全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

Multiplication with the Factor One, a Rare Mathematic Tool for Simplification and Unrevised DIN-ISO-ASTM-14577

DOI: 10.4236/apm.2025.151004, PP. 91-105

Keywords: Instrumental Indentation, One-Point, Spherical, Arithmetic Formulas, Reformulation, Factor One, Twinning Standards, Zerodur, Undue Fittings, Erroneous Standards, DIN-ISO-ASTM-14577 Revision, Petition, Energy-Law-Violation, Faked Data

Full-Text   Cite this paper   Add to My Lib

Abstract:

The search for mechanical properties of materials reached a highly acclaimed level, when indentations could be analysed on the basis of elastic theory for hardness and elastic modulus. The mathematical formulas proved to be very complicated, and various trials were published between the 1900s and 2000s. The development of indentation instruments and the wish to make the application in numerous steps easier, led in 1992 to trials with iterations by using relative values instead of absolute ones. Excessive iterations of computers with 3 + 8 free parameters of the loading and unloading curves became possible and were implemented into the instruments and worldwide standards. The physical formula for hardness was defined as force over area. For the conical, pyramidal, and spherical indenters, one simply took the projected area for the calculation of the indentation depth from the projected area, adjusted it later by the iterations with respect to fused quartz or aluminium as standard materials, and called it “contact height”. Continuously measured indentation loading curves were formulated as loading force over depth square. The unloading curves after release of the indenter used the initial steepness of the pressure relief for the calculation of what was (and is) incorrectly called “Young’s modulus”. But it is not unidirectional. And for the spherical indentations’ loading curve, they defined the indentation force over depth raised to 3/2 (but without R/h correction). They till now (2025) violate the energy law, because they use all applied force for the indenter depth and ignore the obvious sidewise force upon indentation (cf. e.g. the wood cleaving). The various refinements led to more and more complicated formulas that could not be reasonably calculated with them. One decided to use 3 + 8 free-parameter iterations for fitting to the (poor) standards of fused quartz or aluminium. The mechanical values of these were considered to be “true”. This is till now the worldwide standard of DIN-ISO-ASTM-14577, avoiding overcomplicated formulas with their complexity. Some of these are shown in the Introduction Section. By doing so, one avoided the understanding of indentation results on a physical basis. However, we open a simple way to obtain absolute values (though still on the blackbox instrument’s unsuitable force calibration). We do not iterate but calculate algebraically on the basis of the correct, physically deduced exponent of the loading force parabolas with h3/2 instead of false

References

[1]  Ebenstein, D.M. and Wahl, K.J. (2006) A Comparison of JKR-Based Methods to Analyze Quasi-Static and Dynamic Indentation Force Curves. Journal of Colloid and Interface Science, 298, 652-662.
https://doi.org/10.1016/j.jcis.2005.12.062
[2]  Kaupp, G. (2018) Six Polymorphs of Sodium Chloride upon Depth-Sensing Macroindentation with Unusual Long-Range Cracks Requiring 30 N Load. Journal of Material Science & Engineering, 7, 473-483.
https://doi.org/10.4172/2169-0022.1000473
[3]  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
[4]  Kaupp, G. (2020) Valid Geometric Solutions for Indentations with Algebraic Calculations. Advances in Pure Mathematics, 10, 322-336.
https://doi.org/10.4236/apm.2020.105019
[5]  Kaupp, G. (2020) Real and Fitted Spherical Indentations. Advances in Materials Physics and Chemistry, 10, 207-229.
https://doi.org/10.4236/ampc.2020.1010016
[6]  Kaupp, G. (2024) A Way out of World-Wide Indentation Dichotomy in Materials’ Science. Modern Concepts in Material Science, 6, 2-5.
https://doi.org/10.33552/mcms.2024.06.000634
[7]  Kaupp, G. (2013) Penetration Resistance: A New Approach to the Energetics of Indentations. Scanning, 35, 392-401.
https://doi.org/10.1002/sca.21080
[8]  Kaupp, G. (2015) The Physical Foundation of fn = kh3/2 for Conical/Pyramidal Indentation Loading Curves. Scanning, 38, 177-179.
https://doi.org/10.1002/sca.21223
[9]  Oliver, W.C. and Pharr, G.M. (1992) An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments. Journal of Materials Research, 7, 1564-1583.
https://doi.org/10.1557/jmr.1992.1564

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133