Enhancing Phase Clustering in Nanomechanical Property Maps of Multiphase Materials Using Kernel-Averaged Mechanical Mismatch

Abstract

This work presents a novel approach to improve phase identification in nanomechanical property maps of multiphase materials, such as those obtained by nanoindentation or atomic force microscopy (AFM). A major challenge in validating clustering strategies for these data is the lack of ground-truth phase labels in experimental measurements, along with the tendency of overly simplistic synthetic datasets to artificially inflate algorithm performance. To address this gap, we construct controlled yet non-trivial synthetic benchmarks with tunable mechanical contrast, graded interfaces, curved boundaries, and diffuse morphologies, enabling rigorous and realistic evaluation of clustering robustness. Conventional clustering methods based only on elastic modulus (E) and hardness (H) often struggle to separate phases when mechanical contrast is low or when diffuse interphase regions are present. We introduce the Kernel-Averaged Mechanical Mismatch (KAMM), a neighborhood-informed feature that quantifies local mechanical heterogeneity by comparing each point to its neighbors in (E, H) space. When incorporated into a three-dimensional clustering space (E, H, KAMM), this framework improves phase separability, enhances interphase detection, and increases robustness to noise. By enabling more reliable segmentation of mechanical domains under realistic contrast conditions, the proposed method facilitates the generation of representative volume elements (RVEs) and supports more accurate extraction of phase-specific properties in heterogeneous microstructures.

Figures (18)

• Figure 1: Five-region specimen used to illustrate sensitivity of scalar and neighborhood-based descriptors.
• Figure 2: Synthetic specimen families used for benchmarking clustering performance. The configurations span sharp and graded planar interfaces (a--c), periodic circular inclusions with and without interphase layers (d--e), and diffuse, randomly distributed particles (f). Together, these geometries provide controlled yet structurally diverse scenarios for evaluating clustering robustness under varying mechanical contrast and morphological complexity.
• Figure 3: Pixel connectivity schemes used for KAMM, with first-order neighborhood (4 nearest neighbors in light blue) and second-order neighborhood (includes diagonals and two-pixel offsets in dark blue).
• Figure 4: Local mechanical metrics computed on a representative composite indentation map. (a--b) Base mechanical properties. (c--d) Scalar mechanical ratios. (e) Full KAMM field showing boundary sensitivity. (f--g) Single-property mismatch components. (h--i) Alternative mismatch formulations. These features enhance clustering and interphase detection by capturing spatial and mechanical contrast.
• Figure 5: Three-dimensional accuracy maps showing pixel-level clustering accuracy as a function of both hardness contrast ($H_\mathrm{ratio}$) and elastic modulus contrast ($E_\mathrm{ratio}$) for the different clustering algorithms. These maps provide the full contrast-dependent behavior, from which the averaged 2D profiles in Fig. \ref{['fig:kamm_accuracy_noise']} are derived.