Consistency Analysis of I1 and K Criterions for Linear Elastic Fracture of Plane Strain Mode I Crack Subjected to Bidirectional Equal Tensile Stress
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摘要: 采用线弹性有限元方法计算了承受双向等拉应力的平面应变I型裂纹的应力场,分析了裂纹尖端各应力分量间的关系,拟合了各非零应力分量关于裂纹半长度a和裂纹尖端最小网格尺寸l1的函数,分析了应力第一不变量I1与应力场强度因子KI的相关性。结果表明,裂纹尖端各非零应力分量间存在稳定的比例关系;各非零应力分量值和加载应力的比值与裂纹半长度a的1/2次幂呈正比例关系、与裂纹尖端最小网格尺寸l1的1/2次幂呈反比例关系;相同最小网格尺寸条件下,裂纹尖端的应力第一不变量与应力场强度因子的比值l1/KI为与加载应力和裂纹长度无关的常数,证明了承受双向等拉应力的平面应变I型裂纹线弹性断裂的I1准则与K准则具有一致性。Abstract: The stress field of plane strain mode I crack with bidirectional tensile stress is calculated by using linear elastic finite element method, the relationship between stress components at crack tip is analyzed, the function of each non-zero component stress about half of crack length a and minimum grid size l1 at crack tip is fitted, and the correlation between first invariant of stress I1 and stress field intensity factor KI is analyzed. The results show that there is a stable proportional relationship among the non-zero stress components at the crack tip. The ratio of the non-zero stress component and the loading stress is proportional to the 1/2 power of half length of crack a, and is antiproportional to the 1/2 power of minimum mesh size at crack tip l1. Under the same minimum mesh size condition, the ratio I1/KI of the first invariant of stress at crack tip to the intensity factor of stress field is a constant independent of the loading stress and crack length, confirming the consistency of the I1 and K criterions for linear elastic fracture of plane strain mode I crack subjected to bidirectional equal tensile stress.
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Keywords:
- made I crack /
- linear elastic fracture /
- I1 fracture criterion /
- K criterion
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