13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- 6. An indirect technique on the periodic indentation In above sections, a simple and direct method is proposed to estimate the indentation stress intensity factor for singular stress field induced by indentation. In this section, an alternative and indirect technique is considered. (a) (b) Fig.5. Periodic indentation and related periodic crack model. (a) Periodic indentation; (b) Related crack model. For any Mode-I indentation, the related crack model can be found[9]. For various crack configurations, the stress intensity factors had been found and collected in the handbooks such as [14]. Hence, a simple and indirect technique of the crack analogue may be used to solve the indentation stress intensity factor for the Mode-I indentation based on the existing literature for the crack analysis. As a main research object in present work, i.e., periodic indentation, the related crack model can be given in Fig.5(b). For such a periodic array of collinear cracks, the exact solution of the stress intensity factor can be found [14]. 12 1 2 2 ⎪⎭ ⎪ ⎬ ⎫ ⎪⎩ ⎪ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = − t l t N KI ind tan π π π . (23) It varying with the normalized indenter width l/t can be found in Fig.4. 7. Boundary cracking in complete sliding contact 7.1 Energy release rate for boundary cracking From the geometrical point of view, boundary crack initiation can always be defined as a boundary movement in some direction, with the limit 0→s taken and the notch-like boundary becomes a crack, as shown in Fig.2. Then, the energy release rate of boundary cracking can be defined as[10-13] ( ) ( ) α α | sin | cos 0 2 0 1 → → + = s s J G J , (24) where ( ) ( ) ∫ ∫ − = = → → in s i i s s s wn Tu ds wn ds J 1 1 1 0 0 1 , lim (25) and ( ) ( ) ∫ ∫ − = = → → in s i i s s s wn Tu ds wn ds J 2 2 2 0 0 2 , lim . (26) The integration path sin in Eqs.(25) and (26) is any integration path within the substrate, and sin+s Periodic indenters P x2 2t Substrate x1 2l σ=P/2nt 2t 2(t-l) x2 x1 h
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