Non-iterative analysis of indentation results allows for the detection of phase transitions under load and their transition energy. The closed algebraic equations have been deduced on the basis of the physically found...Non-iterative analysis of indentation results allows for the detection of phase transitions under load and their transition energy. The closed algebraic equations have been deduced on the basis of the physically founded normal force ?depth3/2 relation. The precise transition onset position is obtained by linear regression of the FN = kh3/2 plot, where k is the penetration resistance, which also provides the axis cuts of both polymorphs of first order phase transitions. The phase changes can be endothermic or exothermic. They are normalized per μN or mN normal load. The analyses of indentation loading curves with self-similar diamond indenters are used as validity check of the loading curves, also from calibration standards that exhibit previously undetected phase-transitions and are thus incorrect. The phase-transition energies for fused quartz are determined from the loading curves from instrument provider handbooks. The anisotropic behavior of phase transition energies is studied for the first time. Quartz is a useful test object. The reasons for the packing-dependent differences are discussed on the basis of the local crystal structure under and around the inserting tip.展开更多
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 app...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></span><span style="white-space:normal;"><span style="font-family:"">, both to the surface and internally. Their volumes add to the depression volume. These volumes are essential for the exemplified pile-up management. Phase-transitions produce polymorph interfaces that are nucleation sites for cracks. Technical materials must be developed with onset forces higher than the highest thinkable stresses (at airliners, bridges</span></span><span style="white-space:normal;"><span style="font-family:"">,</span></span><span style="white-space:normal;"><span style="font-family:""> etc</span></span><span style="white-space:normal;"><span style="font-family:"">.</span></span><span style="white-space:normal;"><span style="font-family:"">). This requires urgent revision of ISO 14577-ASTM stan</span></span><span style="white-space:normal;"><span style="font-family:"">dards.展开更多
文摘Non-iterative analysis of indentation results allows for the detection of phase transitions under load and their transition energy. The closed algebraic equations have been deduced on the basis of the physically founded normal force ?depth3/2 relation. The precise transition onset position is obtained by linear regression of the FN = kh3/2 plot, where k is the penetration resistance, which also provides the axis cuts of both polymorphs of first order phase transitions. The phase changes can be endothermic or exothermic. They are normalized per μN or mN normal load. The analyses of indentation loading curves with self-similar diamond indenters are used as validity check of the loading curves, also from calibration standards that exhibit previously undetected phase-transitions and are thus incorrect. The phase-transition energies for fused quartz are determined from the loading curves from instrument provider handbooks. The anisotropic behavior of phase transition energies is studied for the first time. Quartz is a useful test object. The reasons for the packing-dependent differences are discussed on the basis of the local crystal structure under and around the inserting tip.
文摘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></span><span style="white-space:normal;"><span style="font-family:"">, both to the surface and internally. Their volumes add to the depression volume. These volumes are essential for the exemplified pile-up management. Phase-transitions produce polymorph interfaces that are nucleation sites for cracks. Technical materials must be developed with onset forces higher than the highest thinkable stresses (at airliners, bridges</span></span><span style="white-space:normal;"><span style="font-family:"">,</span></span><span style="white-space:normal;"><span style="font-family:""> etc</span></span><span style="white-space:normal;"><span style="font-family:"">.</span></span><span style="white-space:normal;"><span style="font-family:"">). This requires urgent revision of ISO 14577-ASTM stan</span></span><span style="white-space:normal;"><span style="font-family:"">dards.
