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.