Important Consequences of the Exponent 3/2 for Pyramidal/Conical Indentations-New Definitions of Physical Hardness and Modulus

Abstract

The now physically founded exponent 3/2 that governs the relation of normal force to depth 3/2 in conical/pyramidal indentation is a physically founded (F N = k h 3/2 ). Strictly linear plots obtain non-iterated penetration resistance k (mN/ µm 3/2 ) as slope, initial effects (including tip rounding), adhesion energy, and phase transitions with their transformation energy and activation energy. The reason for the failing of the Sneddon theory, claiming wrong exponent 2 (as do ABAQUS or ANSYS finite element simulations) is their neglect of long-range effects by shearing. Previous undue trials to rationalize the non-occurrence of exponent 2 are polynomial fittings and "best or variable exponent" iterations for curve fittings that lose all unique information from the loading curve. Also ISO 14577 unloading hardness H ISO and reduced elastic modulus E r-ISO lack physical reality. They are redefined to physical dimensions as new indentation parameters H phys and E r-phys . For the first time physically sound indentation hardness H phys is obtained without iterations solely from loading curves. Also all mechanical indentation parameters relying on Sneddon's exponent 2 are unphysical. They require redefinition with new dimensions. This applies also to visco-elastic-plastic parameters in a recent NIST tutorial. The present ISO-standards create dilemma with physics. But the risk from using wrong mechanical parameters against physics is dangerous, subject to change.