Recent Updates on Volume, Side-Area, and Force Direction of Berkovich and Cubecorner Indenters

To shed new light on this crucial area of study and application, a thorough explanation and extension of the iteration-free physical description of pyramidal indentations using closed mathematical equations are provided. All computations are easily repeatable and ought to be encoded into instruments by their manufacturers to make general use even simpler. The resulting forces and force directions are inferred and presented, along with formulas for the volumes and side-areas of Berkovich and cubecorner as functions of depth. The full comparison of various indenters on the mathematical reality is made possible by all of these. The values of pyramids are significantly different from those of so-called "equivalent cones." The worldwide use of such pseudo-cones is in severe error. Disproved is the previously asserted and employed 3 times greater displacement volume with cube corner than with Berkovich. At the same applied force, both move the same amount. Experimental evidence is used to support the previously unreported mathematical findings for both the sharp-onset phase transitions and the physical indentation hardness. Phase-transition energies are calculated. New fundamental insights are provided by comparing the two indenters. The phase transition onset force is identical for isotropic materials, but the transition energy is greater at the cube corner due to a higher force and flatter force direction. The cube corner is now eligible for studies on fracture toughness. The alleged "friction with the indenter" is not what causes the pile-up. Under pressure, sliding along cleavage planes and channels occurs in anisotropic materials both internally and externally. The depression volume is increased by their volumes. These quantities are crucial for managing pile-ups in the best possible way. Crack-nucleating polymorph interfaces are created during phase transitions. Technical materials must be created with onset forces greater than the maximum stresses imaginable (at airliners, bridges, etc.). This requires urgent revision of ISO 14577-ASTM standards.