Abstract
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.
Highlights
Instrumented indentations require proper calibrations and physically correct analysis
The iterated standard values of hardness H and modulus Er that use the maximal force are in error for all 5 examples: the faulty calibration adds to the unphysical h2, the energy law violation, and the non-consideration of the phase transition onsets that occur before that load
Further phase transitions are detected in macro-indentations for example sapphire transforms at about 12 N load and 5.9 μm depth [2], and so does soda-lime glass at about 14 N at 11.7 μm when the loading curves with a Vickers indenter of [19] are analyzed with the Kaupp plot
Summary
Instrumented indentations require proper calibrations and physically correct analysis. Even worse is the data treatment according to the ISO14577 standard (of the International Organization for Standardization), accepting the highly acclaimed Oliver-Pharr method [3]. As generally known, this is based on very complicated mathematical deductions that clearly forgot to take into account the sidewise forces and energies at conical penetrations. This is based on very complicated mathematical deductions that clearly forgot to take into account the sidewise forces and energies at conical penetrations Their deduced normal force (FN)-depth square (h2) proportionality [4] [5] is invalid. This was published electronically in 2016 and open access in 2017
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