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基于复合材料I型分层损伤机制的解耦内聚力方法

张旭东 段青枫 曹东风 陈翀一 胡海晓 王继军 李书欣

张旭东, 段青枫, 曹东风, 等. 基于复合材料I型分层损伤机制的解耦内聚力方法[J]. 复合材料学报, 2024, 42(0): 1-14.
引用本文: 张旭东, 段青枫, 曹东风, 等. 基于复合材料I型分层损伤机制的解耦内聚力方法[J]. 复合材料学报, 2024, 42(0): 1-14.
ZHANG Xudong, DUAN Qingfeng, CAO Dongfeng, et al. Decoupling cohesion method based on mode I delamination damage mechanism of composite materials[J]. Acta Materiae Compositae Sinica.
Citation: ZHANG Xudong, DUAN Qingfeng, CAO Dongfeng, et al. Decoupling cohesion method based on mode I delamination damage mechanism of composite materials[J]. Acta Materiae Compositae Sinica.

基于复合材料I型分层损伤机制的解耦内聚力方法

基金项目: 国家自然科学基金 (52273080; 12302481; 12172265);2023年湖北省重大攻关项目(JD2023BAA028)
详细信息
    通讯作者:

    段青枫,博士生,研究方向为复合材料结构强度与疲劳断裂 E-mail: absinthe1223@whut.edu.cn

    曹东风,博士,副研究员,博士生导师,研究方向为先进复合材料计算力学 E-mail: cao_dongf@whut.edu.cn

  • 中图分类号: TB332

Decoupling cohesion method based on mode I delamination damage mechanism of composite materials

Funds: National Natural Science Foundation of China (52273080; 12302481; 12172265); Major research and development projects in Hubei Province in 2023 (JD2023BAA028)
  • 摘要: 分层损伤是航空航天复合材料结构分层的主要损伤模式之一。I型分层具有起始断裂韧性值低,损伤模式复杂的特征,深入分析裂纹尖端损伤区多种损伤机制之间的相互关系,及纤维桥接损伤演化过程,对研究I型分层损伤起关键作用。本文针对性采用三种不同层间铺层(0//0,0//45,0//90)设计T700级碳纤维/环氧复合材料层合板并开展I型分层测试。通过观测分层起始以及损伤演化过程,总结DCB试验结果载荷位移曲线及R曲线规律,并根据试样断口形貌、SEM等多种表征方法分析,揭示了裂纹尖端的损伤机制。在此基础上提出了一种分层损伤机制解耦的新方法。该方法基于三个双线性内聚力本构叠加,通过建立内聚力单元模型来解耦不同损伤尺度的分层损伤机制,独立表征了不同损伤机制在分层扩展过程中所作的贡献。仿真模拟所需参数均可从试验获得,计算得到的仿真结果与试验结果具有良好的一致性。

     

  • 图  1  DCB试样件几何特征

    Figure  1.  Geometric characteristics of DCB specimens

    图  2  (a) DCB试验测试装置;(b) DCB试样

    Figure  2.  (a) DCB test equipment; (b) DCB sample

    图  3  DCB试验纤维桥接损伤区和裂纹尖端损伤区示意图

    Figure  3.  Sketch of the double cantilever beam (DCB) test fiber bridging damage zone and crack front damage zone

    图  4  裂纹尖端损伤区损伤机制示意图:(a) 0//0铺层角度基体开裂和基体/纤维分离;(b) 0//0铺层角度基体/纤维分离导致的纤维桥接和错位裂纹;(c) 0//90铺层角度基体剪切开裂和纤维桥接

    Figure  4.  Schematic diagram of damage mechanism in crack tip damage zone: (a) 0//0 ply angle matrix cracking and matrix/fiber separation; (b) fiber bridging and dislocation cracks caused by 0//0 ply angle matrix/fiber separation; (c) 0//90 ply angle matrix shear cracking and fiber bridging

    图  5  解耦内聚力模型示意图

    Figure  5.  Schematic diagram of decoupling cohesive model

    图  6  解耦内聚力本构示意图

    Figure  6.  Decoupling cohesive force constitutive diagram

    ${G_{{\text{prop}}}}$−Steady-state strain energy release rate; ${G_{{\text{ini}}}}$−Initial strain energy release rate; ${G_{{\text{br}}}}$−Strain energy release rate of fiber bridging; $ {\sigma _{{\text{br}}}} $−Maximum bridge stress; $ {\delta _{{\text{br}}}} $−Maximum bridge displacement; $ {\sigma _{\text{m}}} $−Matrix damage strength; $ \sigma _{\text{m}}^{\text{c}} $−Maximum stress after coupling; ${\delta _1}$−Critical displacement at which the matrix damage strength is reached; ${\delta _2}$−Opening displacement of cohesive elements in the matrix when they completely fail; ${\delta _3}$−Maximum displacement in the short fiber bridging area; ${G_{{\text{I-MD}}}}$−Overall strain energy release rate of Element 1; ${G_{{\text{I-M}}}}$−Strain energy release rate of matrix fracture; ${G_{{\text{I-D}}}}$−Strain energy release rate of matrix fiber separation at the same interface without dislocation; ${G_{{\text{I-BR}}}}$−Strain energy release rate of fiber bridging formed by dislocation separation of matrix and fibers; ${G_{{\text{br-L}}}}$−Strain energy release rate in the long fiber bridging area; ${G_{{\text{br-S}}}}$−Strain energy release rate in the short fiber bridging area;$ {\sigma _{{\text{br-L}}}} $−Maximum bridging stress in the long fiber bridging area; $ {\sigma _{\text{br-S}}} $-Maximum bridging stress in the short fiber bridging area; $ {\delta _{\text{f}}} $-Maximum opening displacement of the overall bridging fiber zone at the crack tip; ${G_{{\text{I-L}}}}$-Release rate of strain energy for the separation of basic fibers in the long fiber bridging area; ${G_{{\text{I-S}}}}$-Release rate of strain energy for the separation of basic fibers in the short fiber bridging area; ${K_1}$-Initial interface stiffness of cohesive element for matrix cracking; ${K_2}$-Stiffness of cohesive elements in the short fiber bridging area; ${K_3}$-Stiffness of cohesive elements in the long fiber bridging area

    图  7  DCB试样纤维桥接区域图:(a)长纤维区;(b)短纤维区

    Figure  7.  DCB sample fiber bridging area diagram: (a) Long fiber bridging area; (b) Short fiber bridging area

    图  8  DCB试样纤维桥接区域示意图

    Figure  8.  Schematic diagram of fiber bridging area of DCB sample

    图  9  计算解耦内聚力方法参数流程图

    Figure  9.  Parameter flowchart for calculating decoupling cohesive method

    ${G_{{\text{prop}}}}$−Steady-state strain energy release rate;${G_{{\text{ini}}}}$−Initial strain energy release rate; ${G_{{\text{br}}}}$−Strain energy release rate of fiber bridging; $ {\sigma _{{\text{br}}}} $−Maximum bridge stress; $ {\delta _{{\text{br}}}} $−Maximum bridge displacement; $ {\sigma _{\text{m}}} $−Matrix damage strength; ${\delta _2}$−Opening displacement of cohesive elements in the matrix when they completely fail; ${G_{{\text{I - MD}}}}$−Overall strain energy release rate of Element 1; ${G_{{\text{br - L}}}}$−Strain energy release rate in the long fiber bridging area; ${G_{{\text{br - S}}}}$−Strain energy release rate in the short fiber bridging area; $ {\sigma _{{\text{br - L}}}} $−Maximum bridging stress in the long fiber bridging area; $ {\sigma _{br - S}} $-Maximum bridging stress in the short fiber bridging area; $ {\delta _{\text{f}}} $-Maximum opening displacement of the overall bridging fiber zone at the crack tip; ${G_{{\text{I - L}}}}$-Release rate of strain energy for the separation of basic fibers in the long fiber bridging area; ${G_{{\text{I - S}}}}$-Release rate of strain energy for the separation of basic fibers in the short fiber bridging area; ${K_1}$-Initial interface stiffness of cohesive element for matrix cracking; ${K_2}$-Stiffness of cohesive elements in the short fiber bridging area; ${K_3}$-Stiffness of cohesive elements in the long fiber bridging area

    图  10  不同层间铺层角度下DCB试样的应变能释放率与ICTOD的关系

    Figure  10.  Relationship between strain energy release rate and ICTOD of DCB specimens with different interlayer angles

    图  11  不同层间铺层角度下DCB试样的桥接分布规律

    Figure  11.  Distribution patterns of bridging of DCB specimens at different interlaminar ply angles

    图  12  不同层间铺层角度下DCB试样的载荷-位移曲线:(a)0//0;(b)0//45;(c)0//90

    Figure  12.  Load displacement curves of DCB specimens with different interlayer angles: (a) 0//0; (b) 0//45; (c) 0//90

    图  13  不同层间铺层角度下DCB试样的R曲线

    Figure  13.  R-curve of DCB samples with different interlayer angles

    图  14  不同铺层角度下DCB试样分层断面形貌图:(a) 0//0;(b) 0//90

    Figure  14.  Layered cross-sectional morphology of DCB samples at different layering angles: (a) 0//0; (b) 0//90

    图  15  各铺层角度下DCB试样分层扩展路径及纤维桥接现象侧视图

    Figure  15.  Side view of the delamination propagation path and fiber bridging phenomenon of DCB samples at different ply angles

    图  16  不同铺层角度下DCB试样的仿真结果

    Figure  16.  Simulation results of DCB samples with different layering angles

    图  17  同一时刻下不同内聚力单元应力分布图

    Figure  17.  Stress distribution diagram of different cohesive element at the same time

    表  1  T700级碳纤维/环氧树脂复合材料层合板基础力学性能

    Table  1.   Mechanical properties of T700 level carbon fiber/epoxy resin composite laminate foundation

    Parameter Value
    E11/GPa 117
    E22/GPa 7.47
    E33/GPa 7.47
    ν12 0.33
    ν13 0.33
    ν23 0.3
    G12/GPa 4.07
    G13/GPa 4.07
    G23/GPa 2.31
    Notes: E−Elastic modulus; ν−Poisson’s ratio; G−Shear modulus; 1−Direction of fiber; 2−Direction of matrix; 3−Thickness direction of layer.
    下载: 导出CSV

    表  2  不同层间铺层角度下DCB试样的拟合参数

    Table  2.   Fitting parameters of DCB specimens at different interlaminar ply angles

    Interface ${G_{\text{a}}}$/(J·m−2) ${G_{\text{b}}}$/(J·m−2) ${\delta _{\text{a}}}$/mm $ {\delta _{\text{b}}} $/mm $ {\sigma _{{\text{br}}}} $/MPa $ {\delta _{{\text{br}}}} $/mm
    0//0 20.9 20.5 0.96 0.122 0.18 1.1
    0//45 189.7 185 2.05 0.12 1.63 2
    0//90 192.7 189.5 0.76 0.102 2.11 0.8
    Notes: ${G_{\text{a}}}$; ${G_{\text{b}}}$; ${\delta _{\text{a}}}$; $ {\delta _{\text{b}}} $−Fitting parameters; $ {\sigma _{{\text{br}}}} $−Maximum bridge stress; $ {\delta _{{\text{br}}}} $−Maximum bridge displacement.
    下载: 导出CSV

    表  3  不同层间铺层角度下DCB试样层间断裂韧性

    Table  3.   Interlaminar Fracture toughness of DCB specimens at different interlaminar ply angles

    Delamination interface No. Delamination Toughness/(J·m−2) Average value/(J·m−2)
    $G_{\text{I}}^{{\text{ini}}}$ $ G_{\text{I}}^{{\text{prop}}} $
    0//0 DCB-0-1
    DCB-0-2
    DCB-0-3
    223.50
    238.75
    233.77
    279.22
    261.44
    273.19
    232.01 271.28
    0//45 DCB-45-1
    DCB-45-2
    DCB-45-3
    245.91
    241.17
    251.79
    605.72
    536.17
    604.24
    246.29 582.04
    0//90 DCB-90-1
    DCB-90-2
    DCB-90-3
    237.61
    246.08
    283.79
    588.72
    562.36
    651.04
    255.83 600.71
    Notes: $G_{\text{I}}^{{\text{ini}}}$−Initial interlayer fracture toughness value; $ G_{\text{I}}^{{\text{prop}}} $−Steady state interlayer fracture toughness value; Naming method for sample number: DCB-0-1−Test method-Layer angle-Number.
    下载: 导出CSV
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  • 收稿日期:  2024-01-02
  • 修回日期:  2024-02-08
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