13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- is the same. In copper and austenitic stainless steel, the anisotropy coefficient (Table 1) of cubic elasticity is high ( 3.3 = a ), therefore, one should study the effect of such strongly anisotropic cubic elasticity on GB stress fields. Figure 8. a) GB normal stress b) GB shear stress, with respect to the distance to the GB-SB intersection in close field configuration for: The main grain and the SB obey either cubic elasticity or isotropic elasticity for: Austenitic stainless steel, L=10.71 μm, t=0.09 μm, Σ0 = 393 MPa, αGB = 33°, αSB = 45°, τ0 = 60 MPa Fig. 8 a) and b) show that cubic elasticity may affect strongly GB stresses. The latter decrease and the micro-crack nucleation cannot occur so easily than for isotropic elasticity. Indeed, in the case of anisotropic cubic elasticity, local elasticity modulus become high and Schmid factor drops (about 0.43 in this case) [30] leading to lower values of GB stress fields. 3.4. Comparison to the pile-up based model Fig. 9 gives a comparison between our model of GB normal stress for t=0.09 mm and the pile-up GB normal stress given by Eq. 2. Figure 9. GB normal stress with respect to the distance to the GB-SB intersection in close field configuration for: Model (points) and Pile-up (circles) with L=10.665 μm, t=0.09 μm, Σ0 = 878 MPa, αGB = 33°, αSB = 45°, τ0 = 60 MPa One can clearly observe that the pile-up theory based model overestimates the GB normal stress with comparison to ours which takes into account a finite SB thickness, t. Indeed, GB normal stress seems to be about three times higher in pile-up modeling than in our approach at the same distance from the intersection of the GB and the SB. 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0 1000 2000 3000 4000 5000 6000 r [micron] GB normal stress [Mpa] Anisotropic Slip Band Isotropic Slip Band 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0 1000 2000 3000 4000 5000 6000 r [micron] GB shear stress [Mpa] Anisotropic Slip Band Isotropic Slip Band a) b) 0 0.002 0.004 0.006 0.008 0.01 0.012 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 r [micron] GB normal stress [MPa]
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