13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- A fracture-based model of periodic-arrayed indentation for rock cutting Yu Jun Xie1,*, Bo Yang Xiang1 and Xiao Zhi Hu2* 1 Department of Mechanical Engineering, Liaoning Shihua University, Fushun, 113001, P. R. China. 2 School of Mechanical and Chemical Engineering, The University of Western Australia, Perth, WA 6009, Australia. * Corresponding author: yjxie@lnpu.edu.cn, xiao.zhi.hu@uwa.edu.au. Abstract When an half-space elastic substrate is subject to indentation with rigid, flat-ended and periodic indenters, a periodic singular stress fields and K-dominant regions should arise adjacent to the indenter edges. The concept of indentation stress intensity factor Kind is introduced to describe the singular indentation stress field, which mathematically is very similar to that of a mode I crack. The singular indentation stress field is sufficient to induce cracking from a smooth crack-free surface, which can potentially play a significant role in damage analysis of rock cutting. In the present article, a fracture-based model is proposed for rock breakage by using an energy-based method. The indentation stress intensity factor Kind and indentation cracking equation for rock cutting model have been formulized. Keywords Fracture, Contact mechanics, Indentation stress intensity factors, Indentation. 1. Introduction A rock-cutting tool schematically illustrated in Fig.1 can be modeled by periodic rigid and flat-tipped indenters. It is noted from the work [1-4] that a mixed-mode singular stress field exists in an incompressible substrate at the sliding contact edge of a rigid flat-ended indenter pressing down onto the substrate. Subsequently, the damage in a form of the micro-crack initiation on the contact surface will be induced by such a singular stress field, which can contribute substantially to rock cutting. In the present work, a fracture-based method similar to the classical fracture mechanics is proposed to formularize the cracking or indentation damage induced by the singular indentation stress field next to the corners of the periodic indenters. 2. Periodic indentation configurations The modeling of rock cutting problem to be investigated is illustrated in Fig.1. The periodic indenters is pressed on to the surface of half plane substrate, which occupies the region < < < +∞ x h 2 0 , −∞< < +∞ 1x and is constrained to deform in plane strain normal to the 2 1x x − plane. The substrate is supposed to be elastically isotropic, with Young’s modulus E and Poisson’s ratio μ. The periodic arrayed indenters is supposed to be rigid, with contact width 2l and center-to-center contact spacing 2t. The calculations for indentation stress intensity factors are carried out based on one of the periodic Cell 1 and Cell 2 that lies between 2 2 1 t t x − < < . Two limiting cases of friction are considered: (i) perfect smooth sliding between the indenter and the substrate; and (ii) small frictional sliding contact between the indenter and the substrate. 3. Asymptotic stress field in sliding contact 3.1. Boundary Condition A typical fretting contact problem of a rigid flat-ended indenter with half width a, sliding on a homogeneous, isotropic, elastic body in half plane is shown in Fig.2. The Cartesian coordinates (x1, x2), and the polar coordinates (r, θ), both with the origin at the left edge of the indenter, are selected. Normal force N and tangential force Q act on the indenter and the following normal and shear
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