留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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, 2022, 40(0): 1-10
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, 2022, 40(0): 1-10
Pei WAN, Hui XIA, Chen LIU, Jilong JIA, Xue HE, Anxin DING. Prediction of anisotropic coefficient of thermal expansion for laminated composite using multiscale numerical models[J]. Acta Materiae Compositae Sinica.
Citation: Pei WAN, Hui XIA, Chen LIU, Jilong JIA, Xue HE, Anxin DING. Prediction of anisotropic coefficient of thermal expansion for laminated composite using multiscale numerical models[J]. Acta Materiae Compositae Sinica.

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

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

  • 摘要: 依据复合材料内部纤维在基体内的排布规律以及层合板铺层特性,基于多尺度方法,建立单层板和层合板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代表性体积单元(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RVE模型

    Figure  2.  RVE model of lamina

    图  3  层合板RVE模型

    Figure  3.  RVE model of laminated composite

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

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

    图  5  拉伸模量和剪切模量实验测试

    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位移云图

    Figure  7.  Displacement contour of laminate in in-plane direction and through-thickness direction (b) for AS4/8552 composites

    图  8  单向ECR/Derakane 510C复合材料横向(a)和纵向(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 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/GPaG23GPaν12ν23α1/(10−6−1)α2/(10−6−1)
    T300 carbon fiber233.0423.108.968.270.20.4−0.5410.08
    5208 epoxy4.341.590.3743.92
    P75 carbon fiber550.209.516.893.380.20.4−1.356.84
    934 epoxy4.341.590.3743.92
    CE339 epoxy4.341.590.3763.36
    C6000 carbon fiber233.0423.108.968.270.20.4−0.5410.08
    PMR15 polyimide3.451.310.3536.00
    HMS carbon fiber379.216.217.582.210.20.4−0.996.84
    Borosilicate glass62.7426.200.203.24
    Notes: E1 and E2 are the moduli in “1” and “2” direction; G12 and G23 are the shear moduli in “1-2” plane and “2-3” plane direction; ν12 and ν23 are the Poisson’s ratio in “1-2” plane and “2-3” plane direction; α1 and α2 are the 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%)25.23627.540(9%)18.900(25%)24.383(3%)
    P75/934
    (Vf=0.48)
    −1.051−0.967(8%)−0.922(12%)34.52435.460(3%)23.220(33%)34.045(1%)
    P75/930
    (Vf=0.65)
    −1.076−1.159(8%)−1.128(5%)31.71626.640(16%)17.154(46%)25.018(21%)
    P75/CE339
    (Vf=0.54)
    −1.021−0.918(10%)−0.859(16%)47.41244.64(6%)28.080(41%)42.732(10%)
    C6000/Pi
    (Vf=0.63)
    −0.212−0.225(6%)−0.192(9%)22.42825.74(15%)18.000(20%)22.062(2%)
    HMS/Glass
    (Vf=0.47)
    −0.414−0.324(22%)−0.324(22%)3.7805.976(58%)5.427(44%)4.479(18%)
    Notes: Vf is the fiber volume fraction; SH are the predicted values using Eqs.(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/Derakane510C composites

    PropertyECR glass fiberDerakane 510C
    E/GPa803.35
    ν0.20.35
    Notes: E is the modulus and ν is the Poisson’s ratio.
    下载: 导出CSV

    表  4  单向ECR/Derakane510C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
    Experimental31.637.402.69-0.281-
    Errors/%7.51.10.74-0.35-
    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[26]

    Table  5.   Parameters of mechanical properties of unidirectional AS4/8552 composites[26]

    E1
    /GPa
    E2
    /GPa
    G12=G13=G23
    /GPa
    ν12=ν13ν23α1
    /(10−6−1)
    α2
    /(10−6−1)
    1359.54.90.30.450.0032.6
    Notes: G13 is the shear moduli and Poisson’s ratio in “1-3” plane direction, respectively.
    下载: 导出CSV

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

    Table  6.   Comparison of experimental values from literature and numerical results of laminated AS4/8552 composite

    Equivalent CTEsαx
    /(10−6−1)
    αy
    /(10−6−1)
    αz
    /(10−6−1)
    Numerical2.682.6845.16
    Experimental [26]2.72.745.2
    Error/%0.70.70.08
    Notes: αx, αy and αz are the coefficients of thermal expansion in “x”,“y” and “z” direction, respectively.
    下载: 导出CSV

    表  7  ECR/Derakane510C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/Derakane510C 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
  • [1] DING A, WANG J, NI A, LI S. A new analytical solution for cure-induced spring-in of L-shaped composite parts. Composites Science and Technology. 2019;171: 1-12.
    [2] 丁安心, 王继辉, 倪爱清, 孙亮亮, 李书欣. 热固性树脂基复合材料固化变形解析预测研究进展. 复合材料学报. 2018;35(06): 1361-76.

    DING A, WANG J, NI A, SUN L, LI S. A review of analytical prediction of cure-induced distortions in thermoset composites [J]. Fuhe Cailiao Xuebao/Acta Materiae Compositae Sinica, 2018;35(06): 1361-76(in Chinese)
    [3] 李云波, 李宗利, 姚希望, 肖帅鹏, 刘士达, 童涛涛. 含孔洞和裂隙混合缺陷的干燥水泥砂浆导热系数相互作用直推预测模型. 复合材料学报. 2022;39(01): 361-70.

    LI Y, LI Z, YAO X, et al. Interaction direct deduction prediction model of thermal conductivity of dry cement mortar with mixed defects of cavities and cracks [J]. Fuhe Cailiao Xuebao/Acta Materiae Compositae Sinica, 2022;39(01): 361-70. (in Chinese)
    [4] 周龙伟, 赵丽滨. 基于失效机制的单向纤维增强树脂复合材料退化模型 复合材料学报. 2019;36(06): 1389-97.

    ZHOU L, ZHAO L. Failure mechanisms based degradation model of unidirectional fiber reinforced polymer composites [J]. Fuhe Cailiao Xuebao/Acta Materiae Compositae Sinica, 2019;36(06): 1389-97(in Chinese)
    [5] GAO Z, CHEN L. A review of multi-scale numerical modeling of three-dimensional woven fabric. Composite Structures. 2021;263: 113685.
    [6] FU Y, YAO X, GAO X. Micro-mesoscopic prediction of void defect in 3D braided composites. Composites Part A: Applied Science and Manufacturing. 2021;147: 106450.
    [7] SUN C, VAIDYA R. Prediction of composite properties from a representative volume element. Composites Science and Technology[J]. 1996;56(2): 171-179.
    [8] GARNICH MR, KARAMI G. Finite element micromechanics for stiffness and strength of wavy fiber composites. Journal of composite materials[J]. 2004;38(4): 273-292.
    [9] GARNICH MR, KARAMI G. Localized fiber waviness and implications for failure in unidirectional composites. Journal of composite materials[J]. 2005;39(14): 1225-45.
    [10] 张元冲, J. Harding. 平面织物复合材料机械性能的数值细观力学分析. 应用力学学报. 1989(04): 20-7+114.

    ZHANG Y, HARDING J. A numerical micromechanics analysis of the mechanical properties of a plain weave composite. Chinese Journal of Applied Mechanics[J]. 1989(04): 20-7+114(in Chinese)
    [11] 吕毅, 吕国志, 吕胜利. 细观力学方法预测单向复合材料的宏观弹性模量. 西北工业大学学报. 2007;24(6): 787-90.

    LU Y, LU Z, Lu S. Semi-theoretical and engineering prediction of macroscopic elastic moduli of unidirectional composites. Journal of Northwestern Polytechnical University[J]. 2007;24(6): 787-790(in Chinese)
    [12] 左中鹅, 王瑞, 徐磊. 基于有限单元法的平纹织物复合材料强度预测: 1. RVE的有限元模型. 纺织学报. 2009(12): 45-9.

    ZUO Z, WANG R, XU L. Mechanical strength prediction of plain woven fabric composite: 1. finite element model of composite RVE. Journal of Textile Research[J]. 2009(12): 45-9(in Chinese)
    [13] LU J, ZHU P, JI Q, FENG Q, HE J. Identification of the mechanical properties of the carbon fiber and the interphase region based on computational micromechanics and Kriging metamodel. Computational Materials Science[J]. 2014;95: 172-80.
    [14] 马学仕. 基于均匀化理论的周期性复合材料有效性能预测 [D]. 南京: 南京航空航天大学; 2013.

    MA X. Homogenization method to calculation of effective properties for periodic composite materials [D]. Nanjing: Nanjing University of aeronautics and astronautics, 2013(in Chinese)
    [15] GHOSH S, MUKHOPADHYAY SN. A material based finite element analysis of heterogeneous media involving Dirichlet tessellations. Computer Methods in Applied Mechanics and Engineering[J]. 1993;104(2): 211-47.
    [16] TRIAS D, COSTA J, MAYUGO J, HURTADO J. Random models versus periodic models for fibre reinforced composites. Computational Materials Science[J]. 2006;38(2): 316-24.
    [17] LUCIANO R, BARBERO EJ. Formulas for the stiffness of composites with periodic microstructure. International Journal of Solids and Structures[J]. 1994;31(21): 2933-44.
    [18] RAMM E, RANK E, RANNACHER R, SCHWEIZERHOF K, STEIN E, WENDLAND W, et al. Error-controlled adaptive finite elements in solid mechanics: John Wiley & Sons; 2003.
    [19] 赵琳. 基于单胞解析模型与渐进损伤分析的复合材料强度预报 [D]. 哈尔滨: 哈尔滨工业大学; 2012.

    ZHAO L. Strength prediction of composites based on unit cell analytic model and progressive damage analysis[D]. Haerbin: Harbin Institute of Technology, 2012(in Chinese)
    [20] 张超, 许希武, 严雪. 纺织复合材料细观力学分析的一般性周期性边界条件及其有限元实现. 航空学报. 2013;34(7): 1636-45.

    ZHANG C, XU X, YAN X. General periodic boundary conditions and their application to micromechanical finite element analysis of textile composites[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(7): 1636-1645(in Chinese)
    [21] SUN C, LIAO W. Analysis of thick section composite laminates using effective moduli. Journal of Composite Materials[J]. 1990;24(9): 977-93.
    [22] SUN C, LI S. Three-dimensional effective elastic constants for thick laminates. Journal of Composite Materials[J]. 1988;22(7): 629-39.
    [23] BOWLES DE, TOMPKINS SS. Prediction of coefficients of thermal expansion for unidirectional composites. Journal of Composite Materials[J]. 1989;23(4): 370-88.
    [24] SCHAPERY RA. Thermal Expansion Coefficients of Composite Materials Based on Energy Principles[J]. 1968;2(3): 380-404.
    [25] CHAMIS CCJTOTA. Simplified composite micromechanics equations of hygral, thermal, and mechanical properties[J]. 1984;39(3): págs. 999-1004.
    [26] WISNOM MR, POTTER KD, ERSOY N. Shear-lag analysis of the effect of thickness on spring-in of curved composites. Journal of composite materials[J]. 2007;41(11): 1311-24.
  • 加载中
计量
  • 文章访问数:  179
  • HTML全文浏览量:  83
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-02-17
  • 录用日期:  2022-03-17
  • 修回日期:  2022-03-13
  • 网络出版日期:  2022-04-09

目录

    /

    返回文章
    返回