An improved NG-F model for capturing the three types of indentation size effect

Experimental studies indicate that three types of ISE are observed. However, developing a model to capture three types of ISE is one challenging task in materials science. In this paper, the relationship between k and h (k is the ratio of the plastic zone radius to the contact radius, and h is the indentation depth) is systematically analyzed. Then, an exponential decay function is modified to capture the relationship between k and h. The modified exponential decay function can accurately describe the nonlinear relationship between k and h. However, the modified exponential decay function still fails to capture the complex relationship between k and h. On this basis, the NG-F Model is improved with the modified exponential decay function. An analysis has been done to comprehensive comprehension the influence of the parameters on the improved NG-F model. The parameter analysis has been qualitatively proved that the improved NG-F model can capture three types of ISE. The competition between the relative rate of change of k³ and h is the mechanisms behind the improved NG-F model for capturing the three types of ISE. The improved NG-F model is validated with experimental results of three types of ISE. Surprisingly, the validation demonstrates that the improved NG-F model can successfully predict three types of ISE for different materials. However, the improved NG-F model's predictive accuracy varies across materials, with relatively lower DC values observed for certain NR-ISE and C-ISE materials. This is because the dislocation mechanism underlying the improved NG-F model differs from the mechanisms responsible for these materials.