Singularities of Contact Stress and Electric Field During Indentation of Piezoelectric Ceramics by Cylindrical, Flat Indenter

The finite element method (FEM) was used to simulate and to verify the axisymmetric nanoindentation response of a transversely isotropic piezoelectric ceramics by a conductive rigid flat indenter from half-space to thin film. The cylindrical, flat indenter without prescribed electric force was adopted to mechanically load the piezoelectric ceramics. The results show that the linear relationship between indentation load and indentation displacement is obtained. And the same relationship is obtained between electric potential and indentation displacement. In addition, resultant mechanoelectrical responses were analyzed. The simulation results indicate that the contact stress and electric field exhibit singularities round the edge of the indenter. Both stress and electric field singularities vary exponentially with respect to the thickness of the solids under the indenter. At the same time, the normal stress and electric potential distributions of the direct piezoelectric effects are given. Through the fitting formula of the normal stress, normal electric potential and tangential electric potential from the indentation interior to the contact edge under different indentation depths, the singular constants of electric field and stress field under different thickness of piezoelectric ceramics are proposed, and their variation rules are analyzed.

Automated summary

The finite element method was used to simulate and analyze the axisymmetric nanoindentation response of a transversely isotropic piezoelectric ceramics. The results showed a linear relationship between indentation load and displacement, as well as between electric potential and displacement. Singularities in contact stress and electric field were observed near the edge of the indenter, and they varied exponentially with the thickness of the solids. The study proposed fitting formulas and singular constants for the electric field and stress field under different thicknesses of piezoelectric ceramics.