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平面机织复合材料疲劳分层数值分析方法研究

万傲霜 朱飞扬 云新尧 李顶河

万傲霜, 朱飞扬, 云新尧, 等. 平面机织复合材料疲劳分层数值分析方法研究[J]. 复合材料学报, 2024, 42(0): 1-16.
引用本文: 万傲霜, 朱飞扬, 云新尧, 等. 平面机织复合材料疲劳分层数值分析方法研究[J]. 复合材料学报, 2024, 42(0): 1-16.
WAN Aoshuang, ZHU Feiyang, YUN Xinyao, et al. Investigation on numerical analysis method of fatigue delamination damage of plane woven composites[J]. Acta Materiae Compositae Sinica.
Citation: WAN Aoshuang, ZHU Feiyang, YUN Xinyao, et al. Investigation on numerical analysis method of fatigue delamination damage of plane woven composites[J]. Acta Materiae Compositae Sinica.

平面机织复合材料疲劳分层数值分析方法研究

基金项目: 国家自然科学基金(52205174); 天津市多元投入基金(21JCQNJC00880); 天津市教委科研计划项目(2021KJ050); 中央高校基本科研业务费专项资金(3122021042)
详细信息
    通讯作者:

    万傲霜,博士,讲师,硕士生导师,研究方向为复合材料疲劳与损伤容限设计 E-mail:aswan@cauc.edu.cn

  • 中图分类号: V258+.3

Investigation on numerical analysis method of fatigue delamination damage of plane woven composites

Funds: National Natural Science Foundations of China (52205174); Natural Science Foundations of Tianjin (21JCQNJC00880); Scientific Re-search Project of Tianjin Education Commission (2021KJ050); Fundamental Research Funds for the Central Universities (3122021042)
  • 摘要: 本文基于内聚力双线性本构关系,建立考虑疲劳损伤的内聚力模型,结合有限元分析技术,建立复合材料层合板疲劳分层扩展行为数值分析方法,分别对准静态和疲劳加载下平面机织复合材料II型分层扩展行为进行仿真分析,准静态加载下的载荷-位移曲线仿真结果与试验结果吻合良好,疲劳加载下的分层扩展速率-应变能释放率变程曲线仿真结果与试验结果吻合良好,验证了模型和方法的有效性。在此基础上,建立适用于平面机织复合材料的疲劳失效准则,结合层内渐进疲劳损伤分析模型,建立含初始分层损伤平面机织复合材料层合结构剩余寿命预测方法,预测了含初始分层损伤层合板的剩余寿命和渐进损伤过程,剩余寿命仿真结果与试验结果吻合良好,此外,结果表明疲劳损伤从初始分层损伤处起始,并逐渐向边缘扩展,紧邻初始分层损伤的两层0°单层板较早出现层内经向损伤和纬向损伤,单层板中0°层较45°层损伤更多,最后0°层以经向损伤为主导失效模式,45°层则以纬向损伤为主导失效模式,各层间界面均出现大面积损伤。

     

  • 图  1  内聚力损伤本构模型:(a) 混合模式双线性本构模型;(b) 考虑疲劳损伤的双线性本构模型

    Figure  1.  Cohesive damage constitutive model: (a) Mixed-mode bilinear constitutive model; (b) Bilinear constitutive model considering fatigue damage

    ${T_{\text{n}}}$ and ${T_{{\text{shear}}}}$ are the normal strength and shear strength of interface, respectively; $\delta _{\text{n}}^{\text{f}}$ and $\delta _{{\text{shear}}}^{\text{f}}$ are the displacements in shear direction and normal direction at complete failure state, respectively; ${\sigma _{{\text{emax}}}}$ and ${\sigma _{{\text{ec}}}}$ are the equivalent stress and its critical value; ${\delta _0}$ and ${\delta _{\text{f}}}$ are the equivalent displacements at damage initiation state and complete failure state under quasi-static loading, respectively; $\Delta $ and ${\Delta ^ * }$are the displacement jump and its critical value; ${\Delta _{\text{f}}}$ is the displacements at complete failure state under fatigue loading; $K$ and ${K_{\text{d}}}$ are the initial stiffness and residual stiffness, respectively

    图  2  复合材料疲劳分层扩展数值分析方法流程图

    Figure  2.  Flow chart of numerical analysis method for fatigue delamination propagation of composite materials

    图  3  三点弯曲单端缺口(3-ENF)试样图和有限元模型:(a) 试样图;(b) 有限元模型

    Figure  3.  Three-point end-notched flexure (3-ENF) specimen diagram and finite element model: (a) Specimen diagram; (b) Finite element model

    图  4  网格收敛性分析

    Figure  4.  Mesh convergence analysis

    图  5  平面机织复合材料内聚力层应力云图:(a) S33应力;(b) S23应力;(b) S13应力

    Figure  5.  Stress contour in cohesive interface of the plane woven composites: (a) S33 Stress; (b) S23 stress; (b) S13 stress

    图  6  平面机织复合材料II型分层扩展数值仿真结果:(a) 载荷-位移曲线;(b) 内聚力损伤扩展过程

    Figure  6.  Numerical simulation results of mode II delamination propagation of plane woven composites: (a) Load-displacement curve; (b) Cohesive damage propagation process

    图  7  数值加载方法示意图

    Figure  7.  Schematic diagram of numerical loading method.

    图  8  平面机织复合材料疲劳分层扩展a-N曲线:(a) 仿真结果;(b) 试验结果

    Figure  8.  Fatigue delamination propagation a-N curve of plane woven composites: (a) Simulation results; (b) Experimental results

    图  9  平面机织复合材料疲劳分层扩展da/dNG曲线

    Figure  9.  Fatigue delamination propagation da/dN- ΔG curve of plane woven composites

    图  10  740 N疲劳载荷作用下平面机织复合材料分层损伤扩展过程

    Figure  10.  Delamination damage propagation process of plane woven composites under fatigue load of 740 N

    图  11  含分层损伤平面机织复合材料结构渐进疲劳损伤分析方法流程图

    Figure  11.  Flowchart of progressive fatigue damage analysis method for plane woven composite structures with initial delamination damage

    图  12  含初始分层损伤层合板试样图和有限元模型:(a) 试样图;(b) 有限元模型

    Figure  12.  Sample diagram and finite element model of laminates with initial delamination damage: (a) Sample diagram; (b) Finite element model

    图  13  网格收敛性分析

    Figure  13.  Mesh convergence analysis

    图  14  平面机织复合材料含初始分层损伤层合板剩余寿命

    Figure  14.  Residual life of plane woven composite laminates with initial delamination damage

    图  15  $ N = 1.417 \times {10^6}{\text{cycles}} $时层合板疲劳损伤仿真结果:(a) 各单层板面内疲劳损伤,WAF表示经向损伤,WEF表示纬向损伤;(b) 各层间界面疲劳损伤

    Figure  15.  Simulation results of fatigue damage in composite laminates at $ N = 1.417 \times {10^6}{\text{cycles}} $: (a) Intralaminar fatigue damage of each single layer, WAF represents warp damage, WEF represents weft damage; (b) Interlaminar fatigue damage between each two adjacent layers

    图  16  层合板失效($ N = 1.435 \times {10^6}{\text{cycles}} $)时疲劳损伤仿真结果:(a) 各单层板面内疲劳损伤;(b) 各层间界面疲劳损伤

    Figure  16.  Simulation results of fatigue damage in composite laminates at failure of laminates ($ N = 1.417 \times {10^6}{\text{cycles}} $): (a) Intralaminar fatigue damage of each single layer; (b) Interlaminar fatigue damage between each two adjacent layers

    表  1  单层板和界面层力学性能参数

    Table  1.   Mechanical property parameters of single layer and interlaminar interface

    Single layer Interlaminar interface
    $ E_{11}^{} = E_{22}^{} $/GPa 57 $ K_{\text{n}}^{} $/(N·mm−3) 2.5$ \times $105
    $ E_{33}^{} $/GPa 8.4 $ K_{\text{s}}^{} $/(N·mm−3) 2.5$ \times $105
    $ \mu _{12}^{} $ 0.067 $ K_{\text{t}}^{} $/(N·mm−3) 2.5$ \times $105
    $ \mu _{13}^{} = \mu _{23}^{} $ 0.41 $ T_{\text{n}}^{} $/MPa 50
    $ G_{12}^{} $/GPa 3.25 $ T_{\text{s}}^{} $/MPa 95
    $ G_{13}^{} = G_{23}^{} $/GPa 2.44 $ T_{\text{t}}^{} $/MPa 95
    $ X_{\text{T}}^{} = Y_{\text{T}}^{} $/MPa 679 $ G_{\text{n}}^{\text{C}} $/(N·mm−1) 0.65
    $ X_{\text{C}}^{} = Y_{\text{C}}^{} $/MPa 557 $ G_{\text{s}}^{\text{C}} $/(N·mm−1) 2.7
    $ S_{12}^{} $/MPa 111 $ G_{\text{t}}^{\text{C}} $/(N·mm−1) 2.7
    $ S_{13}^{} = S_{23}^{} $/MPa 66.7 $\eta $ 2.09
    Notes: $ E_{11}^{} $, $ E_{22}^{} $ and $ {E_{33}} $ are the elastic modulus; $ {\mu _{12}} $, $ \mu _{13}^{} $ and $ \mu _{23}^{} $ are the poisson's ratios; $ {G_{12}} $, $ G_{13}^{} $ and $ G_{23}^{} $ are the shear modulus; $ X_{\text{T}}^{} $ and $ Y_{\text{T}}^{} $ are the tensile strengths in warp direction and weft direction, respectively; $ X_{\text{C}}^{} $ and $ Y_{\text{C}}^{} $ are the compressive strengths in warp direction and weft direction, respectively; $ {S_{12}} $, $ S_{13}^{} $ and $ S_{23}^{} $ are the shear strengths; $ K_{\text{n}}^{} $, $ {K_{\text{s}}} $ and $ {K_{\text{t}}} $ are the stiffness of interface; $ T_{\text{n}}^{} $, $ {T_{\text{s}}} $ and $ {T_{\text{t}}} $ are the strengths of interface; $ G_{\text{n}}^{\text{C}} $, $ G_{\text{s}}^{\text{C}} $ and $ G_{\text{t}}^{\text{C}} $ are the fracture toughness; $\eta $ is the power exponent of BK criterion.
    下载: 导出CSV

    表  2  平面机织复合材料等效刚度和峰值载荷结果

    Table  2.   Results of equivalent stiffness and peak load of plane woven composites

    Equivalent stiffness/(N·mm−1) Peak load/N
    Experimental results Test data 342.9, 323.6,
    346.6, 206.5
    1593.9, 1469.0,
    1625.5, 1200.2
    Mean value 304.9 1472.1
    Simulation results 284.2 1318.3
    Deviations 6.76% 10.45%
    下载: 导出CSV

    表  3  材料弹性常数退化方案

    Table  3.   Degradation strategy of material elastic constants

    Elastic constantsWarp failureWeft failure
    $ E_{11}^{} $$ {\gamma _{{\text{wa}}}} $1
    $ E_{22}^{} $1$ {\gamma _{{\text{we}}}} $
    $ E_{33}^{} $11
    $ \mu _{12}^{} $$ {\gamma _{{\text{wa}}}} $$ {\gamma _{{\text{we}}}} $
    $ \mu _{13}^{} $$ {\gamma _{{\text{wa}}}} $1
    $ \mu _{23}^{} $1$ {\gamma _{{\text{we}}}} $
    $ G_{12}^{} $$ {\gamma _{{\text{wa}}}} $$ {\gamma _{{\text{we}}}} $
    $ G_{13}^{} $$ {\gamma _{{\text{wa}}}} $1
    $ G_{23}^{} $1$ {\gamma _{{\text{we}}}} $
    Notes: $ {\gamma _{{\text{wa}}}} $ and $ {\gamma _{{\text{we}}}} $ are the degradation coefficients at warp failure and weft failure, respectively.
    下载: 导出CSV

    表  4  平面机织复合材料含初始分层损伤层合板剩余强度模型参数

    Table  4.   Parameters of residual strength model of plane woven composite laminates with initial delamination damage

    Elastic constants $ C $ $ p $ $ q $ $ {S_0} $ $ {R_0} $
    Warp tension
    (r=0.05)
    $ 3.72 \times {10^{36}} $ −12.27 1.0 0 679
    Warp compression
    (r=20)
    $ 3.28 \times {10^{105}} $ −38.06 1.0 0 557
    Weft tension
    (r=0.05)
    $ 3.72 \times {10^{36}} $ −12.27 1.0 0 679
    Weft compression
    (r=20)
    $ 3.28 \times {10^{105}} $ −38.06 1.0 0 557
    In-plane shear
    (r=0.05)
    $ 3.13 \times {10^{17}} $ −9.71 3.5 0 111
    Notes: $ C $, $ p $ and $ q $ are the model parameters, ${S_{\text{0}}}$ is the fatigue limit, ${R_{\text{0}}}$ is the initial static strength.
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-10-23
  • 修回日期:  2023-12-26
  • 录用日期:  2024-01-16
  • 网络出版日期:  2024-02-01

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