Significant Effects of the Exponent 3/2 for Pyramidal and Conical Indentations: New Meanings of Physical Hardness and Modulus

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 = kh3/2) . Strictly linear plots obtain non-iterated penetration resistance k(mN / m3/2 ) as slope, initial effects (including tip rounding), adhesion energy, and phase transitions with their transformation energy and activation energy. The Sneddon hypothesis fails because it uses the incorrect exponent 2, just like ABAQUS or ANSYS finite element simulations. This is because they ignore long-range effects from shearing. Polynomial fits and "best or variable exponent" iterations for curve fittings, which eliminate all distinctive information from the loading curve, are prior unjustified attempts to explain the absence of exponent 2. Also the 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, only based on loading curves, the physically sound indentation hardness Hphys is determined. Additionally, all Sneddon's exponent 2 dependent mechanical indentation parameters are illogical. They need to be redefined in terms of new dimensions. In a recent NIST lesson, this also applies to the visco-elastic-plastic parameters. The current ISO standards lead to a physics conundrum. However, there is a risk involved in applying the incorrect mechanical parameters to physics, and this risk is unstable.