Reconciliation of nanoscratch hardness with nanoindentation hardness including the effects of interface shear stress

Abstract

The definitions of hardness from nanoscratch and nanoindentation analyses with a spherical indenter were compared and shown to be mathematically equivalent for the case of zero interface shear stress (surface traction). The definition of nanoindentation hardness was taken as the ratio of the resultant force to the area of contact projected on a plane normal to the line of action of the resultant force, whereas in the case of the nanoscratch technique, the hardness and interfacial shear stress were related to the measured normal and lateral forces in a nanoscratch experiment, as well as to the cross-sectional area of the groove. The two definitions of hardness were then applied to nanoscratch experimental data from material systems covering a wide range of hardness values. The calculated values of hardness from the two definitions were based on the contact area, determined from the scratch residual profile and the elastic recovery of the plastically deformed surface, and yielded the same values of hardness within experimental error. The contact angle, and thus the contact area, was shown experimentally to be sensitive to interface shear stress: a positive increase in interface shear stress led to a reduction in contact area as compared to the case of a frictionless contact. For a material with given hardness, normal indenter force, and contact area, a positive or negative interface shear stress is balanced by a positive or negative change, respectively, in the lateral force about the value needed to maintain a static balance for a frictionless nanoscratch contact. A comparison of these effects with experimental data indicates that very hard materials tend to have negative to zero interface shear stress, which correlates to a sink-in effect, whereas the soft materials tend to have positive interface shear stress, which correlates to a pileup effect.