Penetration resistance and penetrability in pyramidal (nano)indentations

Pyramidal nanoindentation loading curves were linearly plotted, normal force versus (penetration depth)(3/2) . The slope is penetration resistance k, its inverse penetrability. Linear correlations verify. All contributions to the indentation are included in the penetrability. Dependencies and uses of the extrapolation tools are exemplified, identified, and discussed. In the case of phase transition including twinning within the loading range a sharp kink occurs, again with verifying correlation in both branches of the linear plot. The exponent 3/2 applies to all types of materials upon conical or pyramidal indentations onto normal flat surfaces, independent of the various mechanistic responses. While common curve fitting procedures of loading curves and finite element (FE) calculations miss phase transitions, gradients, surface effects, elbows, (nano)pores, and change from tip rounding to cone (at very low penetrations), these are recognized by the penetration resistance analysis. Also prominent undisturbed pyramidal or conical micro- and macroindentations provide linear plots with exponent 3/2. Numerous FE simulations create experimentally unsupported "loading curves." This is discussed with typical published examples. An explanation for the deviation from Sneddon's and Love's theory is given by correction for the shear-force part that does not participate in the penetration depth. The validation of the exponent 3/2 instead of previously assumed 2 requires adjustment of mechanical parameters that were defined by using the nonsupported exponent.