Parameter determination method of relative small crack growth rate formula in durability analysis
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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。
Abstract:Relative small crack growth rate formula of structural details is the key to durability analysis using probabilistic fracture mechanics method. In order to determine the applicable range and parameters of the formula, it is necessary to carry out group fatigue tests under multiple stress levels, which is too complex. To solve this problem, in this paper, first, the stress intensity factor correction coefficient is expanded to a polynomial, and the relative small crack growth rate formula for durability analysis is obtained based on the crack growth rate formula of material stable crack growth section. Then, various crack growth of the central hole plate subjected to far-field uniform tensile load is analyzed based on the approximate solution of stress intensity factor and FRANC3D software, and a method is obtained to determine the relative small crack size range and the corresponding crack growth parameters. Finally, the correctness of the method is verified by durability tests of three specimens under constant amplitude alternating stress.
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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 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 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 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 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 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 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 -
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