13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Modeling the propagation mechanism of two random micro cracks in rock Samples under uniform tensile loading Hadi Haeri1, *, Kourosh Shahriar2, Mohammad Fatehi Marji3, Parviz Moarefvand4 1PhD candidate of rock mechanics, Mining Engineering Department, Science and Research Branch, Islamic Azad University, Poonak, Hesarak, Tehran, Iran 2Professor, Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran 3Associate Professor, Head of Mine exploitation Engineering Department, Faculty of Mining and Metallurgy, Institution of Engineering, Yazd University, Yazd, Iran 4Assistant Professor, Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran * Corresponding author: hadihaeri@ymail.com Abstract The breakage mechanism of brittle substances such as rocks under uniform tensile loading is considered. The random micro cracks are mostly produced in all of Polycrystalline substances resulting from stress concentration. This paper focuses on the interaction of two pre-existing micro cracks. The quality of the growing and coalescing of micro cracks in rock-like specimen are studied by using a Fortran Code HDDMCR2D which is based on a two dimensional displacement discontinuity method for the crack analysis (a boundary element computer code based on the linear elastic fracture mechanics (LEFM) theory). In order to improve the accuracy of the results and reduce the errors in calculating displacement discontinuity in the proposed model, the higher-order elements (quadratic elements) are used to discretize a sufficient number of boundary elements. Also to eliminate errors caused by stress and displacement singularity near the crack tip, three special elements has been used to discretize each crack end. In this research, the problems of wing cracks propagated at different angles from the original micro crack tips in an infinite specimen under uniform tension are considered. Keywords micro crack interaction, crack initiation, LEFM, BEM, crack coalescence 1. Introduction The presence of micro cracks in brittle substances may have higher effect on their macro mechanical behavior. It has been observed that the macro mechanical behavior of rocks is due to their micro mechanical structure [1]. The micro cracks initiate from their tips and extend at an angle with respect to the original micro crack plane [2]. In the path of development of micro cracks, the kinked and curved cracks may be produced and these types of cracks usually occur under shear or mixed mode loading [3]. The breakage mechanism of brittle substances with random micro cracks depends on the degree of their interaction and coalescence path that may leads to the formation of a macro crack [4]. In studying the breakage mechanism of brittle substances under uniaxial tensile stress, crack initiation and specimen breakage may happen very soon and the crack initiation is normally expected to occur in a direction perpendicular to the maximum tensile stress. In rocks, crack initiation in tension is preferred due to the lower toughness of rock substances in tension than in shear [5]. The mechanism of propagation and coalescence of micro cracks in forming of macro cracks or rupture of rock is still not a well understood subject and the problem of interaction between the micro cracks and macro cracks is always noted by the researchers [6]. A number of
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