Influence of blank-holder force on the draping process of unbalanced plain woven fabric preform
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摘要: 为研究压边力对非平衡玻璃纤维平纹机织物预制体铺覆成型的作用规律，针对非平衡平纹机织物在成型过程中的大变形特征，基于非正交材料本构，建立织物面内材料变形本构模型；同时考虑面外弯曲刚度，结合壳单元，建立织物的膜(面内变形)-壳(面外变形)双层模型；利用商业有限元软件ABAQUS，结合实验方法，研究织物在不同压边力条件下的成型规律。结果表明，实验组中预制体的纤维剪切角随压边力的增加而增大；摩擦系数设置对有限元模型的模拟结果有重要影响，随着摩擦系数增大，预制体的纤维剪切角随之增大，摩擦系数为0.20时的模拟结果与实验结果最接近；考虑织物弯曲刚度的膜-壳双层单元模型的模拟结果与实验结果基本一致，而单层膜单元模型的模拟结果精度相对较低。Abstract: Considering the nonlinear deformation characteristics of unbalanced plain woven glass fiber fabric, the in-plane deformation behavior based non-orthogonal material constitutive and out-plane bending behavior were involved into a coupling finite element consisting membrane with shell element to predict the deformation behaviors of the fabric during draping process. Using the commercial finite element software ABAQUS combined with experimental method, the influence of boundary conditions on the deformation behavior was discussed. The results show that the fiber shear angle of the preformed blank increases with the increase of blank holder force in the experiments. The fiber shear angle of the preformed blank increases with the improvement of friction coefficient in the finite element model, and the simulate results are closer to the experimental results when the friction coefficient is 0.20. Compared to the model established with single-layer membrane element, the membrane-shell element model considering bending stiffness shows higher agreement with experimental results. Studies show that the bending stiffness is essential to enhance the accuracy of the simulation model, which plays an important role in the prediction of shear angle in draping process.
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Key words:
- plain woven fabric /
- draping process /
- preform /
- numerical simulation /
- shear angle /
- blank-holder force
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图 3 玻璃纤维平纹机织物的单轴拉伸载荷-位移曲线
Figure 3. Uniaxial tensile load-displacement curves of glass fiber plain woven fabric
图 5 玻璃纤维平纹机织物的镜框剪切载荷-位移曲线
Figure 5. Picture frame test load-displacement curves of glass fiber plain woven fabric
图 6 镜框剪切实验几何原理
Figure 6. Principle of picture frame test
γ—Shear angle of fabric; Lframe—Picture frame arm length; d—Displacement of fabric; F—Tensile load; θ—Angle of picture frame
图 7 织物的悬臂测试原理
Figure 7. Principle of cantilever test for fabric
l—Bending length of a fabric
图 9 玻璃纤维平纹机织物经向和纬向的弯曲刚度
Figure 9. Flexural rigidity of glass fiber plain woven fabric in warp and weft direction
图 10 半球形平纹机织物预制体成型装置装配图
Figure 10. Assembly drawing of hemispherical plain woven fabric preform forming device
图 11 半球形平纹机织物预制体成型装置实物图：(a) 冲头；(b) 压边圈；(c) 压边圈圆角；(d) 2.5 kg配重环；(e) 5.0 kg配重环；(f) 模具和框架
Figure 11. Picture of hemispherical plain woven fabric preform forming device: (a) Punch; (b) Blank-holder; (c) Filleted corner; (d) 2.5 kg metal ring; (e) 5.0 kg metal ring; (f) Mold and frame
图 13 半球形平纹机织物预制体成型实验
Figure 13. Forming experiment of hemispherical plain woven fabric preform
图 14 各压边力下半球形平纹机织物预制体成型结果：(a) 25 N；(b) 50 N；(c) 75 N；(d ) 100 N
Figure 14. Forming results of hemispherical plain woven fabric preform under different blank-holder forces: (a) 25 N; (b) 50 N; (c) 75 N; (d) 100 N
图 17 半球形平纹机织物预制体成型模型
Figure 17. Model of hemispherical plain woven fabric preform draping
图 18 平纹机织物膜-壳双层模型
Figure 18. Membrane-shell model of plain woven fabric
t—Thickness of fabric
图 20 半球形平纹机织物预制体在不同压边力下的剪切角
Figure 20. Shear angles of hemispherical plain woven fabric preform under different blank-holder forces
图 21 半球形平纹机织物预制体在不同压边力下的变形机制
Figure 21. Deformation mechanism of hemispherical plain woven fabric preform under different blank-holder forces
图 22 平纹机织物镜框剪切模拟变形图：(a) 位移100 mm；(b) 位移120 mm
Figure 22. Simulation results of picture frame test: (a) 100 mm displacement; (b) 120mm displacement
图 23 平纹机织物镜框剪切模拟与实验结果：(a) 织物剪切应力-剪切角曲线；(b) 反作用力-位移曲线
Figure 23. Simulation and experiment results of plain woven fabric picture frame test: (a) Shear stress-shear angle curve; (b) Reaction force-displacement curve
图 24 不同摩擦系数下半球形平纹机织物预制体模拟与实验结果对比
Figure 24. Comparison of simulation results of hemispherical plain woven fabric preform under different friction coefficients and experimental results
图 25 半球形平纹机织物预制体膜-壳双层模型模拟结果：(a) 25 N；(b) 50 N；(c) 75 N；(d) 100 N
Figure 25. Simulation results of membrane-shell model of hemispherical plain woven fabric preform: (a) 25 N; (b) 50 N; (c) 75 N; (d) 100 N
图 26 半球形平纹机织物预制体单层膜模型模拟结果：(a) 25 N；(b) 50 N；(c) 75 N；(d) 100 N
Figure 26. Simulation results of single-layer membrane model of hemispherical plain woven fabric preform: (a) 25 N; (b) 50 N; (c) 75 N; (d) 100 N
图 27 不同压边力下半球形平纹机织物预制体实验与模拟剪切角对比
Figure 27. Comparison of experimental and simulated shear angles in hemispherical plain woven fabric preform under different blank-holder forces
图 28 不同压边力下半球形平纹机织物预制体模拟剪切角：(a) 单层膜模型；(b) 膜-壳模型
Figure 28. Simulated shear angles of hemispherical plain woven fabric preform under different blank-holder forces: (a) Single layer membrane model; (b) Membrane-shell model
图 29 半球形平纹机织物预制体变形轮廓模拟与实验结果对比
Figure 29. Simulated boundary profiles of hemispherical plain woven fabric preform compared with the experimental results
图 30 半球形平纹机织物预制体中纱线屈曲
Figure 30. Yarn buckling in hemispherical plain woven fabric preform
图 31 半球形平纹机织物预制体中纱线屈曲横截面示意图
Figure 31. Schematic of yarn buckling cross section in hemispherical plain woven fabric preform
h—Offset distance of warp yarn
图 32 半球形平纹机织物预制体局部位移云图：(a)膜-壳模型；(b)单层膜模型
Figure 32. Local displacement nephogram of hemispherical plain woven fabric preform: (a) Membrane-shell model; (b) Single layer membrane model
表 1 无碱玻璃纤维非平衡平纹机织物参数
Table 1. Parameters of E-glass fiber unbalanced plain woven fabric
Parameter Fabric Weave Plain Areal density/(g·m−2) 600 Warp yarns/cm 2.8 Weft yarns/cm 2.5 Yarn thickness/mm 0.6 Warp yarn width/mm 2.9 Weft yarn width/mm 2.5 Fabric image 
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表 2 玻璃纤维平纹机织物经纬向弯曲长度测试结果
Table 2. Bending length of glass fiber plain woven fabric in warp and weft direction
Number of sample Warp/mm Weft/mm Weft/mm 1 118 121 121 2 120 127 127 3 118 127 127 4 117 126 126 5 120 124 124 6 118 128 128
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