Abstract:Shallow nanoindentation enables mechanical characterization of thin films, individual phases and other volume-constrained materials, but measured hardness is often inflated by the indentation size effect (ISE), contact-area errors and tip-geometry artifacts. Classical ISE corrections such as the Nix-Gao require a deep linear regime and are unreliable when only shallow measurements are used. This study investigates how a small experimental dataset can be used to predict a reference hardness with physics-guided feature engineering and augmentation. Approximately 700 experimental indentations were collected from three steel reference specimens covering a hardness range of 2-6.5 GPa and augmented using physically motivated variations representing instrumental noise, session-level drift, and local multiphase boundary blending. The input space combined Oliver-Pharr values with mechanics descriptors, including indentation work partitioning, ($H\text{/}E_{r}$), and the area-invariant compliance proxy ($P_{\max}\text{/}S^{2}$). Ridge Regression (RR), Random Forest, XGBoost, and Neural Networks (NN) were evaluated using a quarantined fourth steel specimen tested at staggered loads. The hardness mapping was nonlinear: RR failed, whereas nonlinear models achieved ($R^2 > 0.98$) internally. A constrained (64-8-64) NN gave the best results, reaching RMSE = 0.470 GPa, MAPE = 5.4% on the quarantined steel. Unlike Nix-Gao analysis, the NN produced stable estimates in the shallow regime. SHAP and latent-space analysis showed reliance on area-invariant and energy-based descriptors. The results demonstrate the feasibility of a this workflow for ISE correction in steels using small datasets and suggest a pathway toward data-efficient characterization of any volume constrained materials.
| Comments: | Preprint, 19 pages, 8 figures, 4 tables |
| Subjects: | Materials Science (cond-mat.mtrl-sci); Machine Learning (cs.LG) |
| Cite as: | arXiv:2604.27775 [cond-mat.mtrl-sci] |
| (or arXiv:2604.27775v1 [cond-mat.mtrl-sci] for this version) | |
| https://doi.org/10.48550/arXiv.2604.27775 arXiv-issued DOI via DataCite (pending registration) |
From: Radmir Karamov [view email]
[v1]
Thu, 30 Apr 2026 12:12:38 UTC (10,252 KB)
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