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

作　　者：Gerd Kaupp Gerd Kaupp(University of Oldenburg, Oldenburg, Germany)

机构地区：[1]University of Oldenburg, Oldenburg, Germany

出　　处：《Advances in Materials Physics and Chemistry》2021年第11期212-241,共30页材料物理与化学进展（英文）

摘　　要：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</span></span><span style="white-space:normal;"><span style="font-family:"">- </span></span><span style="white-space:normal;"><span style="font-family:"">tions with calculated transition energy. The comparison of both indenters pro</span></span><span style="white-space:normal;"><span style="font-family:"">vides 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</span></span><span style="white-space:normal;"><span style="font-family:""> </span></span><span style="white-space:normal;"><span style="font-family:"">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</span></span><span style="white-space:normal;"><span style="font-family:""> under pressure</span></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</span></span><span style="white-space:normal;"><span style="font-family:"">- </span></span><span style="white-space:normal;"><span style="font-family:"">tions with calculated transition energy. The comparison of both indenters pro</span></span><span style="white-space:normal;"><span style="font-family:"">vides 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</span></span><span style="white-space:normal;"><span style="font-family:""> </span></span><span style="white-space:normal;"><span style="font-family:"">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</span></span><span style="white-space:normal;"><span style="font-family:""> under pressure</span></

关 键 词：Closed Mathematical Formulas Force Direction Indenter Volumes and Side-Areas Iteration-less Calculations Equal Base-Area Cones PILE-UP Phase-Transition-Onset and -Energy 

分 类 号：O17[理学—数学]