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

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 Er 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.