Finite element analysis of the spherical indentation of transversely isotropic piezoelectric materials

Finite element analysis was used to analyze the indentation deformation of a transversely isotropic piezoelectric material (PZT-4) by a rigid spherical indenter. Three cases were considered in the analysis, which included (a) the indentation by an insulating indenter, (b) the indentation by a conducting indenter and (c) the indentation of the piezoelectric material with equal electric potential on the top surface. The indentation load was found to be proportional to the 3/2 power of the indentation depth for all three cases. Using the simulation results and the analytical relation for the indentation by a rigid, insulating indenter, semi-empirical relations were developed between the indentation load and the indentation depth and between the electric potential on the indenter and the indentation depth, respectively, for the indentation by a rigid, conducting indenter. The singularity of electric field for the indentation by the conducting indenter led to a stress singularity at the contact edge, which will likely cause a structural damage. The electric analysis found that a non-zero electric potential was induced on the conducting indenter and the surface of the piezoelectric material with equal potential on the top surface. The apparent piezoelectric coefficients determined from the indentation by the conducting indenter and the indentation of the piezoelectric material with equal potential on the top surface decreased with increasing indentation depth.