The exponent 3/2 at pyramidal nanoindentations.

Area of Science:

• Materials Science
• Nanotechnology
• Mechanical Engineering

Background:

• Published nanoindentation loading curves often utilize the Hertzian exponent (2), which is experimentally unsupported for sharp indenters.
• This discrepancy leads to inaccuracies in determining nanomechanical parameters.

Purpose of the Study:

• To demonstrate the generality and significance of the experimentally observed 3/2 exponent in nanoindentation loading curves.
• To provide evidence for the geometric origin of this exponent, independent of material properties and indentation mechanisms.

Main Methods:

• Re-analysis of published nanoindentation loading curves from diverse materials (metals, oxides, semiconductors, biomaterials, polymers, organics).
• Plotting data using the 3/2 exponent to demonstrate linearity and generality across different indentation techniques (load-controlled, depth-controlled, AFM).

Main Results:

• A consistent linearity with a 3/2 exponent to depth was observed for sharp pyramidal or conical indenters across a wide range of materials.
• This linearity holds true regardless of the indentation equipment or control method used.
• Kinks in the linear plots indicate material phase transitions under indentation pressure, corroborated by diffraction and spectroscopy data.

Conclusions:

• The 3/2 exponent is a fundamental geometric characteristic of nanoindentation with sharp tips, applicable across numerous material classes.
• The Hertzian exponent (2) is inappropriate for sharp indenters, and the 3/2 exponent provides a more accurate basis for nanomechanical analysis.
• Nanoindentation loading curves contain rich information, including the detection of pressure-induced phase transitions, which can be revealed by analyzing linearity with the 3/2 exponent.