Journal des sciences et de l'ingénierie des matériaux

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

Abstract

Kaupp G

The now physically founded exponent 3/2 that governs the relation of normal force to depth3/2 in conical/pyramidal indentation is a physically founded (FN = k h3/2). Strictly linear plots obtain non-iterated penetration resistance k (mN/ μm3/2) 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 HISO and reduced elastic modulus Er-ISO lack physical reality. They are redefined to physical dimensions as new indentation parameters Hphys and Er-phys. For the first time physically sound indentation hardness Hphys 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.