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耐久性分析相对小裂纹扩展速率公式的参数确定方法

左冉东 贺小帆 李玉海

左冉东, 贺小帆, 李玉海等 . 耐久性分析相对小裂纹扩展速率公式的参数确定方法[J]. 北京航空航天大学学报, 2021, 47(12): 2594-2601. doi: 10.13700/j.bh.1001-5965.2020.0492
引用本文: 左冉东, 贺小帆, 李玉海等 . 耐久性分析相对小裂纹扩展速率公式的参数确定方法[J]. 北京航空航天大学学报, 2021, 47(12): 2594-2601. doi: 10.13700/j.bh.1001-5965.2020.0492
ZUO Randong, HE Xiaofan, LI Yuhaiet al. Parameter determination method of relative small crack growth rate formula in durability analysis[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(12): 2594-2601. doi: 10.13700/j.bh.1001-5965.2020.0492(in Chinese)
Citation: ZUO Randong, HE Xiaofan, LI Yuhaiet al. Parameter determination method of relative small crack growth rate formula in durability analysis[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(12): 2594-2601. doi: 10.13700/j.bh.1001-5965.2020.0492(in Chinese)

耐久性分析相对小裂纹扩展速率公式的参数确定方法

doi: 10.13700/j.bh.1001-5965.2020.0492
基金项目: 

国家重点研发计划 2017YFB1104003

国家自然科学基金 11772027

航空科学基金 201909051002

详细信息
    通讯作者:

    贺小帆, E-mail: xfhe@buaa.edu.cn

  • 中图分类号: V215.6

Parameter determination method of relative small crack growth rate formula in durability analysis

Funds: 

National Key R & D Program of China 2017YFB1104003

National Natural Science Foundation of China 11772027

Aeronautical Science Foundation of China 201909051002

More Information
  • 摘要:

    结构细节相对小裂纹扩展速率公式是采用概率断裂力学方法进行结构耐久性分析的关键。针对目前需进行多个应力水平下的成组疲劳试验以确定相对小裂纹扩展速率公式适用范围和参数的问题,首先,通过将应力强度因子修正系数展开为多项式,基于材料稳定裂纹扩展段的裂纹扩展速率公式得到了耐久性分析的相对小裂纹扩展速率公式。然后,以受远场均匀拉伸载荷作用的中心圆孔板为对象,分别基于应力强度因子近似解和FRANC3D软件进行裂纹扩展分析,得到相对小裂纹尺寸范围及对应裂纹扩展参数的确定方法。最后,进行了3种试件在等幅交变应力下的耐久性试验,验证了该方法的正确性。

     

  • 图 1  基于应力强度因子近似解的裂纹扩展分析结果

    Figure 1.  Analysis result of crack propagation based on approximate solution of stress intensity factor

    图 2  裂纹描述示意图

    Figure 2.  Schematic diagram of crack description

    图 3  基于FRANC3D模拟的da/dN-an/2曲线

    Figure 3.  da/dN-an/2 curves based on FRANC3D simulation

    图 4  试件尺寸示意图

    Figure 4.  Schematic diagram of specimen size

    图 5  各试验组的da/dN-a1.566曲线

    Figure 5.  da/dN-a1.566 curves of experimental groups

    表  1  模型尺寸

    Table  1.   Model dimension

    序号 宽度w/mm 孔直径d/mm 厚度t/mm au/mm Y0
    1 40 10 5 0.88 1.95
    2 32 8 5 0.72 1.92
    3 24 6 5 0.58 1.86
    下载: 导出CSV

    表  2  da/dN-an/2数据处理结果

    Table  2.   da/dN-an/2 data processing result

    序号 Q/10-6 r2 Q′/10-6 η/%
    1 9.083 0.996 6 9.293 2.32
    2 8.780 0.996 5 9.009 2.61
    3 8.328 0.996 2 8.455 1.52
    下载: 导出CSV

    表  3  初始裂纹位置搭配

    Table  3.   Initial crack position collocation

    序号 搭配方式
    1 0-1
    2 0-2
    3 0-3
    4 0-4
    5 0-5
    6 1-2
    7 1-3
    8 1-4
    9 2-3
    下载: 导出CSV

    表  4  da/dN-an/2数据处理结果

    Table  4.   da/dN-an/2 data processing results

    扩展模式 编号 截距 Q/10-6 r2 η/%
    单边扩展 x=0 0 8.977 0.989 2 3.52
    x=1 0 9.354 0.997 6 0.65
    x=2 0 9.005 0.991 5 3.20
    x=2.5 0 8.976 0.986 1 3.53
    双边对称扩展 x=0 0 8.901 0.994 3 4.41
    x=1 0 9.521 0.993 5 2.39
    x=2 0 9.004 0.991 6 3.21
    x=2.5 0 8.949 0.992 3 3.84
    双边扩展,初始裂纹尺寸相同,位置不对称 0-1-0 0 9.023 0.992 5 2.99
    0-1-1 0 9.255 0.997 9 0.41
    0-2-0 0 9.142 0.994 1 1.65
    0-2-2 0 9.058 0.993 0 2.59
    0-3-0 0 8.867 0.991 9 4.81
    0-3-3 0 9.249 0.993 3 0.48
    0-4-0 0 8.951 0.993 4 3.82
    0-4-4 0 9.237 0.997 6 0.61
    0-5-0 0 8.876 0.991 6 4.69
    0-5-5 0 8.993 0.992 7 3.34
    1-2-1 0 9.215 0.997 6 0.85
    1-2-2 0 9.110 0.990 5 2.01
    1-3-1 0 9.149 0.996 5 1.57
    1-3-3 0 8.947 0.990 7 3.86
    1-4-1 0 9.360 0.997 8 0.72
    1-4-4 0 9.364 0.998 1 0.75
    2-3-2 0 8.883 0.991 9 4.61
    2-3-3 0 9.049 0.991 9 2.70
    双边扩展,初始裂纹位置对称,尺寸不相同 0.1-0.05-0.1(0) 0 8.94 0.990 5 3.92
    0.1-0.05-0.1(1) 0 9.27 0.994 0 0.22
    0.1-0.05-0.1(2) 0 8.90 0.992 0 4.38
    0.1-0.05-0.1(2.5) 0 8.96 0.994 0 3.75
    0.2-0.02-0.2(0) 0 8.88 0.993 4 4.70
    0.2-0.02-0.2(1) 0 9.30 0.999 2 0.09
    0.2-0.02-0.2(2) 0 9.16 0.995 1 1.50
    0.2-0.02-0.2(2.5) 0 9.04 0.995 0 2.75
    下载: 导出CSV

    表  5  试件尺寸及试验结果

    Table  5.   Specimen size and experimental results

    试件编号 宽度/mm 孔半径/mm 厚度/mm 应力水平/MPa 有效试件数
    AL-1 40 5 5 98 8
    AL-2 32 4 5 98 8
    98 7
    AL-3 24 3 5 106 76
    115 15
    下载: 导出CSV

    表  6  各试件的da/dN-a1.566数据拟合结果

    Table  6.   da/dN-a1.566 data fitting result of specimens

    试验组 试件编号 截距 Qi/10-4 r2
    AL-1(98 MPa) 1-1 0 1.029 0.959 9
    1-2 0 1.026 0.901 4
    1-3 0 1.017 0.930 5
    1-4 0 1.122 0.926 5
    1-5 0 1.001 0.932 5
    1-6 0 0.833 0.946 5
    1-7 0 1.067 0.965 8
    1-8 0 0.883 0.931 2
    AL-2(98 MPa) 2-1 0 0.951 0.978 2
    2-2 0 0.850 0.962
    2-3 0 0.863 0.961 9
    2-4 0 1.051 0.974 2
    2-5 0 0.932 0.964 7
    2-6 0 0.802 7 0.943 8
    2-7 0 0.848 0.959 8
    2-8 0 0.939 0.976 2
    AL-3(98 MPa) 3-1 0 0.790 0.898 1
    3-2 0 0.926 0.879 6
    3-3 0 0.770 0.889 4
    3-4 0 0.815 0.934 8
    3-5 0 0.865 0.879 3
    3-6 0 0.998 0.922 9
    3-7 0 0.970 0.938 9
    AL-3(106 MPa) 3-8 0 1.183 0.944 7
    3-9 0 1.237 0.929 2
    3-10 0 0.965 0.886 9
    3-11 0 1.094 0.921 4
    3-12 0 1.120 0.914 8
    3-13 0 1.209 0.878 7
    AL-3(115 MPa) 3-14 0 1.309 0.941 7
    3-15 0 1.288 0.970 6
    3-16 0 1.359 0.979
    3-17 0 1.243 0.976
    3-18 0 1.488 0.980 1
    下载: 导出CSV

    表  7  da/dN-a1.566数据处理结果

    Table  7.   da/dN-a1.566 data processing result

    试件种类 应力水平/MPa au/mm Y0 Q50 Q′ η/%
    AL-1 98 0.88 1.95 9.933×10-5 9.678×10-5 2.63
    AL-2 98 0.72 1.92 9.016×10-5 8.839×10-5 2.01
    AL-3 98 0.58 1.86 8.721×10-5 8.419×10-5 3.59
    AL-3 106 0.58 1.86 1.131×10-4 1.136×10-4 0.45
    AL-3 115 0.58 1.86 1.420×10-4 1.335×10-4 6.37
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-09-02
  • 录用日期:  2020-09-19
  • 网络出版日期:  2021-12-20

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