13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- where hp is the contact depth and Ci are fitting constants obtained from calibration on fused silica. As Fig. 3 showed, in a typical curve of contact stiffness versus squared root of the contact area, the tendency should be linear according to Eq. (6); however, the linearity only remains during the initial stage, before cracking occurs. It is possible to identify in the S-A1/2 curve a critical point associated with the onset of cracking (S*, A1/2 *). To do this, successive linear fits were made until a minimum regression coefficient of 0.99 was reached. According to the Oliver-Pharr methodology [10], it is possible to calculate the load and penetration depth values corresponding to the critical point associated with the cracking initiation, P* and h*. For values (P, h) lower than the critical point, the indentation process took place without cracking. For higher values, the indentation process was characterized by the nucleation and propagation of cracks. The load-penetration depth curve for values lower than the critical one was extrapolated according to the Kick's law [18], 2 P C h = ⋅ , to the maximum penetration depth of 2000 nm, obtaining a hypothetical curve characteristic of a non cracking process. Fig. 4 shows a comparative example between the experimental indentation curve, with cracking and the hypothetical indentation curve without cracking. Now, it is possible to apply the energetic methodology through Eq. (5) with the consideration that the strain energy associated to the cracking process, ∆U, could be obtained from the difference between the hypothetical and experimental indentation curves up to the maximum penetration depth, when the maximum crack length was reached. The indentation fracture toughness values so obtained are included in Table 2. Figure 4. Indentation load versus penetration depth of experimental and hypothetical indentation curve.
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