13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 0 45 90 135 -0.5 0.0 0.5 1.0 1.5 2.0 (c) (Degree) a/c=0.2,r/a=0.008273, =9.730 Klocal=0.200,Klocal/(2 r) 1/2=1.962 ij/Klocal/(2r)1/2 f33=Tz(f11+f22) f33=v(f11+f22) 11 f11 (T-stress neglected) 22 f22 33 f33=v(f11+f22) f11 f33=Tz(f11+f22) 0 45 90 13 0.0 0.5 1.0 1.5 2.0 (d) f33=v(f11+f22) f33=Tz(f11+f22) (Degree) a/c=0.2, r/a=0.0075, =1.900 Klocal=0.1523, Klocal/(2r)1/2=3.5075 ij/Klocal/(2r)1/2 11(T-stress neglected) 22 33 f11 f22 f33=v(f11+f22) 11 f33=Tz(f11+f22) Fig.4 The angular distributions of stress components normalized by the local stress intensity factors in a normal plane of the quarter-elliptical corner crack front line. (a) through-the-thickness straight crack, (b) semi-elliptical surface crack, (c) quarter elliptical corner crack, (d) embedded elliptical crack. As shown in Fig. 4, the angular distributions of stress components in a normal plane of various crack front lines are given in the local Cartesian coordinates. It can be seen that 22 is in good agreement with f22, while the differences between 11 and f11 are great if the T-stress is neglected. When the T-stress is considered, the differences will become very small. In addition, the differences between 33 and f33 for the plane strain state (v(f11+ f22)) are great. If the Tz factor is considered in f33, f33 will be in good agreement with 33. 3. Three-parameter principle J–QT–Tz for the elastic-plastic material The HRR stress components can be expressed as 1 1 , , , , n ij m e ij m e Kr (6) where 1 1 0 0 n J K I n (7) σ0 is the yield stress. By considering the effects of geometry and size on crack-tip constraint, O’Dowd and Shih [8, 9] found that the near-tip stress field is governed by the two parameters of J and Q as follows: 1 1 0 0 0 0 n ij ij ij ij J r Q I n r J (8) The first term is the HRR solution ( 2 ), Q is a function of the stress triaxiality achieved ahead of the plane strain cracks. The λ is set to zero, then Qrr=Qθθ and Qij is the form
RkJQdWJsaXNoZXIy MjM0NDE=