Prediction method for curing deformation of conical C-shaped shell of fiber reinforced composite
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摘要: 采用热压罐固化成形的纤维增强复合材料工件在脱模后通常与模具形状有一定出入,影响成型的精度和质量。为研究曲面零件固化变形规律,将C形圆台壳件的几何形状用母线长度、半高处半径、圆心角、半顶角、厚度五个参数表征,并基于虚功原理和小变形假设推导由于固化工艺中温度改变导致的形状变化公式。结果表明:固化后此类工件的厚度变薄,半高处半径缩小、圆心角增大、母线变短、顶角变小。与有限元模拟正交实验对比,验证了本公式的正确性;给出了基于path-dependent本构关系的固化变形有限元模拟的简化实现方案,与文献相比可以减少80%的计算时间,且实现难度较低。分别用本公式、热弹性有限元模型、path-dependent有限元模型计算某小型固定翼飞机的机头罩固化变形,预测半跨长平均缩小量分别是8.1 mm、7.6 mm、6.1 mm,均与实测值7.7 mm基本吻合;计算结果可以解释该零件的装配变形现象。Abstract: The shape of fiber-reinforced composite work-piece cured in autoclave usually deviates from the original design after demoulding, which influences the product quality. In order to study the cure deformation law of curved parts, the geometry of conical C-shaped shell was described by only five parameters: generatrix length, radius at half height, center angle, half apex angle and shell thickness. Based on the virtual work principle and small deformation hypothesis, the analytic solution of the cure deformation caused by the temperature drop in the curing process was deduced. It is revealed that after curing, the thickness, half-height radius, generatrix length and apex angle decrease, while the center angle of the arc increases. Compared with the finite element simulation orthogonal test, which validates the analytical solution. A simplified scheme of finite element curing simulation by use of the path-dependent constitutive law is given. This simplified finite element deformation prediction method can cut the computing time by 80% and the implementation is much easier. By using this formula, thermoelastic finite element model and path-dependent finite element model, the curing deformation of the nose cover of a small fixed-wing aircraft is calculated, and the predicted average reduction of half-span length is 8.1mm,7.6mm and 6.1mm respectively, which are basically consistent with the measured value of 7.7mm. The assembly deformation characteristics of the part can also be explained based on the proposed analysis.
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Key words:
- composites /
- autoclave /
- curing deformation /
- virtual work principle /
- thermal strain
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表 1 正交实验变量及对应水平选择
Table 1. Orthogonal test variables and corresponding level selections
Level Generatrix length
$h/{\text{mm}}$Radius at half height
$r/{\text{mm}}$Center angle
$\theta /\left( {^{\text{o}}} \right)$Half apex angle
$\phi /\left( {^{\text{o}}} \right)$A B C D 1 100 100 30 5 2 200 200 60 10 3 300 300 90 15 表 2 玻璃纤维增强树脂基复材(Hexcel7781/LY5052/ HY5052,
$ V_{f}=0.49 $ )的等效力学性能Table 2. Equivalent mechanical properties of glass fiber reinforced resin-based composite material (Hexcel7781/LY5052/HY5052,
$ V_{r}=0.49 $ )State Eτ/GPa En/GPa Gττ/GPa Gτn/GPa νττ ντn ατ10–6/°C αn10–6/°C dβτ/∆Xτ dβn/∆Xn Rubbery 18.7 2.3 0.03 0.03 0.002 0.845 5.54 264.8 –7.95×10–5 –3.5×10–2 Glassy 22.95 8.4 2.55 2.43 0.1 0.455 15.2 66.4 –3.65×10–4 –2.2×10–2 表 3 3 mm厚C形模型的不同本构模型运行时间对比
Table 3. Comparison of time costs of different constitutive laws for C-section with 3 mm thickness
Model Time cost/s CHILE(α) 182 CHILE(Tg) 185 Path-dependent 149 Viscoelastic 157 Proposed model 32 表 4 机头罩简化几何模型参数
Table 4. Simplified geometric model parameters of nose cover
Radius Generatrix length, h/mm radius at half height, r/mm center angle,
θ/(°)half apex angle,
φ/(°)Minor radius 782 1315 12 8 Long radius 278.5 80 -
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