Elastic performance prediction and 3D drilling simulation of PW-CFRP
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摘要: 平纹编织结构碳纤维增强树脂基复合材料（plain-woven carbon fiber-reinforced plastic，PW-CFRP）展现出高损伤容限特性，在航空航天领域应用广泛。针对PW-CFRP钻削仿真中由于其材料弹性性能变化导致单一尺度钻削仿真难以体现实际钻削力的问题，研究其弹性性能预测及多尺度三维钻削仿真。基于周期性边界条件的弹性性能参数预测模型，利用预测的材料弹性性能参数，采用多尺度有限元方法，仿真PW-CFRP的三维钻削并开展试验验证。研究结果表明：基于周期边界条件的有限元法能准确预测编织复合材料的弹性常数；在剪切载荷下，其编织单胞的边界面均由平面变成曲面，发生凸凹翘曲变形；基于刚度预测模型基础的PW-CFRP三维钻削仿真模型能够准确预测制孔过程中的轴向力、扭矩；在相同工艺参数下，制孔轴向力和扭矩的仿真预测与试验结果相对误差分别为14.2%和8.5%。Abstract: Plain-woven carbon fiber-reinforced plastic (PW-CFRP) exhibits high damage tolerance and is widely used in the aerospace field. To address the issue that single-scale drilling simulation is difficult to reflect the practical drilling force due to the change in material elastic properties in PW-CFRP drilling simulation, this paper studies the prediction of elastic properties of PW-CFRP and multi-scale three-dimensional drilling simulation. Based on the prediction model of elastic performance parameters with periodic boundary conditions, the three-dimensional drilling simulation of PW-CFRP is carried out using the predicted material elastic performance parameters and the multi-scale finite element method, with experimental verification. The results show that the finite element method based on periodic boundary conditions can accurately predict the elastic constants of braided composites. For the woven unit cell, its boundary surface changes from plane to surface under shear load, and convex-concave warping deformation occurs. The PW-CFRP three-dimensional drilling simulation model, based on the stiffness prediction model, can accurately predict the axial force and torque during the drilling process. Under the same process parameters, the maximum relative errors between the simulation prediction and the experimental results of the drilling thrust force and torque are 14.2% and 8.5%, respectively. The multi-scale drilling simulation of PW-CFRP, from microscopic to mesoscopic to macroscopic, is realized.
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Key words:
- CFRP /
- periodical boundary condition /
- multi-scale analyses /
- elastic constant /
- drilling simulation
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图 2 线性不相关的单一工况下模型受载示意图
Figure 2. Load diagram of model under linear uncorrelated single condition
图 5 PW-CFRP截面实物图与结构示意图
Figure 5. PW-CFRP section physical drawing and structure diagram
图 6 介观尺度编织单胞模型及纤维束材料主方向
Figure 6. Mesoscale braided unit cell model and main direction of fiber bundle material
图 10 纤维单胞的变形和Mises应力云图
Figure 10. Deformation and Mises stress nephogram of fiber unit cell
图 11 编织单胞的变形和Mises应力云图
Figure 11. Deformation and Mises stress nephogram of braided unit cell
图 12 PW-CFRP钻削仿真与试验结果对比
Figure 12. PW-CFRP drilling simulation and experiment results comparison
图 13 PW-CFRP有限元仿真的钻削过程
Figure 13. Drilling process of PW-CFRP finite element simulation
图 14 PW-CFRP钻削轴向力仿真与试验结果对比
Figure 14. Comparison of drilling force simulation and experimental results of PW-CFRP
图 15 PW-CFRP钻削扭矩仿真与试验结果对比
Figure 15. Comparison of drilling torque simulation and experimental results of PW-CFRP
表 1 单胞模型所需施加的线性不相关的宏观应力场
Table 1. Linearly uncorrelated macroscopic stress fields to be applied to single cell model
序号 $ \stackrel{-}{{\sigma }_{x}} $ $ \stackrel{-}{{\sigma }_{y}} $ $ \stackrel{-}{{\sigma }_{{\textit{z}}}} $ $ \stackrel{-}{{\tau }_{x}} $ $ \stackrel{-}{{\tau }_{y}} $ $ \stackrel{-}{{\tau }_{{\textit{z}}}} $ 1 $ \stackrel{-}{{\sigma }_{x}} $ 0 0 0 0 0 2 0 $ \stackrel{-}{{\sigma }_{y}} $ 0 0 0 0 3 0 0 $\stackrel{-}{ {\sigma }_{{\textit{z}}} }$ 0 0 0 4 0 0 0 $ \stackrel{-}{{\tau }_{x}} $ 0 0 5 0 0 0 0 $ \stackrel{-}{{\tau }_{y}} $ 0 6 0 0 0 0 0 $\stackrel{-}{ {\tau }_{ {{\textit{z}} } } }$ 
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表 2 纤维单胞模型的几何结构参数
Table 2. Geometric parameters of fiber unit cell model
序号 S/ μm b/ μm Df / μm Vf 1 8.268 7.161 7 65%
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物理量 取 值 物理量 取 值 纤维 基体 纤维 基体 E11 / GPa 213.0 3.5 μ23 0.30 0.30 E22 / GPa 14.0 3.5 G12 / GPa 9.0 1.1 E33 / GPa 14.0 3.5 G13 / GPa 9.0 1.1 μ12 0.26 0.30 G23 / GPa 4.8 1.1 μ13 0.26 0.30
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表 4 编织单胞模型的几何结构参数
Table 4. Geometric parameters of woven unit cell model
序号 A0 / mm H0 / mm Vf h0 / mm 1 1.8 0.15 55% 0.05
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表 5 碳纤维织物层强度属性[21]
Table 5. Strength properties of carbon fiber fabric layer
PW-CFRP强度参数 数值 X1t=X2t / MPa 2720 X3t / MPa 111 X1c=X2c / MPa 1690 X3t / MPa 214 S12=S13=S23 / MPa 115
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表 6 钻削刀具主要结构尺寸参数
Table 6. Main structure parameters of drilling tool
刀具主要参数 数值 直径 r / mm 4.851 顶角 α /(°) 90 螺旋角 θ /(°) 30 刀长 l / mm 75
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表 7 纤维束等效弹性参数
Table 7. Equivalent elastic parameters of fiber bundle
物理量 数值 物理量 数值 E11 / GPa 137.5 μ23 0.40 E22 / GPa 8.2 G12 / GPa 5.7 E33 / GPa 8.2 G13 / GPa 5.7 μ12 0.29 G23 / GPa 2.8 μ23 0.29
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表 8 织物层等效弹性参数
Table 8. Equivalent elastic parameters of fabric layer
物理量 数值 物理量 数值 E11 / GPa 49.0 μ23 0.297 E22/ GPa 49.0 G12/ GPa 11.0 E33/ GPa 18.3 G13 / GPa 6.4 μ12 0.110 G23 / GPa 6.6 μ23 0.280
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