K}}^{ - 1}}$) ${C_{\rm{f} } } = 1\;390 + 4.5T$ ${K_{\rm{r}}}$/(${\rm{W}} \cdot {{\rm{m}}^{ - 1}} \cdot {{\rm{K}}^{ - 1}}$) ${K_{\rm{r}}} = 0.042\left[ {3.85 + \left( {0.035T - 0.14} \right)\alpha } \right]$ ${K_{\rm{f}}}$/(${\rm{W}} \cdot {{\rm{m}}^{ - 1}} \cdot {{\rm{K}}^{ - 1}}$) $K_{\rm{f}}^{\rm{L}} = 0.742 + 9.02 \times {10^{ - 4}}T$ Notes: ${\rho _{\rm{r}}}$—Density of resin; ${C_{\rm{r}}}$ and ${C_{\rm{f}}}$—Specific heat capacity of resin and fibers; ${K_{\rm{r}}}$ and ${K_{\rm{f}}}$—Heat conductivity coefficient of resin and fibers; $\alpha $—Curing degree; T—Internal instantaneous temperature. 
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表 2 多学科模型及耦合关系
Table 2. Multi-disciplinary model and coupling connections
Disciplinary model Equation Coupling object Mode Output/Input parameter Thermal conduction Fourier heat equation Chemical reaction & Curing kinetic Bi-direction T Chemical reaction Crosslinking equation Thermal conduction & Curing kinetic Bi-direction Q Curing kinetic Partial differential equation Porous filtration & Chemical reaction Bi-direction dα/dt, α Porous filtration Darcy’s law Thermal conduction Uni-direction P, ${V_i}$, h Time-varying behavior Linear equation All models Bi-direction K, C, $\rho $ Viscoelastic mechanics Constitutive equation Filtration in AFP Uni-direction $\sigma $ Notes: AFP—Automatic fiber placement; Q—Chemical reaction heat; P—Tnner forming pressure; Vi—Flow rate during curing process; h—Thickness of the plate or the hat; K—Heat conductivity coefficient; C—Specific heat; ρ—Density of the composite; σ—Stress in AFP.
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表 3 CFRP复合材料板多学科性能
Table 3. Multi-disciplinary behavior of CFRP plate
Parameter Value Parameter Value ${A_1}/{\min ^{ - 1}}$ 2.102×109 $\Delta {E_\mu }/\left( {{\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}}} \right)$ 9.43×104 ${A_2}/{\min ^{ - 1}}$ −2.014×109 ${{R/} }\left( { {\rm{J} } \cdot {\rm{mo} }{ {\rm{l} }^{ - 1} } \cdot { {\rm{K} }^{ - 1} } } \right)$ 8.3143 ${A_3}/{\min ^{ - 1}}$ 1.96×105 ${\mu _\infty }/\left( {{\rm{Pa}} \cdot {\rm{s}}} \right)$ 7.93×10−14 $\Delta {E_1}/\left( {{\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}}} \right)$ 8.07×104 ${r_{\rm{f}}}$/m 4×10−6 $\Delta {E_2}/\left( {{\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}}} \right)$ 7.78×104 ${K_{\rm{c}}}$(Parallel to fiber) 0.6 $\Delta {E_3}/\left( {{\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}}} \right)$ 5.66×104 ${K_{\rm{c}}}$(Vertical to fiber) 14.2 Notes: A1, A2, A3—Frequency factors; ∆E1, ∆E2, ∆E3—Activation energy; $\Delta {E_\mu }$—Activation energy of viscous; ${\mu _\infty }$—Constant; R—Universal gas constant; ${r_{\rm{f}}}$—Radius of carbon fiber; ${K_{\rm{c}}}$—Kozeny constant.
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