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一种厚度无关的复合材料I型分层扩展桥接律构建方法

高佳乐 荣俊杰 席近远 校金友 文立华 侯晓

高佳乐, 荣俊杰, 席近远, 等. 一种厚度无关的复合材料I型分层扩展桥接律构建方法[J]. 复合材料学报, 2024, 42(0): 1-12.
引用本文: 高佳乐, 荣俊杰, 席近远, 等. 一种厚度无关的复合材料I型分层扩展桥接律构建方法[J]. 复合材料学报, 2024, 42(0): 1-12.
GAO Jiale, RONG Junjie, XI Jinyuan, et al. A novel approach to construct a thickness-independent bridging law for large scale bridging in type I delamination of composites[J]. Acta Materiae Compositae Sinica.
Citation: GAO Jiale, RONG Junjie, XI Jinyuan, et al. A novel approach to construct a thickness-independent bridging law for large scale bridging in type I delamination of composites[J]. Acta Materiae Compositae Sinica.

一种厚度无关的复合材料I型分层扩展桥接律构建方法

基金项目: 国家自然科学基金重点项目(52090051);国家自然科学基金青年项目(12102349)
详细信息
    通讯作者:

    荣俊杰,博士,副教授,硕士生导师,研究方向为飞行器结构力学 E-mail: jrong@nwpu.edu.cn

    校金友,博士,教授,博士生导师,研究方向为计算结构力学、复合材料结构设计 E-mail: xiaojy@nwpu.edu.cn

  • 中图分类号: TB332

A novel approach to construct a thickness-independent bridging law for large scale bridging in type I delamination of composites

Funds: Key Project of National Natural Science Foundation of China (52090051); Young Project of National Natural Science Foundation of China (12102349)
  • 摘要: 大范围纤维桥接是复合材料分层扩展中的一种重要的增韧机制,通常用R曲线和桥接牵引-分离定律表征。然而R曲线和桥接牵引-分离定律都与结构厚度有关,需用不同厚度试件分别进行实验测量。近期的研究指出:桥接现象的厚度相关性实质上是由于不同厚度结构弯曲刚度不同所造成的;将裂纹张开的转角引入,构建的桥接牵引-分离转角关系与厚度无关。但是,现有的构造方法需要试件预埋光纤测量应变,试验过程复杂。本文通过弹性约束梁模型解析推导双悬臂梁预制裂纹尖端张开位移和转角,并结合J-积分法构建桥接牵引-分离转角关系,通过实验验证该关系是厚度无关的。进一步基于这种厚度无关的桥接律,提出了一种根据单一厚度试验数据逆推其他任意厚度R曲线与桥接牵引-分离定律的方法。通过不同厚度的碳纤维/环氧树脂、芳纶纤维/环氧树脂复合材料层合板双悬臂梁试验,证明逆推出来的R曲线和桥接牵引-分离关系曲线与用试验直接测量的曲线吻合很好。本文方法基于解析模型,仅需测量载荷-位移曲线即可,避免了裂纹长度的测量以及不同厚度的多次试验,简化了试验流程,为复合材料结构性能表征提供了有力工具。

     

  • 图  1  J-积分法的积分路径

    Figure  1.  Integral path of J-integral method

    $ \delta _{\text{n}}^ * $—Opening displacement of pre-crack tip; $ \delta _{\text{t}}^ * $—Sliding displacement of pre-crack tip; $ {\varGamma _{{\text{loc}}}} $—Integral path locally round the bridging zone; $ {\varGamma _{{\text{tip}}}} $—Integral path of crack tip; $ \sigma \left( \delta \right) $—Relationship between bridging stress and crack opening displacement

    图  2  双悬臂梁试件的几何形状

    Figure  2.  Geometric shape of double cantilever beam specimen

    图  3  弹性梁模型及变形示意图

    Figure  3.  Elastic beam model and its deformation

    $ P $—Load of loading point; $ \varDelta $—Displacement of loading point; $ {k_{\text{e}}} $—Spring restraint stiffness; $ a $—Crack length; $ w $—Beam deflection; $ \xi $—Opening displacement of crack tip in elastic supported beam model; $ \overline \delta $—Opening displacement of crack tip in elastic restraint beam model; $ {K_{\text{e}}} $—Spring stiffness; $ {K_{\text{r}}} $—Torsion spring stiffness; $ \psi $—Corner of beam section

    图  4  实际裂纹拓展(a)、等效裂纹拓展(b)

    Figure  4.  Actual crack growth (a), equivalent crack growth (b)

    图  5  不同厚度碳/环氧树脂复合材料DCB试验的桥接律:(a) $ \sigma - \delta _{\text{n}}^ * $曲线;(b)$ \sigma - \delta _{\text{n}}^ * \theta _{\text{n}}^ * $曲线

    Figure  5.  Bridging law for DCB test of carbon/epoxy composites with different thicknesses: (a) $ \sigma - \delta _{\text{n}}^ * $ curves; (b) $ \sigma - \delta _{\text{n}}^ * \theta _{\text{n}}^ * $ curves

    图  6  $ \sigma - \delta _{\text{n}}^ * \theta _{\text{n}}^ * $曲线构建方法流程图

    Figure  6.  Flow chart of $ \sigma - \delta _{\text{n}}^ * \theta _{\text{n}}^ * $ curve construction

    图  7  逆推法流程图

    Figure  7.  Flow chart of inverse method

    图  8  碳/环氧树脂复合材料DCB试验的I型断裂韧性与裂纹拓展长度的关系对比

    Figure  8.  Comparison of the relationship between mode I fracture toughness and extended crack displacement of carbon/epoxy composites in DCB test

    图  9  碳/环氧树脂复合材料逆推方法结果与试验结果对比图:(a) I型断裂韧性与预制裂纹尖端张开位移的关系;(b)桥接应力与预制裂纹张开位移的关系;(c)I型断裂韧性与裂纹拓展长度的关系;(d)载荷-位移曲线

    Figure  9.  Comparison between the results of the inverse method and the experimental results of carbon/epoxy composites: (a) The relationship between mode I fracture toughness and pre-crack opening displacement; (b) The relationship between bridging stress and pre-crack opening displacement; (c) The relationship between mode I fracture toughness and extended crack displacement; (d) Load-displacement curves

    图  10  2h=2 mm DCB试验纤维桥接现象

    Figure  10.  Fiber bridging phenomenon in 2h=2 mm DCB test

    图  11  芳纶/环氧树脂复合材料DCB试验的载荷-位移曲线

    Figure  11.  Load-displacement curves of aramid/epoxy composites in DCB tests

    图  12  芳纶/环氧树脂复合材料DCB试验的裂纹拓展长度-加载点位移曲线

    Figure  12.  Extended crack displacement-loading point displacement curves of aramid/epoxy composites in DCB test

    图  13  芳纶/环氧树脂复合材料DCB试验的I型断裂韧性R曲线

    Figure  13.  R curves of mode I fracture toughness of aramid/epoxy composites in DCB test

    图  14  不同厚度芳纶/环氧树脂复合材料DCB试验的桥接律:(a)试件的$ \sigma - \delta _{\text{n}}^ * $曲线;(b) $ \sigma - \delta _{\text{n}}^ * \theta _{\text{n}}^ * $曲线

    Figure  14.  Bridging law for DCB test of aramid/epoxy composites with different thicknesses: (a) $ \sigma - \delta _{\text{n}}^ * $ curves; (b) $ \sigma - \delta _{\text{n}}^ * \theta _{\text{n}}^ * $ curves

    图  15  芳纶/环氧树脂复合材料逆推法结果与试验结果对比图:(a) I型断裂韧性与预制裂纹尖端张开位移的关系;(b)桥接应力与预制裂纹张开位移的关系;(c) I型断裂韧性与裂纹拓展长度的关系;(d)载荷-位移曲线

    Figure  15.  Comparison between the results of the inverse method and the experimental results of aramid/epoxy composites: (a) The relationship between mode I fracture toughness and pre-crack opening displacement; (b) The relationship between bridging stress and pre-crack opening displacement; (c) The relationship between mode I fracture toughness and extended crack displacement; (d) Load-displacement curves

    表  1  碳/环氧树脂复合材料DCB试验$ {G_{\text{I}}} - \delta _{\text{n}}^ * $曲线的拟合参数

    Table  1.   Fitting parameters for $ {G_{\text{I}}} - \delta _{\text{n}}^ * $ curves of carbon/epoxy composites in DCB test

    Thickness/mm $ {B_1} $ $ {B_2} $ $ {B_3} $ $ {B_4} $
    6 0.4529 2.392 1.364 0.3562
    10 0.6238 4.389 1.782 0.5032
    14 0.8462 9.091 2.532 0.6392
    Note:$ {B_1} $-$ {B_4} $—Fitting parameters.
    下载: 导出CSV

    表  2  碳/环氧树脂复合材料DCB试件的几何尺寸

    Table  2.   Geometric dimensions of carbon/epoxy composite DCB specimens

    Test piece numberLength/mmWidth/mmThickness/mm
    01340106
    023401010
    033401014
    下载: 导出CSV

    表  3  芳纶/环氧树脂复合材料参数

    Table  3.   Aramid/epoxy composite material parameters

    $ {E_{\text{f}}} $/$ {\text{GPa}} $$ {E_{22}} $/$ {\text{MPa}} $$ {G_{12}} $/$ {\text{MPa}} $
    70.0160425102
    Notes:$ {E_{\text{f}}} $—Flexural modulu in direction 1; $ {E_{22}} $—Elastic modulu in direction 2; $ {G_{12}} $—Shear modulu in direction 12.
    下载: 导出CSV

    表  4  芳纶/环氧树脂复合材料DCB试验$ {G_{\text{I}}} - \delta _{\text{n}}^ * $曲线的拟合参数

    Table  4.   Fitting parameters for $ {G_{\text{I}}} - \delta _{\text{n}}^ * $ curves of aramid/epoxy composites in DCB test

    Thickness/mm $ {B_1} $ $ {B_2} $ $ {B_3} $ $ {B_4} $
    2 0.1501 0.2002 0.07974 0.0483
    6 1.323 0.1978 −0.9344 0.1933
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-11-30
  • 修回日期:  2024-02-04
  • 录用日期:  2024-03-09
  • 网络出版日期:  2024-04-17

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