Clustering analysis of nanoindentation data for shale: Curve-based versus mechanical parameter-based approaches

Clustering analysis of nanoindentation data is generally done to distinguish the mechanical phases and quantitatively obtain their related mechanical properties and fractions in the entire sample. Clustering analysis is carried out based on the mechanical parameters (Young's modulus and hardness) that are obtained from the load–displacement curves of each indent. However, the accuracy of this method and its suitability for the analysis of grid nanoindentation data on a heterogeneous composite material like shale is still unknown. Therefore, this study applied clustering analysis directly on the load–displacement curves in a shale sample for the first time and compared the results with the widely used mechanical parameter-based clustering analysis method. The results showed that the mechanical parameter-based clustering distinguished four mechanical phases with 8.62, 16.07, 24.31, and 37.16 GPa as the average Young's moduli, and hardness values of 0.15, 0.35, 0.80, and 2.56 GPa, respectively. The fractions of these phases are 34.22 %, 27.78 %, 20.89 %, and 7.11 %, respectively. Likewise, the curve clustering method also distinguished four mechanical phases with Young's moduli of 4.75, 7.91, 14.10, and 22.49 GPa, and hardness values of 0.03, 0.08, 0.23, and 0.97 GPa, with fractions of 2.67 %, 12.89 %, 40.44 %, and 44.00 %, respectively. Comparing the results with the sample's mineralogy suggests that parameter-based clustering provides a better distinction between mechanical phases, closely aligning with the mineral fractions obtained from X-ray diffraction (XRD) analysis. Therefore, this approach is recommended for analyzing grid nanoindentation data in composite materials.