On the novel finding of two modified-Nix-Gao models for indentation size effect

Existing modified-Nix-Gao models have been developed to accurately describe the descending indentation size effect (ISE). This raises the question of whether the modified-Nix-Gao models can describe other types of ISE. In this paper, because Nix-Gao-Feng and Nix-Gao-Haušild models are exceptionally straightforward and user-friendly, the two modified-Nix-Gao models are chosen to make a systematic study. To our surprise, the parameters analysis indicates that the two modified-Nix-Gao models are able to describe the transition of descending to ascending ISE. The Nix-Gao-Feng is also capable of predicting a transition in hardness from hardening to softening at shallow indentation depth. However, the two modified-Nix-Gao models does not capture the ascending ISE. Further study reveals that the mechanism behind of this novel finding is attributed to the competition between the relative rate of change of k³ (k is the ratio of the effective radius to the contact radius) and indentation depth with indentation depth. However, two modified-Nix-Gao models gradually transition to a dislocation-dominated descending ISE as indentation depth increases, resulting in the inability of both models to reflect the ascending ISE. The evaluation indicates that the two modified-Nix-Gao models can successfully predict the transition of descending to ascending ISE of different materials, and the minimum determination coefficients (DCs) of both models are more than 0.8 for different materials. Although the DCs of both models are relatively high for some results of the ascending ISE, qualitative comparison and parameter analysis reveal that they fail to fully capture the ascending ISE. This implies that quantitative comparison alone is insufficient to reasonably reflect the predictive accuracy of the models.