13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- 0 ij ij HRR ij Q (θ=0º, r=2J/σ0) (9) The J-Q solution can effectively describe the influence of the in-plane stress parameters when the radial distances (r/(J/ 0)) are relatively small, while the approach can hardly characterize it very well with the increase of r/(J/ 0) and strain hardening exponent n. On the other hand, it can hardly give a proper description of Von Mises equivalent stress e because it seldom considers the out-of-plane stress constraint, so Guo and his collaborators proposed two 3D three-parameter principles of K-T-Tz and J-Q-Tz, combining with the in-plane constraint T or Q, for linear elastic and elastic-plastic materials. Further researches by Guo [13-15, 20-22] show that I( ) is the function of n and Tz, 1 1 0 0 , n z J K I n T (10) where 1 , { cos sin 1 cos 2 1 } , n r z e rr r r rr r r u u n I n T u u n n s u u d (11) 1 2 1 2 2 2 1 n e ru d d n s , (12) 1 1 2 2 n r s e u u d n s , (13) 1 2 3 1 1 2 1 2 2 3 1 2 1 n e n r e u d d d d n s , (14) 2 1 3 4 2 n e r u d d u . (15) The di is the function of Tz and n, , which is same as that in HRR solution. The Eq.(8) can be modified 1 1 0 0 0 0 , , n ij ij z Tij ij z J r T Q I n T r J (16) where
RkJQdWJsaXNoZXIy MjM0NDE=