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Volume, Side-Area, and Force Direction of Berkovich and Cubecorner Indenters, Novel Important Insights

Advances in Materials Physics and Chemistry 2021年第11期11卷 212-241页

作者： Gerd Kaupp University of Oldenburg Oldenburg Germany

The iteration-free physical description of pyramidal indentations with closed mathematical equations is comprehensively described and extended for creating new insights in this important field of research and applications. All calculations are easily repeatable and should be programmed by instrument builders for even easier general use. Formulas for the volumes and side-areas of Berkovich and cubecorner as a function of depth are deduced and provided, as are the resulting forces and force directions. All of these allow for the detailed comparison of the different indenters on the mathematical reality. The pyramidal values differ remarkably from the ones of so-called “equivalent cones”. The worldwide use of such pseudo-cones is in severe error. The earlier claimed and used 3 times higher displaced volume with cube corner than with Berkovich is disproved. Both displace the same amount at the same applied force. The unprecedented mathematical results are experimentally confirmed for the physical indentation hardness and for the sharp-onset phase-transi- tions with calculated transition energy. The comparison of both indenters provides novel basic insights. Isotropic materials exhibit the same phase transition onset force, but the transition energy is larger with the cube corner, due to higher force and flatter force direction. This qualifies the cube corner for fracture toughness studies. Pile-up is not from the claimed “friction with the indenter”. Anisotropic materials with cleavage planes and channels undergo sliding along these

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Exciting News from Indentations onto Silicon, Copper, and Tungsten

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Journal of Applied Mathematics and Physics 2023年第12期11卷 4042-4078页

作者： Gerd Kaupp Department of Chemistry University of Oldenburg Oldenburg Germany

Indentations onto crystalline silicon and copper with various indenter geometries, loading forces at room temperature belong to the widest interests in the field, because of the physical detection of structural phase transitions. By using the mathematically deduced FNh3/2 relation for conical and pyramidal indentations we have a toolbox for deciding between faked and experimental loading curves. Four printed silicon indentation loading curves (labelled with 292 K, 260 K, 240 K and 210 K) proved to be faked and not experimental. This is problematic for the AI (artificial intelligence) that will probably not be able to sort faked data out by itself but must be told to do so. High risks arise, when published faked indentation reports remain unidentified and unreported for the mechanics engineers by reading, or via AI. For example, when AI recommends a faked quality such as “no phase changes” of a technical material that is therefore used, it might break down due to an actually present low force, low transition energy phase-change. This paper thus installed a tool box for the distinction of experimental and faked loading curves of indentations. We found experimental and faked loading curves of the same research group with overall 14 authoring co-workers in three publications where valid and faked ones were next to each other and I can thus only report on the experimental ones. The comparison of Si and Cu with W at 20-fold higher physical hardness shows its enormous influence to the energies of phase transition and of their transition energies. Thus, the commonly preferred ISO14577-ASTM hardness values HISO (these violate the energy law and are simulated!) leads to almost blind characterization and use of mechanically stressed technical materials (e.g. airplanes, windmills, bridges, etc). The reasons are carefully detected and reported to disprove that the coincidence or very close coincidence of all of the published loading curves from 150 K to 298

关键词： phase-transition-onset and -energy Indentation of Silicone Copper Copper Nanoparticles Tungsten with Polymorphs Low-Temperature Indentations Detection of Faked Loading Curves Protection of AI from False Advices Risk of Catastrophic Crashes Physical Hardness Exothermic Copper-transitions Algebraic Calculations Negative-Standard-energy Polymorphs

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