Equivalence of nanoindentations by the load and displacement controlled manners

Nanoindentation experiments have been attracting more attentions to in situ test the mechanical properties of die-attach materials due to the localized loading features. Load controlled manner is usually performed to maintain the indentation strain rate, which results in great challenges for finite element (FE) simulations with the indenter controlled in a displacement manner. In this paper, a validated dimensionless method is adopted to describe the applied load-penetration depth (P-h) curve, where the loading curvature represents the mechanical properties of the materials of interest. Based on a typical FE simulation by using the Berkovich indenter, the relationship between load and displacement controlled methods is investigated. The reaction force on the indenter can be measured from the FE simulations controlled by the applied displacement of the indenter. Meanwhile, the P-h curve of indentations controlled by load can be predicted by the proposed method with the provided loading curvature. As a calibration of the time increment Δt, the calculation results show that the smaller the Δt value is, the influence on the predictions can be ignored. In other words, the predictions of penetration depth can be independent of the Δt value and thus reflect the objective essence of loading process. By taking Δt value as 0.001s for three materials with different constitutive properties, the P-h curves under load and displacement control manners are compared, and excellent agreement is found. The proposed method provides a new and elegant way to realize equivalent load control by displacement control of the indenter for nanoindentation simulations.