13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Introduction of Eq. (13) into Eq. (14) leads to Eq. (15), n ij ij K σ ε = , (15) where ijσ is the normal stress on the cross section of the single bar ij l . Thus the applied load of the specimen can be calculated as Eq. (16), n ij ij F p q p q K σ ε = × × = × × × ∑ ∑ (16) In order to simplify the calculation, use the average deformation of the fracture surfaces for instead, that is to add all deformations of the single bars with the same x coordinate together and divide it by the number of bars. By this means, Eq. (16) can be converted into Eq. (17), n i F p q K k ε = × × × ×∑ (17) where iε is the average strain at ix and the k is the number of bars with the same x coordinate . 3. Conclusions From the results presented in this paper, it is clear that by using FRASTA reconstruction, that is recording the elevation data of fracture surfaces and reconstructing the process of crack extension, it is possible to obtain the plastic deformation with crack extension. Based on the simple bar hypothesis and by dividing the plastic deformation into single bars, the original lengths of these bars can be determined thus the global strains of these bars during the course of failure can also be calculated. According to the relationship between true stress and true strain of the material, the normal stress on the cross section can thus be determined. Multiply the stress with the cross section area, the load acted on each single bar can be got. Adding all loads on all bars together leads to the total applied load of the specimen. Acknowledgements The work was supported by “the National Nature Science Foundation of China” (Contract No. 11242004) and “the Fundamental Research Funds for the Central Universities” (Contract No. 12CX04068A). References [1] T. Kobayashi, D.A. Shockey, Metall. Trans. A 18 (1987) 1941-1949. [2] H. Miyamoto, M. Kikuchi, T. Kawazoe, Int. J. Fracture 42 (1990) 389-404. [3] W.R. Lloyd, Eng. Fract. Mech. 70 (2003) 387-401. [4] Y.G. Cao, K. Tanaka, Int. J. Fracture 139 (2006) 253-266. [5] Y.G. Cao, K. Tanaka, Acta Metall. Sin. (English Letters) 19 (2006) 165-170. [6] Y.G. Cao, S.F. Xue, K. Tanaka, Acta Metall. Sin. (English Letters) 20 (2007) 40-48. [7] Y.G. Cao, X.Y. Sun, K. Tanaka, Acta Metall. Sin. (English Letters) 20 (2007) 417-424. [8] M.F. Kanninen, C.H. Popelar, Advanced Fracture Mechanics, Oxford University Press, New York, 1985.
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