Effect of hydrostatic pressure on indentation modulus

The high pressures generated at a contact during nanoindentation have a quantifiable effect on the measured indentation modulus. This effect can be accounted for by invoking a Murnaghan equation of state-based analysis where the measured indentation modulus is a function of the hydrostatic component of the stress state which is generated beneath the indenter tip. This approach has implications pertinent to a range of mechanical characterization techniques that include instrumented indentation and quantitative atomic force microscopy (AFM) since these techniques traditionally consider only zero-pressure modulus values during data interpretation. To demonstrate the validity of this approach, the indentation modulus of four materials (fused quartz, sapphire, rutile and silicon) is evaluated using a I Pm radius conospherical diamond tip to maximum contact depths of 30 nm. The tip area function is independently determined via AFM while the unloading stiffness from the load-displacement data is determined using standard Oliver-Pharr analysis.