Physical Nanoindentation: From Penetration Resistance to Phase-Transition Energies

Abstract

The ISO standard 14577 is challenged for its violation of the energy law, its wrong relation of normal force F N with impression depth h, and for its iterative treatments. The solution of this dilemma is the use of sacrosanct simplest calculation rules for the loading parabola (now F N = kh 3/2) giving straight lines for cones, pyramids and wedges. They provide the physical penetration resistance hardness k with dimension [Nm −3/2 ] and allow for non-iterative calculations with closed formulas, using simple undeniable calculation rules. The physically correct F N versus h 3/2 plot is universally valid. It separates out the most common surface effects and reveals gradients. It provides unmatched precision, including reliability checks of experimental data. Regression analysis of F N versus h 3/2 plots reveals eventual unsteadiness kink phase-transition onset with the transition-energy. This is shown for all kinds of solid materials, including salts, silicon, organics, polymers, composites, and superalloys. Exothermic and endothermic single and consecutive multiple phase-transitions with their surface dependence are distinguished and the results compared in 5 Tables. The sharp phase-transition onsets and the transition energies provide unprecedented most important materials' characteristics that are indispensable for safety reasons. ISO ASTM is thus urged to thoroughly revise ISO 14577 and to work out new standards for the mechanically (also thermally) stressed materials. For example, the constancy of the first phase-transition parameters must be controlled, and materials must only be admitted for maximal forces well below the first phase-transition onset. Such onset loads can now be easily calculated. The nevertheless repeated oppositions against the physical analysis of indentations rest on incredibly poor knowledge of basic mathematics, errors that are uncovered. The safety aspects caused by the present unphysical materials' parameters are discussed.

Indentation onto Stishovite (SiO<sub>2</sub>), MgO, and a Covered Superalloy: “Pop-In” Repair, Phase-Transition Onsets, Polymorph Energies, and Transition-Energies

“…This view is also supported by the very high penetration resistance values k from the Kaupp-plot (the physical hardness) of 0.0086 to 0.0117 mN/nm 3/2 (Figure 2). These values reach and surmount the ones of superalloys [4].…”

“…Before calculations, the published loading curves must be repaired from any pop-ins by removing such instrumental hold-periods with adjustment of the depth readings. Only required are the well-known formulas, as repeatedly published in [4] (their formulas 3 -7). These correct for surface effects (axis cut F a ) of the physically analyzed loading curves.…”

“…Their phase-transition onsets and endothermic phase-transition energies must be far beyond the maximal forces that occur during turbulent flight. After the author's complaints in [4] [5] that phase-transition under load facilitates catastrophic cracking of titanium alloys, there is now a response. The chosen faster "remedy" is apparently not replacement of the alloy by a better one.…”

The Loading Curve of Spherical Indentions Is Not a Parabola and Flat Punch Is Linear

“…It is the two-dimensional treatment of the three-dimensional impression into solids, with its now obsolete "iron-rule" ("cone exponent 2, sphere exponent 3/2, and flat exponent 1"). The main problem was the impossible equality of exponent 3/2 for conical/pyramidal [11] and for spherical inden- [24] [25]. The therein and in this paper challenged behaviors create high risks and miss the important possibilities for avoiding catastrophic failures by grain formations that initiate catastrophic failures within the polymorph interfaces [22].…”

“…These experimental errors are not corrected and still used in ISO 14577 documents. The unprecedented novelties have already been applied for conical/pyramidal/wedged indentations [5] [25], and further applications are expected for the Equations (2), (7) and (8) when ISO 14577 will be profoundly revised on sound physics but not on historical errors. Unfortunately, there are non-scientific problems for a rapid ISO decision, including severe liability questions [23].…”