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The analysis of nanoindentation force data are based on Sneddon’s solution for a linear elastic half space with a rigid axisymmetric indenter. Berkovich indenters commonly used in indentation experiments are normally modeled as cones. The idea of effective tip shape was presented to better explain the behavior of the unloading curve and pressure distribution under the tip in real experiments. We examine the concept of effective tip in three dimensions by importing real indenter metrology by atomic force microscope directly into finite element analysis and simulate fused silica indentation experiments. We show that fitting the elastic reloading curves overestimates the elastic modulus of fused silica. This is explained by studying the pressure distribution at maximum depth under the effective tip. While the effective tip describes the problem geometrically, it is believed that neglecting the deformed zone in the indented material is responsible for over estimating the modulus value.
Nanoindentation results are very sensitive to tip rounding and neglecting the value of the tip radius produces erroneous estimation of the material elastic properties. In this study we investigate the effect of tip radius on the estimation of the Elastic modulus by means of finite element analysis of Berkovich and conical tips with different tip radii. Our numerical results were already supported by an experimental study on fused silica with Berkovich tips with different tip radii. The use of classical Oliver Pharr equation overestimated the Elastic modulus. A new analytical model that modifies the Oliver Pharr equation to consider the value of the tip radius is employed to derive the Elastic modulus from load displacement curves yielding improved results compared to the classical Oliver Pharr equation.
The relation between intra-operative gas exchange and post-operative oxygen saturation was examined using pulse oximetry (SpO2) 30 h after anaesthesia for upper abdominal surgery. The inspired oxygen partial pressure (PIO2) was varied during anaesthesia to produce a plot of PIO2 vs. SpO2. Gas exchange during anaesthesia was inferred from the relation between PIO2 and SpO2 which was described by its lateral and vertical displacement away from the position of a standard oxygen dissociation curve. With patients breathing air, the SpO2 was measured over a 10-min period at 30 h after surgery. The correlation coefficient of the lateral displacement with post-operative SpO2 was 0.7, and that of the vertical displacement with post-operative SpO2 was 0.66. The correlation coefficient of intra-operative SpO2 at PIO2 = 21 kPa with post-operative SpO2 was 0.69. It can be concluded that gas exchange abnormalities during anaesthesia deduced from the displacement of the PIO2 vs. SpO2 curve correlate with SpO2 30 h post-operatively and may help to identify patients at risk of post-operative hypoxaemia.
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