2026/04/30 by Radmir Karamov, Tagir Karamov
#cond-mat.mtrl-sci #cs.LG
Shallow nanoindentation enables mechanical characterization of thin films, individual phases, and other volume-constrained materials, but the measured hardness is inflated by the indentation size effect (ISE). Classical corrections such as Nix-Gao require a deep linear regime and fail when only shallow measurements are accessible. We present a data-efficient workflow that recovers a high-load reference hardness directly from shallow, size-affected indentation data. Over 700 indentations on three certified steel reference blocks (2-6.5 GPa) were expanded by physics-guided augmentation and used to train conventional regressors (Ridge, Random Forest, XGBoost, neural networks) and a physics-constrained neural network (PCNN) that reconstructs hardness through the bounded form Href = Happ/sqrt(1+q), with the signed correction q learned from dimensionless contact-mechanics descriptors (Er,ref*Pmax/S2, Wp/Wtot, H/Er). On a quarantined fourth steel tested at loads offset from the training schedule, only the constrained formulation generalized: the dimensionless-input PCNN achieved RMSE = 0.28 GPa and MAPE = 3.6%, and remained stable beyond the training load range, where tree-based models failed structurally. Ablation attributed this robustness to the bounded reconstruction and a load-independence regularizer. Deliberate application to fused silica produced systematic failure, delimiting the method to dislocation-mediated crystalline plasticity. A few hundred laboratory indentations thus suffice to train a physically constrained ISE correction operating on single shallow indentations, offering a template for materials lacking analytical size-effect models.