A comparative study of indentation size effect models for different materials

The phenomenon of indentation size effect (ISE) has received great attention in aerospace, nuclear power, microelectronics and medicine. Although researchers have proposed various ISE models, these models often involve different form and number of parameters that can make our wonder which is the best in existed ISE models. Herein, three types of ISE test data, namely, normal ISE, reverse ISE and transition of normal to reverse ISE, are used to evaluate the sixteen ISE models. The comparatively study indicates that Hou-Jennet(H-J), Nix-Gao-Feng (N-G-Fs), Nix-Gao-Haušild (N-G-H), Nix-Gao-Abu Al-Rub (N-G-A) and Nix-Gao-Qius (N-G-Qs) models can accurately predict the normal ISE. The reason for this is that the friction stress that is not related to dislocation activities or the indentation size effect of plastic zone has been introduced into these models. Therefore, these two factors should be considered in future ISE models. The sixteen ISE models are originally proposed to describe the normal ISE of different materials. However, to our surprise, some of these models are able to capture the reverse ISE and the transition of normal to reverse ISE of different materials. The determination coefficients (DC) of the sixteen ISE models are also determined for different materials. For reverse ISE, the highest DC value for Ni Carbide Silicon (NiCSi), TC4 titanium alloy (TC4) and Pulsed electro-deposited Ni (PED Ni) are given by the Exponential (EXP), Nix-Gao-Feng (N-G-Fs) and Nix-Gao-Abu Al-Rub (N-G-A) models, respectively. For the transition of normal to reverse ISE, the Nix-Gao-Yuan-Chen (N-G-YC), Nix-Gao-Feng (N-G-Fs), and Nix-Gao-Haušild (N-G-H) models produce the maximum DC for ZrO₂ ceramic (ZrO₂), Cu single crystals (Cu) and Y₂O₃-ZrO₂ ceramic (Y₂O₃-ZrO₂), respectively. Moreover, the mean DC of the Nix-Gao-Feng (N-G-Fs) model is the maximum among the sixteen ISE models, followed by the Nix-Gao-Haušild (N-G-H) model, but they cannot accurately predict the reverse ISE. Therefore, the Nix-Gao-Feng (N-G-Fs) and Nix-Gao-Haušild (N-G-H) models should be further modified to accurately predict the reverse ISE.