13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- tractions along interface have been solved in closed form [4], ( ) λ λ π λπ − − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − =− a x a x N p x 1 1 1 1 2 sin (1) and ( ) ( )1 1 q x fp x = , (2) where f is the coefficient of friction; λ is determined by ( ) ( ) 0 1 1 2 21 < < − − = λ μ μ λπ , tan f . (3) Fig.1 The two-dimensional indentation model for rock cutting with n periodic indentaters. Fig.2. Indentation configuration, integral path 0 →s and 0 →Δ . Eq.(1) shows that the stress state near the indenter corner may vary in the form ( ) ( ) ⎪⎩ ⎪ ⎨ ⎧ = = = − − 0 0 2 0 1 1 1 x r x a r ij , , λ λ σ as 0→r . (4) For special cases either with 0 5. =μ or 0= f , Eq.(3) leads to 0 5. =λ , showing the same order of stress singularity as that for a sharp crack tip. For 05. =μ , the substrate becomes incompressible. The asymptotic stress boundary conditions of the substrate in the contact area next to the left and right corners then become ar N 2 0 22 π σ θ =− = | (5) and P Periodic indenters x2 2t Substrate Cell 1 x1 x2 x1 x2 x1 2l Cell 2 Cell 1 Cell 2 N N h p(x1) q(x1) Q N x1 x2 θ r α Δ s 2a θ r
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