The Physical Foundation of FN=kh(3/2) for Conical/Pyramidal Indentation Loading Curves: Scientific Explanation

On the basis of fundamental mathematics, it has been possible to physically deduce the relation for conical/pyramidal indentation loading curves (where is normal force, penetration resistance, and penetration depth) for conical/pyramidal indentation loading curves. It has been achieved on the basis of elementary mathematics. The displacement of material, which frequently partially plasticizes as a result of such pressure, is coupled with the productions of volume and pressure by the indentation process. As the pressure/plasticizing depends on the indenter volume, it follows that , where the index stands for pressure/plasticizing and for indentation volume. does not contribute to the penetration only . The exponent on shows that while is experimentally applied; only is responsible for the penetration depth . Thus, is deduced and the physical reason is the loss of for the depth. Unfortunately, when the Love/Sneddon deductions of an exponent 2 on were accepted and applied, this was not taken into account in instruction, textbooks, or the earlier deduction of a number of common mechanical parameters. The author mentions and cites several unexpected experimental verifications and applications of the correct exponent .