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基于多尺度数值模型的复合材料各向异性热膨胀系数预测

万佩 夏辉 刘晨 贾吉龙 何学 丁安心

万佩, 夏辉, 刘晨, 等. 基于多尺度数值模型的复合材料各向异性热膨胀系数预测[J]. 复合材料学报, 2023, 40(2): 1208-1217. doi: 10.13801/j.cnki.fhclxb.20220331.001
引用本文: 万佩, 夏辉, 刘晨, 等. 基于多尺度数值模型的复合材料各向异性热膨胀系数预测[J]. 复合材料学报, 2023, 40(2): 1208-1217. doi: 10.13801/j.cnki.fhclxb.20220331.001
WAN Pei, XIA Hui, LIU Chen, et al. Prediction of anisotropic coefficient of thermal expansion for laminated composite using multiscale numerical models[J]. Acta Materiae Compositae Sinica, 2023, 40(2): 1208-1217. doi: 10.13801/j.cnki.fhclxb.20220331.001
Citation: WAN Pei, XIA Hui, LIU Chen, et al. Prediction of anisotropic coefficient of thermal expansion for laminated composite using multiscale numerical models[J]. Acta Materiae Compositae Sinica, 2023, 40(2): 1208-1217. doi: 10.13801/j.cnki.fhclxb.20220331.001

基于多尺度数值模型的复合材料各向异性热膨胀系数预测

doi: 10.13801/j.cnki.fhclxb.20220331.001
基金项目: 国家自然科学基金(11902231)
详细信息
    通讯作者:

    丁安心,博士,教授,研究方向为高分子和复合材料结构固化成型仿真与监测、结构设计和老化性能评价  E-mail: axding@whut.edu.cn

  • 中图分类号: TB334

Prediction of anisotropic coefficient of thermal expansion for laminated composite using multiscale numerical models

Funds: National Natural Science Foundation of China (11902231)
  • 摘要: 依据复合材料内部纤维在基体内的排布规律及层合板铺层特性,基于多尺度方法,建立单层板和层合板代表性体积单元(RVE)模型,施加相应的边界条件,预测单层板的热膨胀系数和工程常数,进而预测复合材料层合板各向异性的等效热膨胀系数。通过与实验数据对比发现,基于正六边形单层板RVE模型预测的热膨胀系数,相比理论预测值,整体更接近实验值,其中预测的单向T300/5208碳纤维增强环氧树脂基复合材料、P75/934碳纤维增强环氧树脂基复合材料和C6000/Pi碳纤维增强环氧树脂基复合材料的横向热膨胀系数与实验结果的误差分别只有3%、1%和2%;采用单层板RVE预测的单向ECR/Derakane 510C玻璃纤维增强乙烯基酯树脂基复合材料的工程常数与实验值最大相差7.5%;层合板RVE模型预测的正交AS4/8552碳纤维增强环氧树脂基复合材料厚度方向的热膨胀系数与实验结果误差可以忽略,只有0.08%。最后以大型复合结构常用的正交铺层结构为研究对象,基于给出的单层板和层合板RVE模型预测了不同铺层复合材料烟道层合板的等效热膨胀系数,环向铺层比例对厚度方向的热膨胀系数影响较小。

     

  • 图  1  预测层合板各向异性热膨胀系数总体框架

    Figure  1.  Framework for predicting anisotropic coefficient of thermal expansions of laminated composites

    图  2  单层板代表性体积单元(RVE)模型

    Figure  2.  Representative volume element (RVE) model of lamina

    a1, a2 and a3—Dimension in three direction; x1, x2 and x3—Coordinate axes

    图  3  层合板RVE模型

    Figure  3.  RVE model of laminated composite

    x, y, and z—Coordinate axes

    图  4  HMS/Glass复合材料RVE模型的位移云图:(a)纵向方向; (b)横向方向

    MX—Max; MN—Min

    Figure  4.  Contour of displacement for RVE model of HMS/Glass composites: (a) In longitudinal direction; (b) In transverse direction

    图  5  拉伸模量(a)和剪切模量(b)实验测试

    Figure  5.  Experimental testing for tensile (a) and shear (b) moduli

    图  6  ECR/Derakane 510C复合材料单层板RVE模型在横向(a)和纵向(b)方向应力云图

    Figure  6.  Contour of stress in RVE model of unidirectional lamina for ECR/Derakane 510C composites in longitudinal (a) and transverse (b) direction

    图  7  AS4/8552 复合材料层合板RVE在x方向(a)和z方向(b)位移云图

    Figure  7.  Displacement contour of laminate in x direction (a) and z direction (b) for AS4/8552 composites

    图  8  单向ECR/Derakane 510C复合材料纵向(a)和横向(b)热膨胀系数随纤维体积含量Vf的变化

    Figure  8.  Change of coefficient of thermal expansion (CTE) with fiber volume fraction Vf for unidirectional ECR/Derakane 510C composites in longitudinal (a) and transverse (b) direction

    表  1  纤维和树脂的力学性能参数[23]

    Table  1.   Parameters for mechanical properties of fiber and resin[23]

    Constituent materialE1/GPaE2/GPaG12/GPaG23/GPaν12ν23α1/(10−6−1)α2/(10−6−1)
    T300 carbon fiber 233.04 23.10 8.96 8.27 0.20 0.4 −0.54 10.08
    5208 epoxy 4.34 1.59 0.37 43.92
    P75 carbon fiber 550.20 9.51 6.89 3.38 0.20 0.4 −1.35 6.84
    934 epoxy 4.34 1.59 0.37 43.92
    CE339 epoxy 4.34 1.59 0.37 63.36
    C6000 carbon fiber 233.04 23.10 8.96 8.27 0.20 0.4 −0.54 10.08
    PMR15 polyimide 3.45 1.31 0.35 36.00
    HMS carbon fiber 379.21 6.21 7.58 2.21 0.20 0.4 −0.99 6.84
    Borosilicate glass 62.74 26.20 0.20 3.24
    Notes: E1 and E2—Moduli in “1” and “2” direction; G12 and G23—Shear moduli in “1-2” plane and “2-3” plane direction; ν12 and ν23—Poisson’s ratio in “1-2” plane and “2-3” plane direction; α1 and α2—Coefficients of thermal expansion in “1” and “2” direction.
    下载: 导出CSV

    表  2  各复合材料预测与实验测试值的比较

    Table  2.   Comparison of experimental data with predicted values of composites

    Compositeα1/(10−6−1)α2/(10−6−1)
    Experimental[23]SH/CH(Error)Predicted(Error)Experimental[23]SH(Error)CH(Error)Predicted(Error)
    T300/5208
    (Vf=0.68)
    −0.113 −0.153(35%) −0.091(19%) 25.236 27.540(9%) 18.900(25%) 24.383(3%)
    P75/934
    (Vf=0.48)
    −1.051 −0.967(8%) −0.922(12%) 34.524 35.460(3%) 23.220(33%) 34.045(1%)
    P75/930
    (Vf=0.65)
    −1.076 −1.159(8%) −1.128(5%) 31.716 26.640(16%) 17.154(46%) 25.018(21%)
    P75/CE339
    (Vf=0.54)
    −1.021 −0.918(10%) −0.859(16%) 47.412 44.640(6%) 28.080(41%) 42.732(10%)
    C6000/Pi
    (Vf=0.63)
    −0.212 −0.225(6%) −0.192(9%) 22.428 25.740(15%) 18.000(20%) 22.062(2%)
    HMS/Glass
    (Vf=0.47)
    −0.414 −0.324(22%) −0.324(22%) 3.780 5.976(58%) 5.427(44%) 4.479(18%)
    Notes: Vf —Fiber volume fraction; SH are the predicted values using Eq.(11)-(12); CH are the predicted values using Eq.(11) and Eq.(13).
    下载: 导出CSV

    表  3  ECR/Derakane 510C 复合材料组分材料的性能参数

    Table  3.   Properties of constituent materials for ECR/Derakane 510C composites

    Property E/GPa ν
    ECR glass fiber 80.00 0.20
    Derakane 510C 3.35 0.35
    Notes: E—Modulus; ν—Poisson’s ratio.
    下载: 导出CSV

    表  4  单向ECR/Derakane 510C复合材料工程常数预测值与试验结果对比

    Table  4.   Comparison of numerical results with experimental values for engineering constants of unidirectional ECR/Derakane 510C composites

    ItermE1/GPa
    E2/GPa
    G12/GPa
    G23/GPa
    ν12ν23
    Numerical34.037.322.712.510.2820.333
    Experimental31.637.402.690.281
    Error/%7.501.100.740.350
    下载: 导出CSV

    表  5  单层AS4/8552碳纤维增强树脂基复合材料力学性能参数[27]

    Table  5.   Parameters of mechanical properties of unidirectional AS4/8552 composites[27]

    E1
    /GPa
    E2
    /GPa
    G12=G13=G23
    /GPa
    ν12=ν13ν23α1
    /(10−6−1)
    α2
    /(10−6−1)
    1359.54.90.30.450.0032.6
    Note: G13—Shear moduli in “1-3” plane direction, respectively; 1—Longitudinal direction; 2—Transverse direction; 3—Thickness direction.
    下载: 导出CSV

    表  6  AS4/8552复合材料层合板仿真数据与文献[27]实验结果对比

    Table  6.   Comparisons of numerical results and experimental values from literature [27] of laminated AS4/8552 composite

    Equivalent CTEsαx
    /(10−6−1)
    αy
    /(10−6−1)
    αz
    /(10−6−1)
    Numerical2.682.6845.16
    Experimental[27]2.702.7045.20
    Error/%0.700.700.08
    Notes: αx, αy and αzCoefficients of thermal expansion in x, y and z direction, respectively; CTEs—Coefficient of thermal expansions.
    下载: 导出CSV

    表  7  ECR/Derakane 510C复合材料单向布和纤维缠绕层单层板力学性能

    Table  7.   Mechanical properties of lamina composed of unidirectional fabrics and filament wound roving for ECR/Derakane 510C composites

    Engineering constantUnidirectional fabric layerFilament wound layer
    E1/MPa3869031630
    E2=E3/MPa91007400
    G12=G13/MPa33702690
    G23/MPa35942888
    ν12=ν130.2660.281
    ν230.2660.281
    下载: 导出CSV

    表  8  ECR/Derakane 510C复合材料烟道层合板等效热膨胀系数

    Table  8.   Equivalent CTEs of laminate in ECR/Derakane 510C composite duck

    Stacking sequenceαx
    /10−6−1
    αy
    /10−6−1
    αz
    /10−6−1
    RVECLTRVECLTRVE
    [0/90/90]s18.0218.4011.8013.3842.93
    [0/90]s14.6014.1914.8816.1444.64
    [0/0/90]s12.2311.3919.4219.8945.55
    [0/0/0/90]s11.2510.2922.6722.4145.63
    Note: CLT—Classic laminate theory.
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-02-17
  • 修回日期:  2022-03-13
  • 录用日期:  2022-03-17
  • 网络出版日期:  2022-04-01
  • 刊出日期:  2023-02-15

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