Consistency Analysis of I₁ and K Criterions for Linear Elastic Fracture of Plane Strain Mode I Crack Subjected to Bidirectional Equal Tensile Stress

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 K_I 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/K_I 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.