13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- 4.1 Dependency on SB and GB orientation We have performed some calculations for checking the validity of the analytical modeling with respect to GB and SB orientation GBα( and ) SBα . For the sake of simplicity, we have just carried out it for the normal corresponding parameter (Ann) and it is shown in Fig. 12 a) and b) that Ann and a equal respectively to 0.59 and 0.18 for o SB 35 = α and 0.71 and 0.21 for o SB 40 = α . Figure 12. a) GB normal stress (αSB = 35 o , Ann(αGB ,αSB)=0.71 and α(αGB ,αSB)= 0.21) b) GB shear stress (αSB = 40 o , Ann(αGB ,αSB)=0.59 and α(αGB ,αSB)= 0.18), with respect to the distance to the GB-SB intersection in close field configuration for: analytical model (red) and FE calculations (black) with L=10.665 μm, t=0.09 μm, Σ0 = 393 MPa, αGB = 33°, τ0 = 60 MPa Finally, we conclude that the model parameters slightly depend on the GB and SB orientation. 5. Conclusion An analytical approach is adopted to perform a modeling of the GB stress fields with respect to the distance from the intersection of the grain boundary (GB) and the slip band (SB). It allowed tracking the stress singularity induced by the SB impingement on the GB. Afterwards, finite element calculations were computed in order to simulate the effect of the SB and GB characteristics on GB stress fields, such normal and shear components. In addition, model parameters were adjusted with respect to the involved length, thickness and angles in the problem. The model was then validated whatever the SB characteristic sizes. Finally, further works will deal with evaluating critical values (stress and crack length) in order to enhance a double criterion for the prediction of micro-crack initiation. Acknowledgements The current work is funded by the projects DEN/RSTB/RACOC-02-02 and DEN/RSTB/MASOL (CEA, FRANCE). Authors also acknowledge the project “FP7 Project Perform-60 Grant Agreement No FP7-232612” for its support. References [1] J. V. Sharp. Phil. Mag., (1967) 16-77 [2] M. Victoria, N. Baluc, C. Bailat, Y. Dai, M. I. Luppo, R. Schäublin, B. N. Singh. J. Nucl. Mat., (2000) 276-114. [3] E. H. Lee, M. H. Yoo, T. S. Byun, J. D. Hunn, K. Farrell, L. K. Mansur. Acta. Mater., (2001) 49-3277. 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] Analytical model (A nn = 0.711 and α nn = 0.21) FE calculations 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] Analytical model (A nn = 0.711 and α nn = 0.21) FE calculations a) b)
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