Computational Modeling: Nanoindentation and An Ad Hoc Molecular Dynamics-Finite Difference Thermostat

Abstract

Due to anharmonicities in atomic interactions it is expected that the indentation modulus should very with pre-existing stress in the substrate. However, Tsui, Pharr and Oliver have shown in experiment that the indentation modulus for indentations where plasticity is present is essentially independent of the pre-existing stress if the true contact area is used to make the calculation. They show that the dependence is due to errors in the empirical estimates used to determine contact area. Their experiment is repeated using molecular dynamics simulation and the results of various empirical estimates for the contact area have been compared to the true contact determined from the simulation. The results show that the empirical estimates lead to large errors in contact area. As a result, the hardness and modulus are in error. When true contact areas are used the results agree with experiment. By using shallow elastic indentations, it is shown that indentation can be used to predict the true dependence of pre-stress on the indentation modulus predicted given the knowledge of the anharmonicity in the atomic potential which may be predicted using molecular statics calculations. In addition, a new method for temperature control in molecular dynamics simulations is presented. In metals, electronic interactions account for the majority of the heat flow. Approaches such as the embedded atom method do not account for electrons explicitly and thermal transport cannot be accurately modeled. To overcome this, an ad hoc feedback between the molecular dynamics simulation and the continuum heat flow equation has been developed. The method relies on experimental values for the thermal conductivity and heat capacity as inputs for a finite difference solution to the continuum equation. The thermostat was tested for a simple quasi one-dimensional case. Results are in excellent agreement with the analytical solution for heat flow. The method was extended to three dimensions and applied to the problem of substrate heating due to tip sliding. Although the temperature changes in the substrate due to the sliding tip are small, results show significant differences in the force felt by the tip when the thermostat is turned on or off.