13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- These results show that the length of L and G are 20, 30 and 40 μm under three conditions, respectively. These values were almost equal to that of grain size for Ni-Cr-Mo-V steel and it is in good agreement with the dominating region of fracture obtained experimentally by Ritchie [8]. Therefore, our proposed method is found to well predict theoretically the dominating factor of fracture. 5. Conclusions (1) On the basis of the analytical method using the concepts of super atoms, super dislocation and self-similarity, the atomic distribution from super atoms to those with small scale was found to show the self-similarity and the possibility of analyzing the behaviors of actual atoms using projection method was validated. (2) The direct method and Verlet method were found to give the same results on the atomic distribution, however calculating time is different. (3) Using our proposed method, the dominating region of fracture was shown to derive and it was in good agreement with that obtained experimentally by Ritchie. References [1] G.R. Irwin, Handbuch der Physik, Springer 6 (1958) 551. [2] J.R. Rice, Int J Frac Mech, 2 (1966) 426. [3] T. Yokobori, An Interdisciplinary Approach to Fracture and Strength of Solids, 1968, Wolters-Noordhoff Pub. The Netherlands, T. Yokobori, Zairyo kyoudogaku, The 2nd Edition (1974) Iwanami shoten, In Japanese. [4] T. Yokobori, S. Sawaki, S. Nakanishi, Engng Fract Mech, 12 (1979) 125-141. [5] T. Yokobori, A.T. Yokobori, Jr., J of the Japan Institute of Metals, 42 (1978) 88-95. [6] A.T. Yokobori, Jr., T. Kuriyama, Y. Kaji, Advances in Fracture Research, Proc of ICF10, in the content of Special Lecture of CD-rom, Honolulu 2001, Elsevier Science (2001). [7] K.B. Broberg, Cracks and Fracture, Academic Press, (1999). [8] R.O. Ritchie, J.F. Knott, J.R. Rice, J Mech Phys Solids, 21 (1973) 395. [9] A.T. Yokobori, Jr., T. Ohmi, Y. Nagumo, D. Yoshino, Proc. of the 50th Japan National Symposium Strength, Fracture and Fatigue (2006) 57-60. [10] J. Watanabe, T. Iwadare, Y. Tanaka, T. Yokobori, Engineering Fracture Mechanics, 28, (1987) 589.
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