Basic Mathematics for Physically Correct Mechanical Properties from Indentations

This open-access E-Book collects all of the 16 open-access publications with the author’s challenges of false treatments of indentation data in the literature in an up scaled form with cross linking to the more recent results and some replacements of older formulas. Not all of them could be developed in one publication at a time. It depicts the advancements from 2016 to 2022 on the basis of now mathematically deduced empirical results with closed and universal formulas for all types of solid materials. The enforcing ISO 14577 techniques can still not detect the more than common phase-transitions under mechanical stress with formation of dangerous polymorph interfaces. Their now very easy detection (actually since 2004) helps to avoid dangerous failures by cracks in airliners, bridges, buildings, polymers, commodities, etc. This affords only the physically correct calculation of the materials’ mechanical properties without relying on data-treatments, fittings, iterations, and simulations with not repeatable extremely complicated assumptions for concurring with false historical equations.

This will help the scientist, teacher, anonymous reviewer, editor, technician, journalist, and certification agent for more easily finding out how urgent is it to strengthen the falsification of the still not revised ISO-14577- ASTM enforcing standards. ISO-ASTM, industry and academic publications must stop with accepting violation of the energy law. And mechanical intelligence must be freed from faked tabulated mechanical properties, always requiring reliable re-determinations. This is particularly important for one-point technical indentation results that characterise unknown polymorphs depending on the applied very high forces.

Indentations with cones, pyramids, and spheres are described on the basis of sacrosanct calculation rules for mathematically founded closed universal formulas for the dept sensing loading curves. These can locate data-fittings in published loading curves, handle peculiarities like initial surface effects, pop-ins, gradients, pile-ups and of course phase-transition onset and transformation energies. The errors from the ISO-ASTM 14577 standardisations are extremely large and further increased by their false attribution of “equivalent” cone angles to the pyramids for decreasing computer times in simulations. We replace the wrong exponent 2 on depth h versus normal force F_N instead of correctly 3/2 for cones and pyramids, and deduce the variable R/h containing correction factor for spheres. We define the physical indentation hardness and the physical indentation modulus instead of iterated ISO-H and ISO-“Young’s” modulus E_r. Spherical indentations are compared with anvil pressurizations.

The very precisely calculated applications cover all kinds of materials technology, solid-state chemistry, mineralogy, biology, earth crust geology. Actually, all applicants have to be aware of a multitude of not general and extremely complicated multiple simulation schemes and fitting formulas, but that requirement is now removed thanks undeniable calculation rules.  And there arise liability problems against uneducated students and in the case of catastrophic failures of technical materials (crashes of airliners, bridges, buildings, earth quakes, commodities, etc). Not criticised is ISO 14577 valuable high-level standardization for correct experimentation. But properly revised indentation analyses remain a very important fast characterization technique for all kinds of solid materials. Depth-sensing indentations become even more important by this E-Book, despite the deplorable present situation by unappreciated physical correctness.