Hardness contour and heat maps were developed using data analysis and graphing software by Origin Pro 2018b. Fig.1shows the superimposed heat map of a 6× 6 indent matrix upon the post-indent SEM image. The B,G and W letters mentioned in Fig.5specify the indents located precisely on Black, Grey and White phases, respectively. The indent data points are colour coded ac-cording to their values. Superimposition of the hardness heat map onto the post-indent SEM image in Fig.1reveals that the hardness distribution at the nano-scale is inhomogeneous throughout the coating microstructure.
Fig.1. Superimposition of statistically analysed heat map on post-indent SEM image of an indentation matrix of 6x 6 indents to reveal variability in hardness distribution at the local level among different z-contrast phases denoted as B,G and W.
Microstructure-mechanical property mapping is depicted in Fig.2 where the hardness and reduced elastic modulus contour map is laid over the post-indent SEM image. Nanoindentation mapping was performed for a matrix of 6× 6 indents(36 indents)within an area of 50×50 um2using the XPM technique. Initially,the area of interest focused on a region where the three phases were observable under SEM. The identical area was identified through in-situ SPM imaging. After nanoindentation, the area was scanned using in-situ SPM to capture the post-indentation image(Fig.2(a)); which was followed by post-indent SEM(Fig.2(b)).A hardness contour map was coupled with the hardness values andsuperimposed on the post-indent SEM image(Fig.2(c)).A similar model was followed for reduced elastic modulus mapping(Fig.2(d)). Superimposing the images revealed the correlation be-tween microstructure and mechanical properties at local levels. The hardness and reduced elastic modulus variation among different phases is distinctly revealed and the influence at phase boundaries is noticeably visible.
Fig.2(a) is an in-situ SPM image of the coating cross section after indentation has been carried out. The image contrasts correspond to topological variations in the surface where the hills and valleys correspond to harder and softer phases, respectively; and which are created by preferential polishing of the softer phase. This is thus a qualitative indicator of the hardness differences of the various phases. On the other hand, Fig.2(b) is the BSE-SEM image delin-eating the identity of the various phases in the coating. BSE-SEMafter XPM mapping is vital for identifying the exact location of the indents: that is, whether they fall completely within a phase, or at a phase interface. This is important because,(i) in the formercase, the nanohardness can be attributed to that specific phase, while(ii) in the latter case, the nanohardness value is akin to a weighted average of the two phases, depending on the area of theindent falling on either side of the phase boundary. These three features(SPM, BSE-SEM and XPM) are combined to develop XPM maps shown in Fig.2(c) and (d) for nanohardness and reduced elastic modulus, respectively.
Hardness measured by nanoindentation is a function of the sample material response only(equation (1)), whereas Er in-corporates compliance from the indenter(equation(2)). For thisreason, the nanohardness value distinguishes between the alloy and oxide phases within the APS-HEA coating(Fig.2(c)). Calcula-tion of E from the Er values depend on the Poisson's ratios of the respective phases, which can only be estimated. For this reason, the Er map looks largely homogeneous(Fig.2(d)), whereas nanohard-ness maps identify regions rich in alloy or oxide splats. As it was stated in an earlier section,B phase possesses higher hardness compared to G and W phases due to oxide formation, crystal structure and chemistry(Fig.2(c)). In contrast, the reduced elastic modulus showed little difference with respect to the different phases; but follows a similar pattern as hardness mapping at the coating defect location (Fig.2(d)). More importantly, microstructure-mechanical property mapping demonstrates the transition of hardness at the phase interface, which follow a step-by-step decrement instead of a rapid change(Fig.2(c)).
There is also an inherent issue of differences in resolution offered by XPM concerning the size and irregular shape of themicrostructural splats in the coatings. As mentioned earlier,a spacing of 8 um was maintained between indents to avoid overlap between neighbouring indents. Therefore, the contouring function must interpolate values between the two measured data points. As learned recently from Phani et al.[57], the inter-indent spacing can be safely reduced further; hence the resolution of XPM maps for such microstructures may be improved.
The microstructure-mechanical property mapping technique precisely evaluates the localized disparity in properties which, in conjunction with statistical analysis, uncovers mechanical property-microstructural relationships that are obfuscated by traditional Vickers indent methods. The mapping technique boosts both the resolution limit and functionality of the nanoindentation test.A matrix of indents can be spatially arranged over the desired microstructure and variability in mechanical properties across the microstructure can be determined using statistical analysis.
Fig.2.(a) Post-nanoindentation mapping image obtained by in-siru scanning probe microscopy,(b) post nanoindentation mapping SEM image, and (c,d) superimposition of the contour map over the post-indent SEM image to show variation in hardness and reduced elastic modulus across and within different phases.
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