Analytical Prediction of Reciprocating Nanoscratch Depth for Brittle Materials in the Ductile Regime

Based on the multi-trace scratch method, a model which predicts the wear depth of the scratch has been proposed in this study. It assumes that the increment of wear depth in each scratch is positively correlated with the maximum shear stress depth obtained by Hertz contact theory due to the elastic contact between the tip and materials. By establishing the recursive relation between the tip and the sample contact radius at each scratch, the recursive relation of each wear depth increment is obtained. The prediction model of multiple wear depth is established through adding the increment of the wear depth. Considering that the change of the mechanical properties of the brittle materials during the wear experiments, the modified equation of elastic modulus is introduced to improve the accuracy of the prediction model. To verify the reliability of the proposed model, various nanoscratches at the optical glass surfaces are achieved by rubbing against a spherical diamond tip under the condition of indentation-elastic-load. The experimental results show that the prediction model provides the better accurate prediction of the wear depth after modifying the elastic modulus of glass materials. The modified elastic modulus varies with the wear cycles based on the different applied load. Further analysis indicates that it is related to the densification and damage softening induced by shear stress. The theoretical basis of the proposed model is reliable which considering the change of the mechanical properties of the material. These results are expected to be extended to the prediction of nanoscratch deformation evolution of other brittle and hard materials. © 2021 Journal of Mechanical Engineering.