Mechanical Behaviors of Subsurface Bifurcating Cracks
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摘要: 在复杂荷载作用下，利用分布位错技术(DDT)对半无限大平面内的分岔裂纹问题进行研究，并进行了正确性验证. 根据等效应力强度因子判据，初步解释了裂纹产生分岔的原因；研究了不同埋深、荷载比值、分支长度比值、分岔角度情况下的分岔裂纹尖端的应力强度因子；同时，研究了多分支分岔裂纹，计算结果与有限元结果吻合. 结果显示：埋深越深，分岔裂纹扩展越困难，当埋深为d/a=1.5时，分支裂尖应力强度因子削弱程度可达15%左右；较长分支会极大地抑制短分支的扩展，当两分支裂纹长度比达到b/c=2以上时，屏蔽效应可达50%以上；另外，分岔角度和荷载比值会改变分岔裂纹主导的扩展模式.
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关键词:
- 分岔裂纹 /
- 分布位错技术 /
- 等效应力强度因子判据 /
- 应力强度因子 /
- 多分支分岔裂纹
Abstract: Under complex loads, the distributed dislocation technique (DDT) was used to discuss the bifurcating crack problem in a semi-infinite plane, and its correctness was verified. Based on the criterion for the equivalent stress intensity factor, the cause for crack bifurcation was preliminarily explained. The stress intensity factors of bifurcating cracks under different buried depths, loading ratios, bifurcation length ratios, and bifurcation angles were calculated. The multi-branch bifurcating crack was also calculated, with the results agreeing well with the finite element method. The results show that, the deeper the buried depth is, the more difficult the bifurcating crack propagation will be. When the burial depth reaches d/a=1.5, the stress intensity factor at the bifurcating crack tip will decrease by about 15%. Moreover, the longer branch will greatly inhibit the extension of the short branch. When the crack length ratio of the 2 branches reaches more than b/c=2, the shielding effect will reach more than 50%; In addition, the bifurcation angles and loading ratios will change the dominant propagation mode of bifurcating cracks. -
图 1 复杂荷载下的半无限平面分岔裂纹
Figure 1. The semi infinite plane bifurcating crack under complex loads
图 2 坐标变换示意图
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 2. Schematic diagram of coordinate transformation
图 3 非对称分岔裂纹的计算结果对照图
Figure 3. Comparison of calculation results of asymmetric bifurcating crack
图 4 不同角度下的等效应力强度因子及裂纹分岔示意图
Figure 4. Schematic diagram of the equivalent stress intensity factor and the crack bifurcation at different angles
图 5 埋置深度对归一化应力强度因子的影响
Figure 5. Effects of burial depths on normalized stress intensity factors
图 6 荷载比值对归一化应力强度因子的影响
Figure 6. Effects of load ratios on normalized stress intensity factors
图 7 分支长度比值对归一化应力强度因子的影响
Figure 7. Effects of branch length ratios on normalized stress intensity factors
图 8 分岔角度对归一化应力强度因子的影响
Figure 8. Effects of bifurcation angles on normalized stress intensity factors
图 9 多分支分岔裂纹示意图以及有限元网格划分局部图
Figure 9. Schematic diagram of the multiple branch bifurcation crack and the local partial finite element mesh
表 1 多分支分岔裂纹有限元计算与本文结果对照
Table 1. Comparison between the results of finite element calculation of the multi branch bifurcation crack and the results in this paper
KⅠA/(MPa·$\sqrt{\mathrm{mm}}$) KⅠE/(MPa·$\sqrt{\mathrm{mm}}$) KⅠB/(MPa·$\sqrt{\mathrm{mm}}$) KⅠF/(MPa·$\sqrt{\mathrm{mm}}$) FEM 2.832 0.618 1.313 1.686 DDT 2.807 0.613 1.289 1.607 KⅡA/(MPa·$\sqrt{\mathrm{mm}}$) KⅡE/(MPa·$\sqrt{\mathrm{mm}}$) KⅡB/(MPa·$\sqrt{\mathrm{mm}}$) KⅡF/(MPa·$\sqrt{\mathrm{mm}}$) FEM -0.032 4 -1.028 1.132 -0.760 DDT -0.023 8 -1.020 1.165 -0.714 
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