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复合材料II型疲劳分层扩展预测:从应变能释放率-寿命(G-N)曲线到Paris' law

祝曼 王阳 刘强 易敏

祝曼, 王阳, 刘强, 等. 复合材料II型疲劳分层扩展预测:从应变能释放率-寿命(G-N)曲线到Paris' law[J]. 复合材料学报, 2023, 40(9): 5433-5446. doi: 10.13801/j.cnki.fhclxb.20221213.001
引用本文: 祝曼, 王阳, 刘强, 等. 复合材料II型疲劳分层扩展预测:从应变能释放率-寿命(G-N)曲线到Paris' law[J]. 复合材料学报, 2023, 40(9): 5433-5446. doi: 10.13801/j.cnki.fhclxb.20221213.001
ZHU Man, WANG Yang, LIU Qiang, et al. Prediction of mode II fatigue delamination propagation in fibre reinforced composites: From strain energy release rate-life (G-N) curve to Paris' law[J]. Acta Materiae Compositae Sinica, 2023, 40(9): 5433-5446. doi: 10.13801/j.cnki.fhclxb.20221213.001
Citation: ZHU Man, WANG Yang, LIU Qiang, et al. Prediction of mode II fatigue delamination propagation in fibre reinforced composites: From strain energy release rate-life (G-N) curve to Paris' law[J]. Acta Materiae Compositae Sinica, 2023, 40(9): 5433-5446. doi: 10.13801/j.cnki.fhclxb.20221213.001

复合材料II型疲劳分层扩展预测:从应变能释放率-寿命(G-N)曲线到Paris' law

doi: 10.13801/j.cnki.fhclxb.20221213.001
基金项目: 国家自然科学基金 (12102179;12272174);江苏省自然科学基金(BK20200409);中央高校基本科研业务费专项资金(3082021 NS2021001);江苏省“双创博士”计划(JSSCBS20210618)
详细信息
    通讯作者:

    刘强,博士,副教授,博士生导师,研究方向为复合材料极端环境性能评价及工艺力学 E-mail: liuqiang2015@nuaa.edu.cn

    易敏,博士,教授,博士生导师,研究方向为先进材料结构和先进制造的多尺度多场耦合力学 E-mail: yimin@nuaa.edu.cn

  • 中图分类号: TB332

Prediction of mode II fatigue delamination propagation in fibre reinforced composites: From strain energy release rate-life (G-N) curve to Paris' law

Funds: National Natural Science Foundation of China (12102179; 12272174); Natural Science Foundation of Jiangsu Province (BK20200409); the Fundamental Research Funds for the Central Universities (3082021 NS2021001); Jiangsu Provincial Double-Innovation Doctor Program (JSSCBS20210618)
  • 摘要: 疲劳分层是复合材料最常见、最危险的失效模式之一。本文建立了II型加载条件下复合材料疲劳分层扩展的模拟方法。基于对疲劳分层扩展提出的新的物理解释:疲劳分层扩展为一系列连续发生的疲劳分层起始扩展,将疲劳损伤累积描述为层间界面断裂韧性衰减,构建了新的疲劳内聚力单元模型。针对II型加载条件下的材料层间开裂变形场的特殊性,提出了用以描述II型加载条件的层间界面疲劳损伤累积的衰减法则,确立了依据应变能释放率-寿命(G-N)曲线的材料本构参数标定方法。引入疲劳内聚力单元模型,预测了复合材料II型疲劳分层扩展行为,与疲劳分层扩展实验所得Pairs' law能够很好地吻合。本文新提出的疲劳分层模拟方法相较于已有模型的优势在于:无需追踪裂纹扩展路径,降低了模型的应用难度,提高了计算效率;模型所需材料参数标定仅依赖于实验G-N曲线,无需实验Paris' law,参数标定所需的疲劳实验数量及时间大幅减少。

     

  • 图  1  分层增量起始扩展假设示意图

    Figure  1.  Sketch of incremental-onset hypothesis

    Δa—Delamination length; FDO—Fatigue delamination onset; FDP—Fatigue delamination propagation

    图  2  内聚力本构关系:(a) 静力学双线性本构关系;(b) 疲劳本构关系

    Figure  2.  Cohesive constitutive law: (a) Static bi-linear constitutive law; (b) Fatigue constitutive law

    图  3  应变能释放率-寿命(G-N)曲线示意图

    Figure  3.  Sketch of strain energy release rate-life (G-N) curve

    图  4  疲劳损伤算法的有限元分析流程图

    Figure  4.  Flow chart describing implementation of fatigue damage algorithm in FEM analysis

    SERR—Strain energy release rate; N_hist—Historcial cycle number

    图  5  三点弯端部切口弯曲(ENF)实验的有限元模型:(a) 几何模型示意图;(b) 网格尺寸

    Figure  5.  FEM model of 3-point bending end-notched flexure (ENF) test: (a) Sketch of geometric model; (b) Mesh size

    b—; a0—Initial crack length; Pmax—Maximum applied load

    图  6  疲劳模拟中的包络加载策略

    Figure  6.  Envelop loading strategy in fatigue delamination

    Pmax—Maximum applied load

    图  7  标定得到的IM7/8552碳纤维/环氧树脂复合材料II型本征G-N曲线

    Figure  7.  Intrinsic G-N curve calibrated from mode II FDO test of IM7/8552 carbon/epoxy composites

    α—Material parameter; SERR—Strain energy release rate

    图  8  有限元(FEM)复现的IM7/8552碳纤维/环氧树脂复合材料II型疲劳分层起始扩展(FDO)实验

    Figure  8.  Representing mode II fatigue delamination onset (FDO) test of IM7/8552 carbon/epoxy composites by finite element (FEM)

    图  9  FEM预测的IM7/8552碳纤维/环氧树脂复合材料II型Paris法则

    Figure  9.  Prediction of mode II Paris' law of IM7/8552 carbon/epoxy composites from FEM

    图  10  直接通过实验G-N曲线作为输入参数预测得到的IM7/8552碳纤维/环氧树脂复合材料II型Paris法则

    Figure  10.  Predicted mode II Paris' law of IM7/8552 carbon/epoxy composites with input direct from experimental G-N curve

    图  11  直接通过实验G-N曲线作为输入参数模拟得到的IM7/8552碳纤维/环氧树脂复合材料 I型(a)和II型(b)实验G-N曲线

    Figure  11.  Represented experimental G-N curves of IM7/8552 carbon/epoxy composites for mode I (a) and mode II (b) by using input from experimental G-N curve

    图  12  I型 (a) 和II型 (b) 加载模式下IM7/8552碳纤维/环氧树脂复合材料层间裂纹尖端附近应变场

    Figure  12.  Strain field around inter-laminar crack tip under mode I (a) and mode II (b) load condition in IM7/8552 carbon/epoxy composites

    图  13  IM7/8552碳纤维/环氧树脂复合材料裂纹尖端附近界面材料点输入应变能分布

    Figure  13.  Distribution of supplied strain energy release rate on the material points around the crack tip in IM7/8552 carbon/epoxy composites

    表  1  IM7/8552碳纤维/环氧树脂单向纤维复合材料层合板的相关材料参数[8]

    Table  1.   Material properties of IM7/8552 carbon fiber/epoxy unidirectional laminates[8]

    Intra-ply propertiesE11/GPaE22=E33/GPaν12=ν13ν23G12=G13/GPaG23/GPa$G_{\text{c}}^{{\text{static}}}$/
    (N·mm−1)
    $\sigma _0^{{\text{static}}}$/MPaK0/
    (N·mm−3)
    16111.380.320.4365.173.980.73990106
    下载: 导出CSV

    表  2  ENF实验测试IM7/8552碳纤维/环氧树脂复合材料起始扩展(FDO)寿命Ntest及柔度增加百分比[8]

    Table  2.   List of experimental fatigue delamination onset (FDO) life Ntest and percentage of compliance increase in ENF test of IM7/8552 carbon/epoxy composites[8]

    $ {G_{\sup }}/G_{\text{c}}^{{\text{static}}} $50%40%30%20%
    FDO life Ntest156257159741642
    13344998711080
    170746127534114
    116545224641643
    199436242038271
    Average Ntest155487170533350
    Compliance increase/%1.060.770.950.73
    下载: 导出CSV

    表  3  IM7/8552碳纤维/环氧树脂复合材料G-N曲线的拟合参数

    Table  3.   Fitting parameters of G-N curves for IM7/8552 carbon/epoxy composites

    α101520
    ξ1 0.739 0.739 0.739
    λ1 −0.146 −0.148 −0.149
    ξ2 1.048 1.042 1.040
    λ2 −0.219 −0.221 −0.222
    ξ3 0.371 0.361 0.355
    λ3 −0.103 −0.101 −0.100
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-10-04
  • 修回日期:  2022-11-12
  • 录用日期:  2022-11-25
  • 网络出版日期:  2022-12-15
  • 刊出日期:  2023-09-15

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