13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- ( ) ( ) ( )2 2 2 0 2 1 2 1 | f f E K J I ind s + − − = − → π π μ , for the plane strain condition. (32) From Eqs.(24), (29) and (32), the total energy release rate of boundary cracking induced by the sliding contact at any angle α can be found as ( ) ( ) ( ) ( ) α π π μ α α sin | sin cos | 2 2 2 0 2 0 1 1 2 1 f f E K J G J I ind s s ob ob + − − = + = − → → . (33) Setting 0= αd dG , i.e., 0= cα cos , we have 2 π α = c ， (34) where cα is the critical cracking angles, which is vertical to the contact boundary. Cracking occurs when G reaches its critical or maximum value. The critical or maximum energy-based driving force for boundary cracking can then be solved from Eq. (33), i.e. ( ) ( )2 2 2 1 2 1 f f E K G I ind + − − = − π π μ max . (35) From the Eqs.(27) and (35), the critical condition of substrate boundary cracking beneath the contact surface can be found as ( ) ( ) IC I ind f f G E K G + − = − = − 2 2 2 1 2 1 π π μ max . (36) Finally, the normalized critical load P can be expressed as ( ) ( )] [ . tan l t f f n tK P IC c − + − = 0 5 1 1 2 1 2 2 1 2 π π π (37) for a given indenter size 2l from Eqs.(23), (28) and (36). Fig.7 shows the effect of perimeter l/t on the normalized critical loads. Fig.7. The effect of the normalized indenter width on the normalized critical load. 8. Conclusions A fracture model of periodic indentation for rock cutting is proposed and formulated by using an energy-based method. The present approach specifies the contribution of indentation on the rock 0.0 0.2 0.4 0.6 0.8 1.0 0.0 4.0 8.0 12.0 16.0 Normalized indenter width l/t f =0.0, 0.5, 0.1, 0.15, 0.2 Normalized critical load Pc/n(πt) 1/2KIC
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