Determination of hardness from nanoscratch experiments: Corrections for interfacial shear stress and elastic recovery Academic Article uri icon


  • A frequent application of the nanoscratch technique is to estimate hardness of ultrathin films when substrate effects are encountered with the nanoindentation technique. A model based on the work of Goddard and Wilman, which assumes a rigid-plastic behavior of the deformed surfaces, is commonly used for the determination of hardness from scratch tests, yet it overestimates the hardness of materials by as much as a factor of three at very shallow indentation depths on the order of 1-10 nm. The Goddard and Wilman model was extended in this paper to include the effects of the component of the shear stress tangential to the meridianal plane and the elastic recovery of the plastically deformed surfaces assuming elastic-perfectly-plastic material behavior. The proposed model was subsequently verified by performing nanoscratch experiments on fused quartz, which is homogeneous and isotropic with no known surface layers and with known hardness. The hardness was calculated using both the model based on the work of Goddard and Wilman and the extended model. The hardness calculated using the extended model was in very close agreement with the accepted value of bulk hardness of fused quartz over the range of scratch depths tested, showing the importance of the effects of elastic recovery and interfacial shear stress. The model was further verified for the case of a pure aluminum sample and the native thin film coating of alumina that forms on the surface upon air exposure.

author list (cited authors)

  • Tayebi, N., Conry, T. F., & Polycarpou, A. A.

citation count

  • 45

publication date

  • September 2003