_{1}

-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
.

We continue with our efforts since the early 2000 nds to convince ISO (International Standardization Organization) and the American branch ASTM (American Society for Testing Materials) to properly correct their ISO 14577 standard. This standard enforces the analysis of (nano) indentation curves to the whole materials sciences. However, conical or pyramidal indentation does not penetrate against a projected or iterated contact area with violation against the first energy law, which contradicts experiment. The diamond indentation rather creates the semi-angle dependent volume of the cone or the pyramid that is geometrically well known and available from all indentation compendia. A pyramid volume can also be calculated like a cone with its “effective cone angle”, as repeatedly used in indentation compendia. Therefore, the mathematic calculation is indeed possible for the loading parabola that relates the force with the depth^{3/2}. The physically and mathematically founded deduction of the parabola exponent 3/2 with the linear F_{N}-h^{3/2} plot is thus universally proved. It needs only the use of basic calculation rules that are sacrosanct to everybody. Any deviations from the exponent 3/2 of the loading parabola are thus experimental errors. Materials with gradients are no exceptions. They still require exponent 3/2 on h: tangents to the loading F_{N}-h^{3/2} plot (instead of straight lines in that case) provide the physical hardness (k-values) depth-dependent, which will also be valuable in these cases, as discussed in [^{2}, as erroneously proposed since 1939 by Love [^{2} > 0.999 - 0.9999) had the advantage to physicochemical correctly identify and remove the various surface effects (including tip rounding). Importantly, it also detected phase-transitions with their onset data. But strange resistance arose against the iteration-less calculations. And surprisingly, this did not change after the break-through, when elementary calculation rules quantified the universal fraction of applied energy that is responsible for the elastic plus plastic deformations with mathematical precision. We apply 20% of the applied work and use the proved exponent 3/2 on h. But 33.33% violation is still tolerated by using the false exponent 2. Only the proved calculation settles the violation of the energy law with the factor 0.8 (Equation (4)), but it is strictly connected to the exponent 3/2. This could again only be published after a large delay in 2013 [

The author’s very successful non-iterative plots (F_{N} against h^{3/2}, Equation (1)) were unduly scolded as “Kaupp-fitting” [_{1} and k_{2} (mN/µm^{3/2}) (physical hardness). This culminated in the determination of the first phase-transition energies [

As the still exacting of false exponent 2 on h by ISO 14577 cannot reproduce experimental loading parabolas, people tried with “excuses” by exponent fittings, polynomial and least squares iterations. Hardness was defined as F_{N} over projected or iterated areas because the false exponent 2 on h was not removed [_{N} values. Such argumentation shows however little expertise in basic mathematics: all parabolas F_{N} = k h^{n} loose more and more of their flexure at increasing F_{N} for all exponents n. However the k values of parabolas depend strongly on the exponent n and even worse, k is not a dimensionless constant, but its dimension is [N/m^{n}]. The requirement of equal dimension on both sides of every equation has been poorly disregarded. The same mathematical error is made with exponent fitting: for example [^{−4}, but without dimensions. Why did the anonymous referees and editors of that paper not stop the print of such nonsense? The same paper [^{2}, which of course cannot prove anything. Also, any claim that such FE-calculations would reproduce experimental results are incorrect, even if such claim was made with curves on different pages in the same publication (e.g. in [

Despite such, unfortunately, continuing fights against the iteration-free mathematical treatment on the clear-cut physical foundation and mathematical proof [^{3/2} for the loading parabola [^{3/2}]. It is simply obtained as the slope of the first regression line (Equation (1) or Equation (2)) always with correlation coefficient >0.999 - 0.9999) of the Kaupp-plot before the first phase-transition onset. It provides also for the first time the checking of the experimental correctness of previous calibrating measurements [

The own measurements were performed with a fully calibrated Hysitron Inc. Triboscope^{(R)} Nanomechanical Test Instrument with 2D transducer and levelling device, connected to a Nanoscope AFM, using all of about 15,000 data pairs. The apex radii of the cube corner (55 nm) and Berkovich (110 nm) diamond indenter were directly measured by AFM in tapping mode. The levelling to ±1˚ was in x and y direction. Loading times were 30 s up to 10 mN load. Most initial data are from digitized published loading curves (Plot Digitizer 2.5.1 program; https://www.softpedia.com/) up to the microindentation regions with about 500 points. It was necessary for avoiding any bias suspicion that had sometimes been expressed by anonymous Reviewers. Fittings or iterations whatsoever were never performed. The crystal structure models were calculated using the Schakal 97 program [

The own or digitized data pairs of F_{N} and h were read into Excel^{(R)} for the calculation and print of the Kaupp-plot and calculation of the regressions up to and from the at first roughly judged kink position after the cut-off of the initial surface effect points. This is exemplified in _{1} and y_{2} that contain the slopes k and axis-cuts F_{a} (Equation (2)). The y denotes F_{N} and the x denote h^{3/2}, while the regression certainties are calculated as R^{2}. All transition energy values are normalized per force unit for the respective polymorph ranges.

We repeat here the evaluation formulas from [

F N = k h 3 / 2 . (1)

F N = k h 3 / 2 + F 1-a . (2)

W 1-applied = 0. 5 h kink ( F N-kink + F 1-a h kink ) . (3)

W 1-indent = 0. 8 W 1-applied . (4)

W 2-indent = 0. 4 k ( h 5 / 2 − h kink 5 / 2 ) + F 2-a ( h − h kink ) . (5)

full W applied = 0. 5 F N-max h max . (6)

W transition = full W applied − ∑ ( W applied ) . (7)

The slopes of the different linear branches (^{3/2}] (but not N/m^{2}). They are obtained together with the axis cuts (F_{a}). The initial

Material | k_{1} and k_{2} (mNµm^{3/2}) | F_{Nmax}_{ } (mN) | F_{Nkink} (mN) | h_{kink}_{ } (µm) | W_{transition}/mN (mNµm/mN) | Literature for Data Origin |
---|---|---|---|---|---|---|

Aragonite CaCO_{3} (-110) | 39.396 48.962 | 1.0 | 0.4086 | 0.04644 | 0.002758 | Kearney, Phys Rev Lett 2006, 96, 255505 |

Calcite CaCO_{3} (100)^{a)} | 17.911 23.176 | 10.0 | 0.3655 | 0.08266 | 0.01599 | Guillonneau, J Mater Res 2012, 22, 2551 |

Calcite CaCO_{3} (100)^{b)} | 33.156 48.943 | 40.0^{b)} | 11.869 | 0.4940 | 0.10692 | Presser, J Mater Sci 2010, 45, 2408 |

Sapphire Al_{2}O_{3} | 236.05 267.08 | 90.0 | 34.326 | 0.2763 | 0.13453 | Page, J Mater Res 1992 7 450 |

Zirconium dioxide ZrO_{2} | 134.74 210.88 | 33.0 | 8.7514 | 0.1665 | 0.02828 | Zeng, Acta Mater 2001, 49, 3539 |

Tungsten W | 95.57 114.50 | 85.0 | 35.607 | 0.5525 | 0.070059 | Oliver-Pharr, J Mater Res 1992, 7, 1584 |

InGaAs_{2} (001) | 36.272 32.477 | 2.7 | 1.2703 | 0.1070 | −0.005380 | Kaupp, Scanning 2013, 35, 392 |

Mica, Muscovite KAl_{2}[(OH,F)_{2}/AlSi_{3}O_{10})] | 34.522 3.566 | 50.0 | 11.556 | 0.4434 | 0.01016 | Hutchinson, Acta Metall Mater 40 295, 1992 |

Ce(C_{2}O_{4})_{2}(CO_{2}H) (001) “MOF” | 52.848 64.907 | 20.0 | 8.0745 | 0.3102 | 0.06554 | Tan, J Am Chem Soc 2009, 131, 14252 |

Pine latewood radial | 0.1342 0.1705 | 1.8 | 0.5469 | 2.5625 | 0.23926 | Brandt, Acta Biomater 2000, 6, 4345 |

Pine latewood axial | 0.2098 0.3043 | 3.0 | 0.9631 | 2.7638 | 0.36510 | ditto |

Saccharin (011)^{c)} | 1.9543 2.3179 | 6.0 | 1.7108 | 0.9426 | 0.08293 | Kira, Cryst Growth Design 2010, 10, 4650 |

Benzylidene-butyrolactone (010)^{c)} | 0.4807 0.5724 | 2.1 | 1.0634 | 1.6671 | 0.07893 | Kaupp, Angew Chem 1996, 35, 2774 |

^{a)}After initial twinning; ^{b)} second transition of calcite; ^{c)}cube corner indenter; the organic structures are in

surface effect (water layer, surface treatments, roughness, possible zero-error, tip rounding, etc) has to be carefully separated from the desired bulk properties. Its detailed elucidation requires separate indentation but at much lower depths (here up to 100 µN load). Most metals and semiconductors have hydrated oxide/hydroxide (rarely nitride) layers, often despite surface hardening by polishing. All of these contribute to F_{a} and have to be corrected for (Equation (2), Equation (3) and Equation (5)), but their varying values are not bulk materials constants and are thus not tabulated.

Phase-transitions upon indentations cover all types of materials and the penetration resistances = physical hardnesses) of the two branches in their Kaupp-plots (they profit from the physical and mathematical proved Equations (1)-(7). Typical examples are collected in _{N}- and h_{kink}-values do not systematically relate to their unprecedented transition-works that are normalized per mN of their ranges. We did not transform the mNµm or µNnm units into Joules for easier transformation possibility into different units. These quantities relate to the chemistry of the materials and the transitions can be mostly endothermic but also exothermic. It is seen that the less stable aragonite has a lower endothermic W_{transition} than the calcite polymorph. The second transition of calcite affords about 7 times more energy than its first one. Surprisingly, the W_{transition} of the very hard sapphire is only 8.4 times higher (at 94 times higher transition onset) than the first one of calcite. Furthermore, W_{transition} of sapphire is only 1.6 and1.7 times higher than the ones of the organic crystals in this _{2}O_{3} from its trigonal space group (R-3c) does not require considerable molecular migrations. The proportion of transition energies between Al_{2}O_{3} (m.p. 2050˚C) and ZrO_{2} (m.p. 2715˚C) (4.75 fold) is much higher than the one of physical hardnesses k (1.25 fold). This underlines the independence of transition energies from such qualities as hardness, or melting point, etc. The high pressure polymorphs of sapphire are probably either the orthorhombic (Pbcn) or the (Pbnm) polymorph of Al_{2}O_{3}, both with a volume decrease of 3.1% [_{2} (P2_{1}/c) transforms probably into the denser monoclinic polymorph (still P2_{1}/c) or the orthorhombic polymorph with (Pbcm) structure, both with higher density. The hard metal tungsten (m.p. 3400˚C) has a lower hardness than the two oxides, but its transition energy is 2.5 times higher than the one of ZrO_{2}, which is quite remarkable.

Surprisingly, the semiconductor InGaAs_{2} exhibits a significantly exothermic phase-transition, and mica (Muscovite) has a very low normalized endothermic transition energy, smaller than the two organics. Both of them experience very easy phase-transitions and they can only be detected by our iterative-free precise technique.

The metallorganic MOF, wood, and organics exhibit phase-transition energies that are not very different from the ones of the inorganics. The anisotropy of radial or circular pinewood is remarkable. Clearly, the non-iterative technique is very sensitive and avoids all of the strange recent techniques that are wiping out all of the important information from phase-transitions with incredible data treatments.

The phase-transitions of organic polymers under mechanical load are initial bond-breakings into radicals. This requires relatively high energy if these primary cleavage products are not stabilized by substituents. Therefore, their phase-transition onset must relate to the bond energies of the weakest chain bond. Further reactions of the so formed radical pairs are manifold, but overall there is hardening by cross-linking, which is well known for the technical treatments of polymers, e.g. upon extrusions, etc.

Polymer | k_{1} and k_{2 } mNµm^{3/2} | F_{N-max } (mN) | F_{N-kink } (mN) | h_{kink}_{ } (µm) | W_{transition}/mN mNµm/mN | Bond energy (kJ/mol^{a}^{)}) | Literature of data origin |
---|---|---|---|---|---|---|---|

hd-PE | 0.65776 1.08782 | 1.0 | 0.3247 | 0.6299 | 3.0159 | 363.2 | This work |

it-PP | 11.030 14.001 | 3.0 | 1.8840 | 0.3064 | 3.1463 | 362.3 | This work |

PS--6C | 0.02955 0.04303 | 0.450 | 0.1243 | 2.6202 | 0.5401 | 272.8 | CSM Webinar 14.02.2010 |

PMMA | 4.0252 4.9629 | 1.6 | 0.7758 | 0.3422 | 0.04116 | n.a.^{b}^{)} | Brisccoe, Appl Phys 1998, 31, 2315 |

Cast PC | 2.6385 3.3079 | 1.10 | 0.3779 | 0.2713 | 0.02083 | Loss of CO_{2} | ditto |

^{a)}86th Handbook of Chemistry and Physics, CRC Press, 2006; ^{b)}not available, probably loss of the side group rather than chain breakage.

(PS, 1.04 g/cm^{3}) decreases the bond energy, due to stabilization of the radicals, and thus also the phase-transition energy is decreased. The methylester groups in the side chain of polymethylmethacrylate PMMA (1.19 g/cm^{3}) are 13 times more effective with decreasing the transition energy when compared with polystyrene PS. The h_{kink} of PMMA is 7.7 times lower even though the required onset force is 6.2 fold higher. But it appears that the elimination of methylformate (HCO_{2}CH_{3}) is energetically easier than the chain breakage. Polycarbonate Macrolon^{(R)} (PC) contains no C-C breakage chain. But the ArO-C(O)OAr bond (Ar = aryl) is cleaved, starting the energetically favorable loss of CO_{2}. This is the largest decrease of phase-transition energy of the polymers in _{transition} when compared with the C-C breakage of PE. The analyses of cross-linked polymer indentations promise further interesting insights.

Material | k-value mNµm^{3/2} | h_{kink} (µm) | F_{N-kink} (mN) | W_{transition}_{ } mNµm/mN | Origin of Data |
---|---|---|---|---|---|

Soda Lime Glass | 77.909 105.28 122.01 | 0.4925 0.7739 1.1173^{a)} | 23.6782 58.9005 up to 120 mN | 0.1173 0.4744 0.6228^{b)} | Oliver-Pharr 1992, J Mater Res 7, 1584 |

Al (only the experimental) | 9.7181 11.613 | 1.2105 2.0997^{a)} | 12.1330 up to 32 mN | 0.1418 1.2095^{b)} | K. Zeng, Acta Mater 2001, 49, 3539 |

Al (only data up to 90 mN) | 12.036 13.377 | 3.1086 3.8963^{a)} | 60.4343 up to 90 mN | 0.2230 2.4958^{b)} | Oliver-Pharr 1992, J Mater Res 7, 1584 |

Si (001), B-doped, p-type | 112.14^{c) } 121.75 155.62 160.62 | 0.1501 0.2522 0.3309 0.4917^{a)} | 6.5328 15.2899 25.2002 up to 50 mN | 0.00687 0.02687 0.1942 0.3014^{b)} | T.F. Page, 1992, J Mater Res 7, 450 |

Si (100) | 123.2 145.44 151.53 | 0.4077 0.7245 0.81968^{a)} | 29.1622 81.0015 up to 100 mN | 0.1545 0.4684 0.5659^{b)} | S.V. Hainsworth 1996, J Mater Res 11, 1987 |

^{a)}h_{end} (µm); ^{b)}final W_{applied}/mN; ^{c)}k_{2} = 124.80 from a separate measurement up to 11 mN after cut-off of the initial effect at 1 mN, including the hydrated oxide layer.

Vickers, Brinell, Rockwell, etc. hardness measurements. Interestingly, already microindentations (mN to low N-ranges) are a rich but hitherto undetected field of consecutive phase-transitions. _{end} and W_{applied}/mN values indicate only the experimental range. The undoubtedly amorphous soda lime glass exhibits two endothermic phase-transitions at the microindentation range (sharp kinks with linear branches in the Kaupp-plot) and exists thus in 4 or together with the macroindentation 5 polymorphic forms, the structures of which are subject to further studies. We can only conclude from the absence of cracks or pop-ins that there are different degrees of density under load that increases the penetration resistance from state to state. The transition energies of the first two transitions of soda lime glass vary by a factor of roughly 4, which is quite remarkable. Aluminium requires about 12.1 and 60.4 mN load for its first and second phase-transition and its proper use as a calibration standard ends already below the values of the first one. Some onset-depths are still in a range of nanoindentations. Also the transition work for both transitions is similar to the one of much harder sapphire and smaller than the ones of pinewood (

The transitions of cubic silicon (Ed3m), exhibiting an exceptional pop-out of the unloading curve, found more theoretical interest. Several polymorphs (including an amorphous phase) were detected by electron diffraction, Raman spectroscopy, and electric conductance onset from the loading curve [_{N-kink} and the phase-transition energies W_{transition}. We have thus to consider how the Berkovich indenter with its skew faces at the face angle (semi angle θ = 65.3˚) interacts orthogonally with the interior of the crystal at the opposite angle, due to the penetrated Berkovich. The equally skew face structures around the Berkovich are calculated by rotations from the indented face by rx ± 65˚ and ry ± 65˚. This models 8 opposing skew faces because the corresponding rotations around 245˚ and 115˚ are mirrored or doubly mirrored.

the phase changes. Clearly, that makes them less endothermic. Conversely, in the correspondingly calculated

The multiple phase transitions of silicon (Berkovich) are also face specific and this is described in detail in Section 3.3,

The crystal of α-iron on (100) and (110) exhibits different exothermic phase-transition values. For strontium titanate with three endothermic phase-transition energies, two of them have closer together values, but the lowest and largest values are far apart. This is again not consistently reflected by the different onset forces and onset depths (

Material | k_{1} and k_{2 } µN/nm^{3/2} | Indenter | h_{kink}_{ } nm | F_{N-kink } µN | W_{transition} µNnm/µN | Data Origin |
---|---|---|---|---|---|---|

Fe (100) | 0.3590 0.2618 | Cube Corner | 103.0337 | 461.9156 | −40.0372 | Smith, Phys Rev B2003, 67 245405 |

Fe (110) | 0.2332 0.1986 | Cube Corner | 109.0949 | 358.9707 | −33.5112 | ditto |

SrTiO_{3} (100) | 3.0436 3.7145 | Berkovich | 69.7824 | 1738.2160 | 6.489 | Kaupp, Scanning 2013, 35, 392 |

SrTiO_{3} (110) | 2.5217 3.3841 | Berkovich | 65.7308 | 1355.4438 | 7.020 | ditto |

SrTiO_{3} (111) | 2.7591 4.0878 | Berkovich | 102.8636 | 2860.4600 | 14. 821 | ditto |

skew face at the semi-angle, which is θ = 35.26˚ for the cube corner. A rotation from the surface faces around x and y by ±35˚ yield these skew surfaces. The eight by 35˚inclined faces around the three-sided indenter pyramid are completely represented with only two images for symmetry reasons of the bcc cubic crystal under (100) (

The crystal face on (100) and the skew faces under it in

Conversely,

The analogous analysis has been successful with the exothermic phase-transition of α-SiO_{2} with cube corner in [

As already shown for the endothermic phase-transitions of silicon in Section 3.3, the analysis of the strontiumtitanate using Berkovich with θ = 65.3˚ is equally successful (not imaged here, due to many images that are required). The minimal endothermic work (6.5 µNnm/µN) is required under (100), where channels are available on the skew faces to facilitate the conversion. Conversely, under (111) the strongest endothermic energy (14.8 µNnm/µN) is observed, as there are no channels at the skew faces that enforce the transition to stay blocked

in space, which increases the endothermic work. Consistently, under (110) the value (7.0 µNnm/µN) stays between the extremes, as there are some smaller channels allowing for minor migration of the transformed material. Again, channels facilitate migrations for the endothermic phase-transitions and decrease the endothermic work. When migrations are blocked more work is required for the phase-transition. The face-dependency of phase-transition energies is thus well understood by crystal structure analysis.

The sudden first order sharp phase-transitions form polymorph interfaces that are shifted away from the indenter after their onset when the load increases. These polymorph interfaces are preferential sites for the nucleation of large far-distant cracks. This has already been imaged in connection with the multiple consecutive phase-transitions of sodium chloride in [_{trans} in

Material | max. F_{N } µN | k_{1},k_{2} and k_{3 } µN/nm^{3/2} | h_{kink}; h_{end}_{ } nm | F_{N-kink } µN | W_{transition}_{ } µNnm/µN | Data Origin |
---|---|---|---|---|---|---|

γ-TiAl^{a}^{)} | 3000 | 0.3213 0.4353 | 312.100 | 1787.7591 | 25.0885 | Zambaldi 2010, Acta Mater 58, 3516 |

Zr_{41}Ti_{14}Cu_{12.5}Ni_{10}Be_{22.5}^{a) } Vileroy105 | 500,000 | 0.90332 1.14282 | 2532.967 | 107,930.106 | 291.4861 | Moser 2006, Phil Mag 86, 5715 |

Fe_{43}Cr_{16}Mo_{16}C_{15}B_{10} (I)^{b)} | 7.21378 9.54375 | 505.499 1021.109 | 74,517.819 | 87.3435 | Li, Intermetallics, 2007, 15, 706 | |

Fe_{43}Cr_{16}Mo_{16}C_{15}B_{10} (II)^{c)} | 300,000 | 11.64109 | 2532.967 | 176,653.607 | 176.2607 | ditto |

Mg_{65}Cu_{25}Gd_{10}^{b)} | 62,000 | 1.53921 1.93759 | 846.241 | 36,893.360 | 105.5932 | ditto |

Cu_{60}Zr_{30}Ti_{10}(I)^{b)} | 2.1803 2.6791 | 158.674 245.244 | 4056.1699 | 21.9236 | Jiang, Mater Sci Eng, A2006, 430, 350 | |

Cu_{60}Zr_{30}Ti_{10}(II)^{c)} | 18,000 | 2.8397 | 366.2825 | 8999.645 | 141.8416 | ditto |

^{a)}Cube corner; ^{b)}Berkovich; ^{c)}Second transition.

the alloy’s use beforehand. However, these published examples do certainly not represent alloys that are in practical use, as the actual alloys are secret and only available to the industrial personnel.

_{2}O_{3}, ThO_{2}, La_{2}O_{3}, Al_{2}O_{3}, etc. [_{1}= 0.90332 µN/nm^{3/2} or with other units 29.652 mN/µm^{3/2}) that are much smaller than those of Fe_{43}Cr_{16}Mg_{16}C_{15}B_{10} (k_{1}= 7.21378 µN/nm^{3/2} or with other units 228.12 mN/µm^{3/2}), while the W_{transition} ratio is 291/87, respectively. The Newton-range is almost reached with Vileroy-105. Its first transition is at highest force and also the transition energy is highest, whereas the well-known iron-based superalloy surmounts the kink force only at its second phase-transition but with much lower transition energy. The magnesium based alloy is inferior and the copper-based alloy has two phase-transitions at still lower forces and transition energies.

The here achieved maximal loading forces (0.5 N, corresponding to HV 0.05) are at or below the lower level of industrial Vickers, Brinell, Rockwell, etc. hardness measurements. These are certainly highly standardized by ASTM, but unable to detect phase-transitions. It is to be expected that further as yet undetected phase-transitions will occur at the much higher loads (for example from Vickers hardness HV 0.5 to HV 10) in all cases.

The field of superalloys for technical constructions is widespread and extremely important, and so is the improvement of the stability of superalloys when being at work. Any alloy must only be admitted to forces below its first phase-transition onset. Both the onset force and the transition energies must be as high as possible. We present here a simple systematic way to improve the engineers’ efficiency, but this depends on the profound change of the present ISO and ASTM standards that are the basis of the manufacturer’s certification. Physical mathematically proved standards must be urgently created, edited, and enforced. Present ISO-ASTM hardness or indentation moduli are not physical quantities and they are unsuitable for the safety. Their biggest flaw is their inability to detect or even know of phase-transitions under load. The here described improvements are, of course, worldwide indispensable, but unfortunately not easily achieved for various unscientific reasons.

We showed here that undeniable sacrosanct basic calculation rules prove the physically founded Equation (1) [

The authors declare no conflicts of interest regarding the publication of this paper.

Kaupp, G. (2019) Physical Nanoindentation: From Penetration Resistance to Phase-Transition Energies. Advances in Materials Physics and Chemistry, 9, 103-122. https://doi.org/10.4236/ampc.2019.96009