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CFRP薄壁结构多尺度建模及耐撞性分析

朱国华 竺森森 胡珀 王振 赵轩

朱国华, 竺森森, 胡珀, 等. CFRP薄壁结构多尺度建模及耐撞性分析[J]. 复合材料学报, 2023, 40(6): 3626-3639. doi: 10.13801/j.cnki.fhclxb.20220720.002
引用本文: 朱国华, 竺森森, 胡珀, 等. CFRP薄壁结构多尺度建模及耐撞性分析[J]. 复合材料学报, 2023, 40(6): 3626-3639. doi: 10.13801/j.cnki.fhclxb.20220720.002
ZHU Guohua, ZHU Sensen, HU Po, et al. Multi-scale modeling and crashworthiness analysis of CFRP thin-walled structures[J]. Acta Materiae Compositae Sinica, 2023, 40(6): 3626-3639. doi: 10.13801/j.cnki.fhclxb.20220720.002
Citation: ZHU Guohua, ZHU Sensen, HU Po, et al. Multi-scale modeling and crashworthiness analysis of CFRP thin-walled structures[J]. Acta Materiae Compositae Sinica, 2023, 40(6): 3626-3639. doi: 10.13801/j.cnki.fhclxb.20220720.002

CFRP薄壁结构多尺度建模及耐撞性分析

doi: 10.13801/j.cnki.fhclxb.20220720.002
基金项目: 国家重点研发计划(2021 YFB2501705);国家自然科学基金 (51905042);长安大学中央高校基础研究基金 (300102221201)National Key R&D Program of China (2021YFB2501705); National Natural Science Foundation of China (51905042); The Fundamental Research Funds for the Central Universities, CHD (300102221201)
详细信息
    通讯作者:

    朱国华,博士,副教授,硕士生导师,研究方向为汽车轻量化  E-mail: guohuazhu@chd.edu.cn

  • 中图分类号: TB332

Multi-scale modeling and crashworthiness analysis of CFRP thin-walled structures

  • 摘要: 碳纤维增强树脂基复合材料(CFRP)具有较高的比强度、比刚度及显著的轻量化效果,因此CFRP薄壁结构被作为能量吸收装置广泛应用于工程领域。以单向碳纤维复合材料为研究对象,利用扫描电镜获取其微观胞元结构参数及纤维体积分数,构建能够准确反映其微观形态的代表性体积单元(Representative volume element,RVE),通过加载周期性边界条件及单位载荷,获取材料宏观等效弹性参数,并开展实验验证。随后,开发基于微观力学的失效准则及损伤演化方程,并结合材料力学特点,构建CFRP宏观损伤模型,最终形成一套基于微观失效的多尺度损伤模型。在此基础上,对CFRP薄壁圆管在轴向准静态载荷下的压溃性能进行数值仿真,并与实验结果进行对比,验证了多尺度模型的仿真精度。最后,基于验证后的多尺度有限元模型,研究了碳纤维铺层角度及碳纤维体积分数对CFRP薄壁结构耐撞性的影响。结果表明:铺层角度和碳纤维体积分数对CFRP圆管耐撞性能具有较大影响。

     

  • 图  1  碳纤维增强树脂基复合材料(CFRP)薄壁管制造工艺流程图

    Figure  1.  Manufacturing process of carbon fiber reinforced plastics (CFRP) thin-walled tubes

    图  2  试验现场布置图

    Figure  2.  Experimental setup

    图  3  CFRP的截面SEM图像

    Figure  3.  SEM images of cross section for CFRP

    图  4  (a) 单向碳纤维复合材料六面体代表性体积单元(RVE)模型;(b) RVE参考点

    Figure  4.  (a) Hexagonal representative volume element (RVE) model of UD-CFRP; (b) Reference points at RVE

    F, M—Fiber and matrix, respectively; Number—Selection order of reference points; a=c=1; b= $\sqrt 3 $

    图  5  多尺度分析框架

    Figure  5.  Multiscale analysis framework

    图  6  多尺度模型的数值算法流程

    Figure  6.  Numerical calculation procedure for the multi-scale model

    SAFs—Stress amplification factors; RVEs—Representative volume elements

    图  7  CFRP薄壁结构单位应力施加

    Figure  7.  Application of unit macro stress for CFRP thin-walled structure

    图  8  CFRP薄壁结构RVE模型在宏观六工况下的微观应力分布

    Figure  8.  Microscopic stress distribution for RVEs of CFRP thin-walled structure under six loading cases

    图  9  CFRP薄壁结构0°拉伸试件试验结果

    Figure  9.  Experimental results of 0° samples of CFRP thin-walled structure

    图  10  CFRP薄壁结构90°拉伸试件试验结果

    Figure  10.  Experimental results of 90 ° samples of CFRP thin-walled structure

    图  11  CFRP薄壁结构有限元模型

    Figure  11.  Finite element model of CFRP thin-walled structure

    图  12  网格大小敏感性分析

    Figure  12.  Mesh size sensitivity analysis

    图  13  CFRP薄壁结构实验与仿真载荷-位移对比曲线

    Figure  13.  Comparison of load-displacement curves between experiment and simulation for CFRP thin-walled structure

    图  14  CFRP薄壁结构变形结果对比

    Figure  14.  Comparison of deformation modes for CFRP thin-walled structure

    图  15  不同铺层角度的CFRP圆管载荷-位移曲线

    Figure  15.  Comparison of load-displacement curves for CFRP tubes with different fiber orientations

    图  16  不同铺层角度CFRP薄壁圆管轴向压溃后的变形结果

    Figure  16.  Crushing process of CFRP tubes with different fiber orientations

    图  17  不同体积分数的CFRP薄壁圆管载荷-位移曲线

    Figure  17.  Comparison of load-displacement curves for CFRP tubes with different fiber volume fractions

    图  18  不同纤维体积分数CFRP薄壁圆管的变形过程

    Figure  18.  Deformation process of CFRP thin-walled circular tubes with different fiber volume fractions

    表  1  T300碳纤维力学性能

    Table  1.   Mechanical properties of T300 carbon fiber

    Mechanical propertyValue
    $ E_{\text{f}\text{1}} $/GPa185
    $ E_{\text{f}\text{2}}\text{=}E_{\text{f}\text{3}} $/GPa13
    $ {G}_{\text{f}\text{12}}\text{=}{G}_{\text{f}\text{13}} $/GPa15
    $ {G}_{\text{f}\text{23}} $/GPa9
    $ {\nu}_{\text{f}\text{12}}\text{=}{\nu}_{\text{f}\text{13}} $0.28
    $ {\nu}_{\text{f}\text{23}} $0.35
    Notes: Ef1, Ef2, Ef3, Gf12, Gf13, and G—Elastic moduli of T300 carbon fiber fibers in the 1, 2, 3, 12, 13, and 23 directions, respectively; vf12, vf13, and vf23—Poisson's ratios in the 12, 13, and 23 directions, respectively.
    下载: 导出CSV

    表  2  基体力学性能

    Table  2.   Mechanical properties of matrix

    Mechanical propertyValue
    $ {E}_{\mathrm{m}} $/GPa2.6
    $ \nu $0.33
    Note: Em and v—Micro elastic modulus and Poisson's ratio of the matrix, respectively.
    下载: 导出CSV

    表  3  CFRP薄壁结构宏观单位应力加载

    Table  3.   Appling macro unit stress of CFRP thin-walled structure

    n$ {\overline{\sigma} }_{\text{1}} $$ {\overline{\sigma} }_{\text{2}} $$ {\overline{\sigma} }_{\text{3}} $$ {\overline{\tau} }_{\text{12}} $$ {\overline{\tau} }_{\text{23}} $$ {\overline{\tau} }_{\text{13}} $
    1100000
    2010000
    3001000
    4000100
    5000010
    6000001
    Notes: $ {\overline{\sigma} }_{\text{1}} $, $ {\overline{\sigma} }_{\text{2}} $ and $ {\overline{\sigma} }_{\text{3}} $—Macro-stress in the 1, 2 and 3 direction of CFRP, respectively; $ {\overline{\tau} }_{\text{12}} $ , $ {\overline{\tau} }_{\text{23}} $, $ {\overline{\tau} }_{\text{13}} $—Macro shear stress in the 12, 23 and 13 direction of CFRP, respectively.
    下载: 导出CSV

    表  4  CFRP薄壁结构宏观弹性参数计算方法

    Table  4.   Calculation method of macro elastic parameters for CFRP thin-walled structure

    Loading caseLoading conditionCalculation formula
    1$ {\overline{\sigma }}_{{1}} $=1$ {{E}}_{{1}}=\dfrac{{\overline{\sigma }}_{{1}}}{{}{\bar{{ \varepsilon }}}_{{1}}} , {\upsilon }_{{12}} =−\dfrac{{\bar{{ \varepsilon }}}_{{2}}}{{}{\bar{{ \varepsilon }}}_{{1}}} , {\upsilon }_{{13}} =−\dfrac{{\bar{{ \varepsilon }}}_{{3}}}{{}{\bar{{ \varepsilon }}}_{{1}}} $
    2$ {\overline{\sigma }}_{{2}} $=1$ {{E}}_{{2}}=\dfrac{{\overline{\sigma }}_{{2}}}{{\bar{{ \varepsilon }}}_{{2}}} , {\upsilon }_{{21}} =−\dfrac{{\bar{{ \varepsilon }}}_{{1}}}{{}{\bar{{ \varepsilon }}}_{{2}}} , {\upsilon }_{{23}} =− \dfrac{{\bar{{ \varepsilon }}}_{{3}}}{{}{\bar{{ \varepsilon }}}_{{2}}} $
    3$ {\overline{\sigma }}_{{3}} $=1$ {{E}}_{{3}} =\dfrac{{\overline{\sigma }}_{{3}}}{{}{\bar{{ \varepsilon }}}_{{3}}},{\upsilon }_{{31}} =− \dfrac{{}{\bar{{ \varepsilon }}}_{{1}}}{{}{\bar{{ \varepsilon }}}_{{3}}} ,{\upsilon }_{{32}}=− \dfrac{{\bar{{ \varepsilon }}}_{{2}}}{{}{\bar{{ \varepsilon }}}_{{3}}} $
    4$ {\overline{\tau }}_{{12}} $=1$ {{G}}_{{12}}=\dfrac{{\overline{\tau }}_{{12}}}{{\bar{\gamma }}_{{12}}} $
    5$ {\overline{\tau }}_{{23}} $=1$ {{G}}_{{23}}=\dfrac{{\overline{\tau }}_{{23}}}{{\bar{\gamma }}_{{23}}} $
    6$ {\overline{\tau }}_{{13}}=1 $$ {{G}}_{{13}} = \dfrac{{\overline{\tau }}_{{13}}}{{\bar{\gamma }}_{{13}}} $
    Notes: E1, E2 and E3—Macroscopic elastic modulus in the 1, 2 and 3 direction of CFRP, respectively; G12, G23 and G13—Macroscopic shear modulus in the 12, 23 and 13 direction of CFRP, respectively; ${\bar \upsilon} _{ij} $ (i, j=1, 2, 3)—Poisson's ratio of CFRP in the ij direction; $ {\bar\varepsilon} _i $(i=1, 2, 3)—Strain of CFRP in the i direction; $ {\bar \gamma} _{ij} $ (i, j=1, 2, 3)—Strain of CFRP in the ij direction.
    下载: 导出CSV

    表  5  CFRP弹性参数预测结果与试验结果对比

    Table  5.   Comparison of CFRP elastic parameters between numerical and experimental results

    Property$ { {E} }_{ {1} } $
    /GPa
    $ { {E} }_{ {2} } $=$ { {E} }_{ {3} } $/GPa$ {{G}}_{{12}}={{G}}_{{13}} $/GPa$ {{G}}_{{23}} $
    /GPa
    $ {\upsilon }_{{12}}{=}{\upsilon }_{{13}} $$ {\upsilon }_{{23}} $
    Test131.57.60.29
    RVE132.67.54.33.50.290.39
    Error/%2.139.210
    下载: 导出CSV

    表  6  CFRP多尺度损伤模型输入参数

    Table  6.   Input parameters of CFRP multi-scale damage model

    ParameterValueParameterValue
    $ {E}_{\text{1} } $/MPa 132600 $ {E}_{\text{f}\text{1}} $/MPa 185000
    $ {E}_{\text{2} } $/MPa 7500 $ {E}_{\text{f}\text{2}} $/MPa 13000
    $ {E}_{\text{3} } $/MPa 7500 $ {\text{X}}_{\text{f}}^{\text{0,}\text{T}} $/MPa 3470
    $ {\nu}_{\text{12}} $ 0.29 $ {\text{X}}_{\text{f}}^{\text{0,}\text{C}} $/MPa 2100
    $ {\nu}_{\text{13}} $ 0.29 $ {E}_{\text{m}} $/MPa 2600
    $ {\nu}_{\text{23}} $ 0.39 $ {\text{Y}}_{\text{m}}^{\text{0,}\text{T}} $/MPa 77
    $ {G}_{\text{12}} $/MPa 4300 $ {\text{Y}}_{\text{m}}^{\text{0,}\text{C}} $/MPa 121
    $ {G}_{\text{13}} $/MPa 4300 $ \text{γ} $ 1.5
    $ {G}_{\text{23}} $/MPa 3500 $ \rho $/(t·mm−3) 1.4×10−9
    Notes: $\rm X_f^{0,T} $ and $\rm X_f^{0,C}$ —Longitudinal tensile strength and compressive strength of T300 fiber, respectively; $\rm Y_m^{0,T} $ and $\rm Y_m^{0,C} $—Final tensile strength and compressive strength of matrix, respectively; $\gamma $—Damage shape parameter of matrix; p—Beta damping parameter of CFRP.
    下载: 导出CSV

    表  7  CFRP层间失效模型输入参数

    Table  7.   Input parameters of CFRP inter-laminar failure model

    DescriptionVariableValue
    Damage initiation/MPa$ {{t}}_{\text{n}}^{\text{0}} $49.2
    $ {{t}}_{\text{s}}^{\text{0}} $59.5
    $ {{t}}_{\text{t}}^{\text{0}} $59.5
    Fracture energies/(J·m−2)$ {{G}}_{\text{n}}^{\text{C}} $490
    $ {{G}}_{\text{s}}^{\text{C}} $1060
    $ {{G}}_{\text{t}}^{\text{C}} $1060
    BK$ {\eta} $2.284
    Notes: $ {{t}}_{\text{n}}^{\text{0}} $—Maximum nominal stress in the normal-only mode; $ {{t}}_{\text{s}}^{\text{0}} $—Maximum nominal stress in the first shear direction (for a mode that involves separation only in this direction); $ {{t}}_{\text{t}}^{\text{0}} $—Maximum nominal stress in the second shear direction (for a mode that involves separation only in this direction); $ {{G}}_{\text{n}}^{\text{C}} $—Ttype I critical fracture energies in n direction; $ {{G}}_{\text{s}}^{\text{C}} $— Type II critical fracture energies in n direction; $ {{G}}_{\text{t}}^{\text{C}} $—Critical fracture energies in t direction; $\eta $—A bonding attribute parameter.
    下载: 导出CSV

    表  8  CFRP薄壁结构耐撞性能指标结果对比

    Table  8.   Comparison of crashworthiness index results for CFRP thin-walled structure

    PropertyFp/kNWe/kJWs/(J·g−1)Fm/kNEc
    Experimental 35.0 2.230 48.02 27.88 0.80
    Simulation 37.8 2.218 47.76 27.73 0.73
    Error/% 8 0.54 0.54 0.5 7.9
    Notes: Fp—Maximum peak force that occurs during the entire crushing process; We—Total energy absorbed by the structural component during the impact process; Ws—Amount of energy absorbed by energy absorbing structure per unit mass; Fm—Average force is the energy absorbed during the impact process per unit distance; Ec—Ratio of the average force to the maximum peak force.
    下载: 导出CSV

    表  9  不同铺层角度的CFRP薄壁圆管耐撞性能指标结果

    Table  9.   Crashworthiness index results of CFRP tubes with different fiber orientations

    Ply angleFp/kNWe/JWs/(J·g−1)Fm/kNEc
    [0°]831.6170336.721.30.674
    [±15°]432.9165335.620.70.629
    [±30°]433.4175437.821.90.656
    [±45°]434.7189940.923.70.683
    [±60°]438.3231649.929.00.757
    [±75°]442.9249653.731.20.727
    [90°]842.4223648.128.00.660
    下载: 导出CSV

    表  10  不同体积分数的CFRP薄壁圆管耐撞性能指标结果

    Table  10.   Crashworthiness indicators of CFRP tubes with different volume fractions

    Volume fraction/vol%m/gFp/kNWe/JWs/(J·g−1)Fm$ / $kNEc
    3038.9529.8164942.320.60.692
    5042.5234.8193345.524.20.694
    7246.4437.8221847.827.70.733
    8849.5639.9249450.331.20.781
    Note: m—Mass of carbon fiber.
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-06-07
  • 修回日期:  2022-06-23
  • 录用日期:  2022-07-07
  • 网络出版日期:  2022-07-22
  • 刊出日期:  2023-06-15

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