Mechanical characterization of dielectric ceramics, which have drawn extensive attention in wireless communication, remains challenging. The micromechanical properties with the microstructures of dielectric ceramic BaO–Sm₂O₃–5TiO₂ (BST) were assessed by nanoindentation, microhardness, and microscratch tests under different indenters, along with the X-ray diffraction (XRD), scanning electron microscopy (SEM), and Raman spectroscopy. Accurate determination of elastic modulus (E_IT) (i.e., 260 GPa) and indentation hardness (H_IT) (i.e., 16.2 GPa) of brittle BST ceramic by the instrumented indentation technique requires low loads with little indentation-induced damage. The elastic modulus and indentation hardness were analyzed by different methodologies such as energy-based approach, displacement-based approach, and elastic recovery of Knoop imprint. Consistent values (about 3.1 MPa·m^1/2) of fracture toughness (K_C) of BST ceramic were obtained by different methods such as the Vickers indenter-induced cracking method, energy-based nanoindentation approaches, and linear elastic fracture mechanics (LEFM)-based scratch approach with a spherical indenter, demonstrating successful applications of indentation and scratch methods in characterizing fracture properties of brittle solids. The deterioration of elastic modulus or indentation hardness with the increase in indentation load (F) is caused by indentation-induced damage and can be used to determine the fracture toughness of material by energy-based nanoindentation approaches, and the critical void volume fraction (f^*) is 0.27 (or 0.18) if elastic modulus (or indentation hardness) of the brittle BST ceramic is used. The fracture work at the critical load corresponding to the initial decrease in elastic modulus or indentation hardness can also be used to assess the fracture toughness of brittle solids, opening new venues of the application of nanoindentation test as a means to characterize the fracture toughness of brittle ceramics.

Three-dimensional finite element modeling of the contact between a rigid spherical indenter and a rough surface is presented when considering both the loading and unloading phases. The relationships among the indentation load, displacement, contact area, and mean contact pressure for both loading and unloading are established through a curve fitting using sigmoid logistic and power law functions. The contact load is proportional to the contact area, and the mean contact pressure is related to the characteristic stress, which is dependent on the material properties. The residual displacement is proportional to the maximum indentation displacement. A proportional relationship also exists for plastically dissipated energy and work conducted during loading. The surface roughness results in an effective elastic modulus calculated from an initial unloading stiffness several times larger than the true value of elastic modulus. Nonetheless, the calculated modulus under a shallow spherical indentation can still be applied for a relative comparison.