A physically based model for indenter tip shape calibration for nanoindentation

A new function that describes the shape of three-sided pyramidal indenters is introduced. This function differs from the polynomial tip shape function conventionally used in nanoindentation tip shape calibration in that the new function includes fewer fitting parameters with clearer physical meaning. Specifically, two of the fitting parameters integrated into the new function are the indenter's tip radius and the slope of the indenter's equivalent cone. Tip shape calibration data were collected with four different diamond indenter tips, and both the new function and the standard polynomial function were fit to the data. It is found that the new function can fit calibration data nearly as well as the standard polynomial function and better than existing physically based functions. Although the tip radius parameter obtained by fitting the new model to data deviates from the tip radius determined from Hertzian elastic contact, the two values are correlated.