Undue Hardness/Modulus Ratio Claims instead of Physical Penetration Resistance and Applications with Mollusk Shells

Abstract

The Nanoindentation is a precise technique for the elucidation of mechanical properties. But such elucidation requires physically based interpretation of the loading curves that is widely still not practiced. The use of indentation hardness H and indentation modulus E r is unphysical and cannot detect the most important phase-transitions under load that very often occur. The claim that H versus E plots relate linearly for all different materials is neither empirically found nor correctly deduced. It is most dangerous by producing incorrect materials properties and misleading. The use of H/E (that is also called "elasticity index") in complicated formulas for brittle parameter, yield strength, toughness, and so-called "true hardness" is also in error. The use of H/E cannot reveal the true qualities of materials without considering phase-transitions under load that require the correct exponent 3/2 on h for the loading curves (instead of disproved 2). This is exemplified with the physical data of different mollusk shells that experience phase-transitions, a new bionics model, and different contributions for their strengthening. The data are compared to the ones of aragonite and calcite and vaterite.

Volume, Side-Area, and Force Direction of Berkovich and Cubecorner Indenters, Novel Important Insights

“…non-linear force application). The kink is sharp, but there might be some short soft transitions in buffering biological materials [7] or at too rapid penetration. The bearing analysis routine [8] [9] is used for the measurement of depression and pile-up volumes with respect to the plane through the respective edges and corners.…”

“…The latter is subtracted from full W applied to obtain the transition work W transition up to h 2 [1] [6] (h 2 is freely chosen; perhaps at the depth where another kink deviation starts). The transition-energy is calculated according to (7). Its normalization is now by division through the depth difference (8) (no longer through the force difference) for better comparison of different indenter tips.…”