Basic Mathematics for Physically Correct Mechanical Properties from Indentations

This book dealt with basic mathematics for physically correct mechanical properties from indentations. 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. The book also stated the force vs depth loading curves of conical, pyramidal, wedged and for spherical indentations on a strict mathematical basis by explicit use of the indenter geometries rather than on still world-wide used iterated “contact depths” with elastic theory and violation of the energy law. The book also specified physical deduction of the loading curves for spherical and flat punch indentations, in particular as the parabola assumption for not self-similar spherical impressions appears impossible. This book contains various materials suitable for students, researchers and academicians. Keywords: Depth-sensing indentations with conical, pyramidal, spherical, and flat indenters pop-in repair pile-up reasons basic algebra and trigonometry with calculation rules challenge of false ISO 14577-ASTM standards with ISO-H, ISO-Er, HV, etc and energy law violation undue data-treatment, fitting, iteration, and simulation correct loading curve formulas H/E ratio challenge false historical concepts and false Johnson formula physical hardness=penetration resistance k (mN/µm3/2) physical hardness=penetration resistance k (mN/ m3/2) physical indentation modulus Er-phys without iteration force direction and side-area pyramids' non-equivalence with pseudo cones phase-transition onset and transition energy detection catastrophic crack nucleation at ( multiple) polymorph intersections long-range cracks formation applications in crystallography for crystal structures failure of technical materials including airliners turbines, bridges, superalloys, etc earth sub-mantle crust exploration and earth quakes comparison with anvil pressurizations detailed interpretations in solid-state chemistry, plastics, biology, and medicine chances for updates for reliable mechanical intelligence, requiring warning and case-wise new indentation