Depth Criteria for Indentation-Based Characterization of Individual Components and Composite Matrices in Heterogeneous Rocks

Indentation testing is widely used to characterize microscale mechanical properties and provide input parameters for cross-scale modeling of heterogeneous rocks. However, the indentation-depth ranges over which the measured Young’s modulus and hardness represent an individual constituent or the composite matrix remain unclear. In this study, finite element modeling, dimensional analysis, and indentation experiments were used to investigate the depth-dependent response of rock particle–matrix systems and to establish depth criteria for the Oliver–Pharr (OP) and slope–energy (SE) methods. As the normalized indentation depth h_m/L increases, where h_m is the maximum indentation depth and L is the particle size, the indentation response evolves from particle-dominated, through a particle–matrix transitional regime, to matrix-dominated behavior, while the indentation-derived Young’s modulus shifts from the constituent value toward the matrix value. This transition results from matrix-induced changes in contact stiffness, projected contact area, and indentation work ratio. Particle morphology controls the initial deviation from constituent properties, whereas indenter angle and tip radius govern the convergence toward matrix properties. With a relative-deviation tolerance of approximately 10%, reliable constituent-property measurement requires h_m/L ≲ 0.01 together with a sufficiently large absolute indentation depth relative to the indenter tip radius and characteristic length scales associated with surface roughness and indentation-size effects. For the matrix side, the FEM predicts matrix-dominated depth limits of h_m/L ≳ 0.4 for the OP method and h_m/L ≳ 0.8 for the SE method under typical conditions where the particle yield strength exceeds that of the matrix. The OP-based depth limit is supported by the present indentation experiments, whereas the SE-based depth limit remains a numerical prediction requiring further direct experimental validation.