Dilemma between Physics and ISO Elastic Indentation Modulus

Abstract

This paper challenges the ISO standard 14577 that determines the elastic indentation modulus by violating the first energy law, and omitting easily detected phase change onsets as well as initial surface effects under load. The double iteration for incorrect fitting indentation modulus to Hook's law Young's modulus of a standard with up to 11 free parameters must be cancelled and discontinued. The iterative evaluation of the elastic modulus E r-ISO can by far not be reproduced by iteration-free direct calculation of E r , when using the underlying formulas for S, h c , A hc , and . For cubic aluminium the divergence amounts to a factor of 3.5 or 3.1, respectively (both smaller for the non-iterated calculations). Every interpretation of indentation moduli as single unidirectional "Young's moduli" is false. They are mixtures from all directions and include shear moduli. The three different packing diagrams of body centered cubic -iron exemplify the mixture of three independent Young's moduli (and thus also three shear moduli) even in this simple but already anisotropic case. More linear moduli ensue in lower symmetry crystals as exemplified with -quartz. The first physical indentation modulus is deduced by removal of the physical errors of E r-ISO , or after indenter compliance correction E ISO . E phys does no longer violate the energy law. Five face-dependent elastic indentation moduli of -quartz at the obsolete E r-ISO level and two tensional Hook-law Young's moduli are compared with all of its six resonance ultrasound spectroscopy (RUS) evaluated Young's moduli, and with the bulk modulus. The dilemma between ISO and physics is particularly detrimental, as E ISO is used for the calculation of very frequently applied mechanical parameters. These propagate the errors into failure risks of falsely calculated materials with severe violation of the basic energy law and other physical laws for daily life. Difficulties with the urgent settlement by new ISO standards are discussed. First suggestions for the use of E phys , or S phys , or eventually measured bulk modulus K are made. This should be urgently evaluated and discussed.

Undue Hardness/Modulus Ratio Claims instead of Physical Penetration Resistance and Applications with Mollusk Shells

“…[17] with similar H/E ratios containing log/log plots. Unfortunately, E r numbers are not well defined and depend strongly on the details of their detection, as outlined in [9], so that one has to choose from sometimes extremely different values for E r when comparing different methods.…”

“…It is empirically known since 2004 [4] and 2013 with extensive table for all types of materials [5] and undoubtedly physically deduced one year before 2016 [3] and also in 2020 [6] that pyramidal and conical indentations follow the exponent 3/2 on the depth h (but not 2) in the force (F N ) vs depth curves, the slope of which is the penetration resistance, that is the physical hardness when calibrated with the indenter cone or effective cone. It was deduced in 2013 [7] and in 2017 [8] that the Oliver-Pharr iterations that are still ISO 14577 standard violate the energy law for hardness H [7] and in 2017 [8] also for E r since 2017 [9] (ISO denotes International Standardization Organization). Furthermore, elastic moduli from indentations are not "Young's moduli", as used in [1] and [2].…”

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

“…The first goals of indentations are hardness and elastic modulus and when these are unphysical, their errors are perpetuated in the there from defined further characterizations of the materials. For example 12 different applications of the indentation modulus from viscoelasticity to fracture toughness are listed in [18].…”

Real and Fitted Spherical Indentations

“…The second obvious error is claiming "Young's modulus" that is a unidirectional property, totally different from an indentation modulus. A very complex "equation for fitting" of the depth values is published as equation (9) in (6) [6] is penetration depth; P is "load" (force). The "fit parameters" are a 0 and P adh .…”

“…The therefrom determined "Young's moduli" are dangerously misleading. The enormous trouble when Young's moduli are equalized with indentation moduli has been amply exemplified in [9]. The publication of moduli from "fitted" data [6] They shall help to repeat the mechanical characterization with true experimental data, when these are unavailable from the recent authors for genuine publications.…”