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基于结构参数的平纹机织复合材料等效弹性性能预测

朱俊 桂林 李果 于梦海 王继辉

朱俊, 桂林, 李果, 等. 基于结构参数的平纹机织复合材料等效弹性性能预测[J]. 复合材料学报, 2023, 40(2): 804-813. doi: 10.13801/j.cnki.fhclxb.20220424.004
引用本文: 朱俊, 桂林, 李果, 等. 基于结构参数的平纹机织复合材料等效弹性性能预测[J]. 复合材料学报, 2023, 40(2): 804-813. doi: 10.13801/j.cnki.fhclxb.20220424.004
ZHU Jun, GUI Lin, LI Guo, et al. Prediction of the effective elastic properties for plain woven fabric composite based on the structural parameters[J]. Acta Materiae Compositae Sinica, 2023, 40(2): 804-813. doi: 10.13801/j.cnki.fhclxb.20220424.004
Citation: ZHU Jun, GUI Lin, LI Guo, et al. Prediction of the effective elastic properties for plain woven fabric composite based on the structural parameters[J]. Acta Materiae Compositae Sinica, 2023, 40(2): 804-813. doi: 10.13801/j.cnki.fhclxb.20220424.004

基于结构参数的平纹机织复合材料等效弹性性能预测

doi: 10.13801/j.cnki.fhclxb.20220424.004
基金项目: 国防基础科研计划(JCKY2018207B206;TDGC-CL-19-031-2)Defense Industrial Technology Development Program (JCKY2018207B206; TDGC-CL-19-031-2)
详细信息
    通讯作者:

    王继辉,博士,教授,博士生导师,研究方向为聚合物基复合材料 Email:jhwang@whut.edu.cn

  • 中图分类号: TB332

Prediction of the effective elastic properties for plain woven fabric composite based on the structural parameters

  • 摘要: 经向纤维束与纬向纤维束纵横交错引起的纤维弯曲(也称为波纹)是平纹机织复合材料固有特征。首先,提出了一种精确描述平纹机织复合材料单胞3D结构特征的数学表达式。其次,基于经典层合板理论和等应力假设,考虑平纹机织复合材料厚度方向非对称引起的弯曲-拉伸耦合效应及单胞结构特征,建立了含结构参数的平纹机织复合材料等效弹性性能多参数解析模型。通过数个典型算例验证了建立的多参数解析模型,结果表明:该多参数解析模型预测值与相关文献中有限元模型预测值、解析模型预测值、实验值等均吻合较好;该多参数解析模型预测值尤其是Z向弹性性能预测值,比文献中解析模型预测值更接近于实验值。在此基础上,进一步探讨了纤维束波纹比(包括纤维束波动方向波纹比与纤维束横截面波纹比)、经向与纬向纤维束构成的预成形体厚度、纤维束中弯曲部分的长度、相邻纤维束之间间距等结构参数对平纹机织复合材料弹性性能影响。该多参数解析模型建模方法为研究纺织复合材料力学性能提供了参考。

     

  • 图  1  平纹机织复合材料及其单胞

    hw—Thickness of the fiber strand; aw—Width of the fiber strand

    Figure  1.  Plain woven fabric composite and the unit cell

    图  2  平纹机织复合材料单胞横截面

    The subscript ‘f’ refers to fill strand, and the subscript ‘w’ refers to warp strand; a, h, u, θ—Width and thickness of the fiber strand cross-section, length of the curved section of the fiber strand within the unit cell, and the local off-axis angle of the fiber strand, respectively; g—Spacing between the adjacent fiber strands within the unit cell; ht and h—Thickness of the preform consisting of the warp and fill fiber strands and the total thickness for the unit cell, respectively

    Figure  2.  Cross section of unit cell for plain woven fabric composite

    图  3  波纹比对E玻璃纤维/乙烯基酯树脂平纹机织复合材料弹性性能影响(案例1#)

    Figure  3.  Effects of the waviness ratio on the elastic properties of E-glass/vinyl ester plain woven fabric composite for case 1#

    图  4  经向与纬向纤维束构成的预成形体厚度对E玻璃纤维/乙烯基酯树脂平纹机织复合材料弹性性能影响(案例2#)

    Figure  4.  Effects of the thickness of the preform consisting of the warp and fill fiber strands on the elastic properties of E-glass/vinyl ester plain woven fabric composite for case 2#

    表  1  E玻璃纤维/乙烯基酯树脂复合材料及其组分材料弹性常数

    Table  1.   Elastic constants for E-glass/vinyl ester composite and the constituents

    (a) Elastic constants of E-glass/vinyl ester composite[15]
    E1/GPaE2=E3/GPaG12=G13/GPaG23/GPav21=v31v23
    57.518.87.447.260.250.29
    Notes: E1, E2, E3—Moduli in 1-, 2- and 3-direction, respectively; G12, G13, G23—Shear moduli in 1-2, 1-3 and 2-3 plane, respectively; v21, v31, v23—Major Poisson’s ratios in 1-2, 1-3 and 2-3 plane, respectively.
    (b) Elastic constants of the constituent fiber and resin matrix[13]
    ConstituteE/GPaG/GPav
    E-glass fiber73.030.400.20
    Vinyl ester resin matrix 3.4 1.490.35
    Note: E, G, v—Elastic modulus, the shear modulus and the major Poisson’s ratio of the constituents, respectively.
    下载: 导出CSV

    表  2  本文模型中E玻璃纤维/乙烯基酯树脂平纹机织复合材料单胞的结构参数

    Table  2.   Unit-cell structural parameters of E-glass/vinyl ester plain woven fabric composite in present model

    af=aw/mmhf=hw/mmgf=gw/mmht=h/mmlx=ly/mmuf=uw/mm
    0.60.0500.100.60.6
    Note: lx, ly—Length, width of the unit cell, respectively.
    下载: 导出CSV

    表  3  E玻璃纤维/乙烯基酯树脂平纹机织复合材料弹性性能

    Table  3.   Elastic properties of E-glass/vinyl ester plain woven fabric composite

    ResultsEx=Ey/GPaEz/GPaGyz=Gxz/GPaGxy/GPavyxvzx=vzy
    Present model25.5213.034.825.280.140.31
    Experimental data[13]24.80±1.10 8.50±2.604.20±0.706.50±0.800.10±0.010.28±0.07
    Analytical model[13]25.3313.465.245.190.120.29
    Analytical model[15]25.8013.265.025.120.150.31
    Notes: Ex, Ey, Ez—Moduli in X-, Y- and Z-direction, respectively; Gxy, Gyz, Gxz—Shear moduli in X-Y, Y-Z and X-Z plane, respectively; νyx, vzx, νzy—Major Poisson’s ratios in X-Y, X-Z and Y-Z plane, respectively.
    下载: 导出CSV

    表  4  超高分子量聚乙烯纤维(UHMWPE)/环氧树脂复合材料及其树脂基体弹性常数[31]

    Table  4.   Elastic constants of ultra high molecular weight polyethylene fiber (UHMWPE)/epoxy composite and the constituent resin matrix[31]

    MaterialE1/GPaE2=E3/GPaG12=G13/GPaG23/GPav21=v31v23
    PE/epoxy6.40292.53811.149500.910550.23340.39372
    Epoxy resin matrix1.00001.00000.384620.384620.30000.30000
    下载: 导出CSV

    表  5  超高分子量聚乙烯纤维/环氧树脂平纹机织复合材料弹性性能

    Table  5.   Elastic properties of UHMWPE/epoxy plain woven fabric composite

    ResultsEx=Ey/GPaEz/GPaGyz=Gxz/GPaGxy/GPavyxvzx=vzy
    Present model3.2132.0840.8050.8700.1510.332
    Finite element model[27]3.4102.2100.8180.8560.1630.301
    下载: 导出CSV

    表  6  E玻璃纤维/乙烯基酯树脂平纹机织复合材料单胞结构参数

    Table  6.   Structural parameters of the unit cell for E-glass/vinyl ester plain woven fabric composite

    Caseaf=aw/mmhf=hw/mmgf=gw/mmh/mmlx=ly/mmuf=uw/mm
    1#0.6
    0-0.3
    0
    h=ht=hf+hw
    0.60.6
    2#0.6
    0-0.05
    00.100.60.6
    3#0.60.0500.100.6
    0-0.6
    4#0.60.05
    0-0.5
    0.100.60.6
    下载: 导出CSV

    表  7  纤维束中弯曲部分的长度对E玻璃纤维/乙烯基酯树脂平纹机织复合材料弹性性能影响(案例3#)

    Table  7.   Effects of the length of the curved section of the fiber strand on elastic properties of E-glass/vinyl ester plain woven fabric composite for case 3#

    uf=uw/mmEx=Ey/GPaEz/GPaGyz=Gxz/GPaGxy/GPavyxvzx=vzy
    0.134.93318.5317.4517.0740.1220.300
    0.233.23017.3656.9936.7160.1240.304
    0.331.43216.4526.5316.3570.1270.303
    0.429.51615.5526.1095.9970.1300.304
    0.527.53414.6455.7095.6370.1330.306
    0.625.51613.7305.3245.2770.1370.308
    下载: 导出CSV

    表  8  相邻纤维束之间间距对E玻璃纤维/乙烯基酯树脂平纹机织复合材料弹性性能影响(案例4#)

    Table  8.   Effects of the spacing between the adjacent fiber strands on elastic properties of E-glass/vinyl ester plain woven fabric composite for case 4#

    gf=gw/mmEx=Ey/GPaEz/GPaGyz=Gxz/GPaGxy/GPavyxvzx=vzy
    0.125.51613.7305.3245.2770.1370.308
    0.222.44212.2714.7244.7070.1420.312
    0.320.10811.1964.2914.2890.1470.316
    0.418.28310.3703.9643.9710.1520.320
    0.516.821 9.7143.7073.7190.1570.324
    0.615.623 9.1773.5003.5150.1620.328
    下载: 导出CSV
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  • 收稿日期:  2022-01-17
  • 修回日期:  2022-04-12
  • 录用日期:  2022-04-16
  • 网络出版日期:  2022-04-25
  • 刊出日期:  2023-02-15

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