Study on the optimization strategy of variable stiffness laminate considering out-of-plane fiber waviness
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摘要: 针对变刚度层合板在自动铺放制造过程中因间隙/重叠缺陷产生大量纤维面外起伏缺陷的问题，提出采用铺层偏移法与断送纱策略两种铺层优化策略来进行变刚度层合板的铺层设计，在研究过程中同时引入考虑间隙/重叠缺陷建模的方法。根据变刚度层合板铺层的特点提出缺陷重复单元的概念，通过对缺陷重复单元的分析来反映纤维面外起伏的影响，并提出通过纤维面外系数来表征变刚度层合板的纤维面外起伏尺度，最后对不同优化策略的变刚度层合板的屈曲性能进行分析。研究表明：基准设计方案、铺层偏移法与断送纱策略所对应的纤维面外起伏系数为0.83、0.95、0.93，所提出的优化策略对变刚度层合板的纤维面外起伏尺度有着明显的抑制作用。铺层偏移法优化后的[±<50/65>]6s变刚度层合板最大厚度超差为33%，所对应的屈曲载荷为9117.1 N，屈曲载荷提升17.6%；断送纱策略优化后的[±<50/65>]6s变刚度层合板最大厚度超差为50%，所对应的屈曲载荷为9716.3N，屈曲载荷提升25.3%。Abstract: Aiming at the problem of a large number of out-of-plane fiber waviness defects due to gap/overlap defects formed in the automated fiber placement process of variable stiffness laminate, two optimization strategies of ply offset and cut strategy were proposed to design variable stiffness laminate, and the modeling method considering gap/overlap defects was introduced. According to the characteristics of variable stiffness laminate, the influence of out-of-plane fiber waviness was reflected through the analysis of defect-repeating elements, and the out-of-plane fiber coefficient was proposed to characterize the scale of waviness in variable stiffness laminate. Finally, the bending performance of variable stiffness laminate with different optimization strategies was analyzed. The coefficients of out-of-plane waviness corresponding to the benchmark scheme, the optimization strategy of ply offset method and the cut strategy are 0.83, 0.95 and 0.93. The proposed optimization strategy has an obvious inhibitory effect on the scale of out-of-plane waviness of variable stiffness laminate. The maximum thickness deviation of [±<50/65>]6s variable stiffness laminate optimized by ply offset method is 33%, the corresponding buckling load is 9117.1 N, increasing by 17.6%; The maximum thickness deviation of [±<50/65>]6s variable stiffness laminate optimized by the cut strategy is 50%, the corresponding buckling load is 9716.3N, increasing by 25.3%.
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图 1 变刚度层合板参考路径曲线
Figure 1. Path curve of variable stiffness laminate
$ {T_0} $—Initial fiber angle; $ {T_1} $—End fiber angle; a—Length of laminate; b—Width of laminate
图 2 窄丝束预浸料曲率约束分析试验
Figure 2. Curvature constraint analysis test of prepreg tow
R—Radius of curvature
图 3 考虑间隙/重叠的变刚度层合板有限元模型建模步骤
Figure 3. Modeling steps of finite element model of variable stiffness laminate considering gap/overlap defects
图 4 变刚度层合板缺陷区域的计算
Figure 4. Calculation of defect area of variable stiffness laminate
t—Tangent vector; k—Secondary normal vector
图 5 铺层偏移法示意图
Figure 5. Schematic diagram of ply offset method
$ {D_{{\text{vs}}}} $—Interlaminar offset distance
图 6 断送纱策略示意图
Figure 6. Schematic diagram of cut strategy
$ {N_{\text{d}}}{w_{\text{t}}} $—Boundary control parameter
图 7 变刚度层合板铺层缺陷重复单元示意图
Figure 7. Schematic diagram of defect-repeating unit of variable stiffness laminate
图 8 含缺陷变刚度层合板试样尺寸与缺陷分布
Figure 8. Dimension of variable stiffness laminate sample with defects and defect distribution
图 9 不同优化策略下[±<50/65>]6s层合板局部试样的铺层厚度
Figure 9. Ply thickness of local specimens of [±< 50/65>]6s laminate under different optimization strategies
图 10 不同优化策略下[±<50/65>]6s层合板的局部试样
Figure 10. Local samples of [±<50/65>]6s laminate under different optimization strategies
图 11 不同设计策略下[±<50/65>]6s层合板局部试样的载荷-位移曲线
Figure 11. Load-displacement curve of local specimen of [± <50/65>]6s variable stiffness laminate under different optimization strategies
图 12 [±<50/65>]6s层合板局部试样的仿真应力-应变曲线与实际应力-应变曲线
Figure 12. Simulated stress-strain curves and actual stress-strain curves of local samples of [±<50/65>]6s laminate
E'u—Actual axial tensile modulus obtained from tensile test of large end of defect
图 14 HyperMesh软件中<50/65>铺层重叠区域
Figure 14. Overlap area of <50/65> ply in HyperMesh software
图 15 不同优化策略下的[±<50/65>]6s层合板整体厚度
Figure 15. Overall thickness of [±<50/65>]6s laminate under different optimization strategies
图 16 [45/90/−45/0]3s层合板屈曲载荷
Figure 16. Buckling load of [45/90/−45/0]3s laminate
U—Strain
图 17 不考虑缺陷建模的[±<50/65>]6s层合板屈曲载荷
Figure 17. Buckling load of [±<50/65>]6s laminate without considering defect
图 18 采用铺层偏移法优化的[±<50/65>]6s层合板屈曲载荷
Figure 18. Buckling load of [±<50/65>]6s laminate optimized by ply offset method
图 19 采用断送纱策略优化的[±<50/65>]6s层合板屈曲载荷
Figure 19. Buckling load of [±<50/65>]6s laminate optimized by cut strategy
表 1 考虑间隙/重叠建模所需的材料力学性能
Table 1. Mechanical properties of materials considering gap/overlap modeling
EM118 carbon
fiber/A10
epoxy laminate$ {E_1} $/GPa $ {E_2} $=$ {E_3} $/GPa $ {G_{12}} $=$ {G_{13}} $/GPa $ {G_{23}} $/GPa $ {v_{12}} $=$ {v_{13}} $ $ {v_{23}} $ 140 7.5 3.69 4 0.3 0.4 $ h $/mm $ {\rho _{\text{l}}} $/(g·mm−3) 0.15 1.85 Epoxy resin $ {E_{\text{r}}} $/GPa $ {v_{\text{r}}} $ $ {\rho _{\text{r}}} $/(g·mm−3) 2 0.25 1.117 Notes: E1, E2, E3—Elastic modulus of laminate; G12, G13, G23—Shear modulus of laminate; v12, v13, v23—Poisson’s ratio of laminate; h—Thickness of laminate; ρl—Density of laminate; Er—Elastic modulus of resin; vr—Poisson’s ratio of resin; ρr—Density of resin. 
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表 2 [±<50/65>]6s层合板纤维面外起伏系数τc
Table 2. Coefficient τc of [±<50/65>]6s laminate with out-of-plane fiber waviness
Name Baseline Ply offset Cut strategy ${\tau _{\rm{c}}}$ 0.83 0.95 0.93
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表 3 不同优化策略的[±<50/65>]6s层合板铺层厚度与屈曲载荷
Table 3. Ply thickness and buckling load of [±<50/65>]6s laminate with different optimization strategies
Ply type Ply angle Maximum thickness
deviation before
optimization/%Design
factorBuckling load
before
optimization /NOptimization
strategyMaximum thickness
deviation after
optimization/%Buckling load
after
optimization /NBuckling change/% Linear ply [45/90/−45/0]3s − − 7751.5 − − − − Curved ply [±<50/65>]6s +100 No defect − − − − +10.3 [±<50/65>]6s 100% Coverage 8551.4 Ply offset +33.3 9117.1 +17.6 [±<50/65>]6s 100% Coverage − Cut strategy +50 9716.3 +25.3
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