Data-Efficient Indentation Size Effect Correction in Steels Using Machine Learning and Physics-Guided Augmentation

TL;DR

This paper develops a machine learning approach with physics-guided augmentation to accurately correct indentation size effects in steel hardness measurements using small datasets.

Contribution

It introduces a data-efficient workflow combining feature engineering, augmentation, and nonlinear models, achieving high accuracy in ISE correction with limited experimental data.

Findings

Nonlinear models achieved R^2 > 0.98 in hardness prediction.

The neural network provided stable estimates in shallow indentation regimes.

Physics-guided augmentation improved model robustness and accuracy.

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.