13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- in this section. Let ob s s = in Eq. (3) as shown in Fig. 6 adjacent to the right corner of the indenter and s be within the Kind-dominant region. Because 0= iT and 0 1 = n on the integration path ob s , the energy-based driving force for boundary cracking in x1 and x2 directions in this case can be found in [12-16] ( ) 0 lim 1 0 0 1 ∫ = = → → ob ob ob s s s wnds J . (29) and ( ) E K J I ind s π µ 2 1 2 2 2 0 − → − = | , (plane strain). (30) From Eqs. (4), (29) and (30), the total energy release rate of boundary cracking induced by the sliding contact at any angle α can be found as ( ) ( ) ( ) α π µ α α sin | sin cos | E K J G J I ind s s ob ob 2 1 2 2 0 2 0 1 − → → − = + = . (31) Setting 0= αd dG , i.e., 0 cos = cα , we have 2 π α = c ， (32) 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. (31), i.e. ( ) E K G I ind π µ 2 1 2 2 − − = max . (33) From the Eqs. (5), and (33), the critical condition of substrate boundary cracking beneath the contact surface can be found as ( ) E K G G IC ind C π µ 2 1 2 2 − − = = max . (34) for Mode-I indentation, where the IC ind K − is the boundary fracture toughness for Mode-I indentation. Then, K-based fracture criterion for Mode-I indentation can be given by IC ind I ind K K − − = (35) From Eqs. (34) and (6), it can be determined that IC IC ind K FK = − , (36) where F is an enlarging factor, and is given by 2 25066 . = =π F . (37) Therefore, Eq. (36) indicates that the common fracture toughness for a Mode-I tensile crack can also be determined by the indentation test method presented in this study. Recently, this indentation method has been successfully used to determine the fracture toughness of glass [16] and brittle polymers [17]. 6. Conclusions A fracture-based modelling for boundary cracking induced by indentation singular stress field has been investigated by using energy-based method. The concept of indentation stress intensity factor is introduced to descript the intensification of the indentation singular stress field. Typical calculation method on ISIFs has been given by using the partial J-integral. This study presents also an energy-based fracture mechanics analysis for the ISIF and the indentation-induced boundary
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