Indentation Loading Curves

A physical deduction of the FN = kh 3/2 relation (where FN is normal force, k penetration resistance and h penetration depth) for conical/pyramidal indentation loading curves has been achieved on the basis of elementary mathematics. The indentation process couples the productions of volume and pressure to the displaced material that often partly plasticizes due to such pressure. As the pressure/plasticizing depends on the indenter volume, it follows that FN = Fp 1/3 · Fi 2/3 , where the index p stands for pressure/plasticizing and i for indentation. Fp does not contribute to the penetration, only Fi. The exponent 2/3 on Fi shows that experimentally FN is applied but only FN 2/3 is responsible for the penetration depth h. Thus, FN = kh 3/2 is deduced and the physical reason is the loss of FN 1/3 for the depth. Unfortunately, this has not been considered in teaching, textbooks, and the previous deduction of numerous common mechanical parameters, when the Love/Sneddon deductions of an exponent 2 on h were accepted and applied. The various unexpected experimental verifications and applications of the correct exponent 3/2 are mentioned and cited. Undue mechanical parameters require correction for safety reasons.