An MD simulation study to the indentation size effect of polystyrene and polyethylene with various indenter shapes and loading rates

Several nanoindentation MD simulations were conducted to investigate the indentation size effect (ISE) of Polystyrene (PS) and Polyethylene (PE) at nano-scale using different indenters and loading rates. A strain gradient elasticity model in which the ISE is related to the Frank energy caused by finite bending stiffness and neighboring interactions of chains was imported to describe the ISE in this work. Two large-scale molecular substrates for PS and PE were constructed to compare the ISE performance during indentation simulations. The spherical indenter was firstly considered, and an uptrend of the calculated hardness and modulus with increasing indenter radius was found for both PS and PE. A conical indenter consisting of 25 virtual rigid spheres used in LAMMPS was designed. Considering different tip sizes and loading rates, indentation simulations using these conical indenters were conducted. The uptrend of hardness curves at the initial indentation stage was also found in conical cases. Through fitting the hardness curves, the strengthening effects of tip size and loading rate were certified, especially for PS. At nano-scale, the dominant effect of benzene ring component on ISE performance was confirmed. The downtrend of ISE was found to exist at nano-scale for PE although it was not obviously found in experimental cases and the contributing factors for this kind of ISE were discussed.