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ICF13A

13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- peak stress before the microcrack nucleation and that after the microcrack nucleation have negligible dependence on the mesh size. Engineering strain Engineering stress (MPa) 0 0.1 0.2 0.3 0.4 0.5 0.6 0 300 600 900 1200 Tm=1.870 with tough boundary Tm=1.870 with strong boundary Tm=1.940 with tough boundary Tm=1.940 with strong boundary G'IC=60Jm-2 andT' m=1.479'0 Engineering strain Engineering stress (MPa) 0 0.1 0.2 0.3 0.4 0.5 0.6 0 300 600 900 1200 Tm=1.870 with tough boundary Tm=1.870 with strong boundary Tm=1.940 with tough boundary Tm=1.940 with strong boundary G'IC=60Jm-2 andT' m=1.479'0 (a) (b) Figure 3. The results with mesh size 10 μm when 0 m is (a) 10-2 and (b) 10-3 μm Engineering strain Engineering stress (MPa) 0 0.1 0.2 0.3 0.4 0.5 0.6 0 300 600 900 1200 Tm=1.870 with tough boundary Tm=1.870 with strong boundary Tm=1.940 with tough boundary Tm=1.940 with strong boundary G'IC=60Jm-2 andT' m=1.479'0 Engineering strain Engineering stress (MPa) 0 0.1 0.2 0.3 0.4 0.5 0.6 0 300 600 900 1200 Tm=1.870 with tough boundary Tm=1.870 with strong boundary Tm=1.940 with tough boundary Tm=1.940 with strong boundary G'IC=60Jm-2 andT' m=1.479'0 (a) (b) Figure 4. The results with mesh size 5 μm when 0 m is (a) 10 -2 and (b) 10-3 μm The cohesive zone size has been studied extensively. The widely-used estimate in plane strain condition is Rice’s model [12], which gives the cohesive zone size to be . For the CGL, the estimated cohesive zone sizes are 7690 and 7190 μm. The mesh sizes, 10 and 5 μm, are much smaller than them. For the NGIL, the estimated cohesive zone size is 3.24 μm, smaller than the mesh sizes. Due to its brittle nature, the size of cohesive zones in the NGILs is relatively easy to reach the level of the NGIL thickness. The cohesive zones in the NGILs contain 4 and 8 cohesive elements when the mesh size is 10 and 5 μm, respectively. Therefore, there is no need to further refine the mesh in the NGILs. The above justifies using two levels of mesh size. Note that in Figs. 3 and 4, at each level of 0 m , the main results are fairly consistent despite the fact that the mesh sizes are not apparently smaller than the estimated cohesive zone size for the NGILs. Previous

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