13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- Figure 4. The micro crack initiation angle 0 as a function of micro crack inclination Angle ψ 4. The initiation and propagation of two non-parallel pre-existing micro cracks In addition to the formation and growth of micro cracks in a rock mass, the reciprocal effects among the micro cracks may also be considered in the breakage process of the rock. The micro crack interactions can be modeled by the present numerical method which may allow micro cracks to interact reciprocally. It can be concluded that by increasing the number of micro cracks, the induced stresses among the original micro crack tips may have a significant effect on their initiation and some new micro cracks may also be produced. In fact, in rock specimens a series of micro cracks may remain closed during loading and propagation. In order to find out how the micro cracks connect under uniform tension (parallel to y axis), two micro cracks (of the same size as shown in Fig. 5), are considered. The body containing the micro cracks is an infinite plane, and the plane strain condition is assumed. It is under a uniform far field tensile stress, mpa 10 with modulus of elasticity, E=10 GPa, Poisson’s ratio, =0.2, fracture toughness, KIC=1.8MPa m1/2. In the present research, the effects of micro cracks randomness and spacing are considered. The mode I and mode II stress intensity factors, KI and KII, near the original tips of two random micro cracks are estimated numerically. The non-dimensional mode I and mode II stress intensity factors, b kI and b kII are mainly used in the micro crack analyses. The negative sign of KI value shows the micro crack closure, while the positive and negative signs in KII only show the direction of relative shear between the two surfaces of micro crack.
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