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(a) Illustration of the projected area of the residual imprint in the nanoindentation test and (b) schematic of area calculation for the pile-up corrected nanoindentation hardness. Blue, gray, and red triangles are defined by the contact depth in the Oliver–Pharr method, the pile-up around the corner, and the pile-up around the edge, respectively. Yellow line triangle is the integration of solid triangles, which has the same area with them
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Nanoindentation hardness tests are used to measure indentation hardness at the micro- and nanoscales and further to predict Vickers hardness on larger scales. Hence, the relationship between Vickers and nanoindentation hardness has gained considerable research interest. Here we introduce the concept of Meyer hardness as a mean contact pressure corr...
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Context 1
... shown in Fig. 2a, we consider the gray-colored contact area caused by the pile-up h p corner ð Þ at the corners of the imprint; the red-colored contact area caused by the pile-up h p edge ð Þ at the edges of the imprint even though the value of h p corner ð Þ is considerably smaller than h p edge ð Þ because of the lower plastic flow at corners [28]. ...Context 2
... caused by the pile-up h p edge ð Þ at the edges of the imprint even though the value of h p corner ð Þ is considerably smaller than h p edge ð Þ because of the lower plastic flow at corners [28]. The polygon of the imprint containing pile-up was modeled as a triangle with yellow line to use the area function in nanoindentation tests, as shown in Fig. 2b. After the calculation given in Supplement A, the actual projected area with the pile-up A actual h ð Þ is given ...Context 3
... nanoindentation Berkovich imprint was also used to explain the Vickers imprint. In Fig. 2a, the central blue area represents the Oliver-Pharr area; the gray area, the pile-up around the corner; and the red area, the pileup around the edge. Figure 7 Schematic of nanoindentation using the Oliver-Pharr method based on [15]. ...Citations
... In the case of heavy-ion-irradiated materials, the original Nix-Gao model has recently been used for the shallow-depth region without the softer substrate effect to estimate the bulk-equivalent hardness [39]. With the recent multiscale hardness relation [44] correlating H 0 and the conventional Vickers hardness, the nanoindentation hardness can be bridged to the bulk mechanical properties. Simultaneously, Korsunsky's model [45] and its variation, which are based on a weighted average value of hardness in films and substrates, have also been assumed to evaluate the composite indentation hardness of an irradiated subsurface and its unirradiated substrate in ion-irradiated materials. ...
... (10), (18), and (22), the calculated H 0,unirr and H 0,irr were 2.67 and 3.70 GPa, respectively. According to various Fe-Cr alloys [44], the hardness correlation is expressed as ...
... Previous studies posited that the relationship between nanoindentation hardness and Vickers hardness is generally linear [59][60][61]. Observations from Figure 6 also suggest an approximately linear relationship. This correlation may persist regardless of its linearity due to material characteristics, testing errors, and inherent coupling effects. ...
... This adaptability to enhance precision with additional data input demonstrates the neural networks' robustness in modeling complex relationships, even when they deviate from linearity. Previous studies posited that the relationship between nanoindentation hardness and Vickers hardness is generally linear [59][60][61]. Observations from Figure 6 also suggest an approximately linear relationship. This correlation may persist regardless of its linearity due to material characteristics, testing errors, and inherent coupling effects. ...
This research presents a comprehensive analysis of deep neural network models (DNNs) for the precise prediction of Vickers hardness (HV) in nitrided and carburized M50NiL steel samples, with hardness values spanning from 400 to 1000 HV. By conducting rigorous experimentation and obtaining corresponding nanoindentation data, we evaluated the performance of four distinct neural network architectures: Multilayer Perceptron (MLP), Convolutional Neural Network (CNN), Long Short-Term Memory network (LSTM), and Transformer. Our findings reveal that MLP and LSTM models excel in predictive accuracy and efficiency, with MLP showing exceptional iteration efficiency and predictive precision. The study validates models for broad application in various steel types and confirms nanoindentation as an effective direct measure for HV hardness in thin films and gradient-variable regions. This work contributes a validated and versatile approach to the hardness assessment of thin-film materials and those with intricate microstructures, enhancing material characterization and potential application in advanced material engineering.
... The nanoindentation equipment used in this study employed the Oliver-Pharr method to generate nanoscale hardness data. However, it was found that this method underestimates the actual contact depth due to the pile-up phenomenon [45]. The proposed modifications by Slagter et al. (Section 2.3.5) were implemented to overcome this limitation and provide more accurate hardness measurements. ...
... where H is the hardness for a given indentation depth, h; H o is the hardness in the limit of infinite depth; and h * is a characteristic length that depends on the material and shape of the indenter tip. In this study, the Nix-Gao model was employed to calculate the bulkequivalent nanoindentation hardness from depth-dependent nanoindentation hardness [45]. By using this model, the relationship between the measured hardness during nanoindentation and the intrinsic hardness of the material was established. ...
