13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- 5. Conclusions A numerical model on the basis of computing the stress intensity factors and wing crack initiation angles for cracked substances under normal uniform tension is presented. In the present work, based on the Linear Elastic Fracture Mechanics (LEFM), the maximum tangential stress criterion or -criterion is implemented into code HDDMCR to investigate the interaction of micro cracks. In order to verify the validity of the proposed model, analytical solution of a typical sample problem e.g. a center slant micro crack under uniform tension is used, and its propagation mechanism is compared with numerical solution. In the present model, quadratic collocations with three special crack tip elements for each micro crack tip at the same time are implemented into code HDDMCR2D. The numerical simulation is carried out considering infinite planes with two micro cracks under uniform tension. Comparing the parallel and non-parallel micro cracks, the effects of inclinations of two micro cracks show that these factors have a strong influence on the breaking path. 6. References [1] A. Golshani, Y. Okui, M. Oda, T. Takemura, Micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite, int. j. Mechanics of Materials, 38 (2005) 287-303. [2] J. Niu, S.W.U. MAO, Analysis of asymmetric kinked cracks of arbitrary size, location & orientation – Part I. Remote compression, Int. J. Frac., 89(1998) 19–57. [3] M. F. Marji, I. Dehghani, Kinked crack analysis by a hybridized boundary element/boundary collocation method, Int. j Solids and Structures, 47(2010)922–933. [4] T. Li, W. Yang, Expected coalescing length of displacement loading collinear micro cracks. Theoret. Appl. fracture mechanics, 36(2001) 17-21. [5] C. H. Park, Coalescence of Frictional Fractures in Rock Materials, PhD Thesis, Purdue University West Lafayette, Indiana, 2008. [6] H. Haeri, Numerical Modeling of the Interaction between Micro and Macro Cracks in The Rock Fracture Mechanism Using Displacement Discontinuity Method. PhD Thesis, department of mining engineering, Science and Research branch, Islamic Azad University, Tehran, Iran, during work, 2011. [7] E. Hoek, Z.T Bieniawski, Brittle Rock Fracture Propagation in Rock under Compression, South African Council for Scientific and Industrial Research Pretoria, Int. J. Frac. Mech., 3(1965) pp. 137-15.5. [8] H. Horii, S. Nemat-Nasser, Compression-Induced Micro crack Growth in Brittle Solids: Axial Splitting and Shear Failure, Journal of Geophysical Research, 90(1985) 3105-3125. [9] M. Sagong, A. Bobet, Coalescence of multiple flaws in a rock-model material in uniaxial compression, Rock Mechanics and Mining Sciences, 39(2002) 229-241. [10] Y.P. Li, L.Z. Chen, Y.H. Wang, Experimental research on pre-cracked marble under compression, Int.J. Solids and Structures, 42(2005) 2505-2516. [11] T. Y. Ko, H.H. Einstein, J. Kemeny,. Crack Coalescence in Brittle Material under Cyclic Loading, Golden Rocks , 41st U.S. Symposium on Rock Mechanics (USRMS), ARMA/USRMS 2006, pp.06-930.
RkJQdWJsaXNoZXIy MjM0NDE=