00 for flat indenter) [21]. h max is the maximum penetration depth, and S is the contact stiffness. A c is the projected contact area under the peak indentation depth. The contact stiffness S can be calculated from the slope of the initial portion of the unloading curve and S = dP/dh, which can be obtained by curve fitting of 25% to 50% unloading data [22]. Based on relationships

developed by Sneddon, the contact stiffness S can also be expressed by (10) where β is a constant Blebbistatin price and depends on the geometry of the indenter (β = 1.034 for a Berkovich indenter, β = 1.012 for a Vickers indenter, and β = 1.000 for a cylinder indenter). Because both the sample and the indenter have elastic deformation during the ABT-888 mouse indentation process, the reduced modulus E r is defined by (11) where E and ν are the elastic modulus and Poisson’s ratio for the sample; E i and ν i are the elastic modulus and Poisson’s ratio for the indenter, respectively. For the diamond indenter, E i  = 1,141 GPa and ν i = 0.07. The indenter was assumed to be rigid as mentioned above, and the value of E i is infinite; v s is equal to 0.278 [23]. According to the Oliver-Pharr method mentioned above, the nanoindentation hardness, contact stiffness, and elastic modulus of the materials can be obtained. The comparison of indentation depths at different loading

stages are shown in Table  3. Table 3 The applied load versus penetration depth in loading stage   Depth 0.5 nm 1.0 nm 1.5 nm 2.0 nm Applied load to the indenter (nN) Machining-induced surface 118.83 SDHB 246.22 336.51 522.40 Pristine surface 167.74 268.15 487.05 530.47 Table  3 shows the comparison

of indentation loads at different penetration depths of the pristine single-crystal copper specimen and machining-induced surface. It can be noted that the indentation loads on the machining-induced surface are much smaller than those on the pristine surface with the same indentation depth, respectively. No remarkable difference was found when the maximum indentation penetration depth is larger than 2.0 nm. The amplitude value of the indentation curve on the pristine surface is much larger than the other. It is due to the dislocation MGCD0103 price embryos which developed and propagated in the specimen under the diamond indenter. However, when the maximum penetration is smaller than 2.0 nm, the hardness of the diamond-turned surface becomes distinctly lower than that of the pristine copper. At a sufficiently small load, the indentation response will be mainly due to the surface effects. At a slightly larger indentation penetration depth, the indentation loads are much smaller than those of the pristine single-crystal copper surface. It can be concluded from these results that the machining-induced surface is softer than pristine single-crystal copper. In conventional metal machining, the near-surface layer is much harder than the original material in the surface. Such a surface-hardening phenomenon is due to work-hardening effects.