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.

[1]  Fuqian Yang,et al.  Analysis of the axisymmetric indentation of a semi-infinite piezoelectric material: The evaluation of the contact stiffness and the effective piezoelectric constant , 2008 .

[2]  Fuqian Yang,et al.  Effect of electric field on the nanoindentation of zinc sulfide , 2009 .

[3]  Fuqian Yang,et al.  Nanomechanical characterization of ZnS nanobelts , 2005 .

[4]  Jiecai Han,et al.  A Circular Indenter on a Piezoelectric Layer , 2006 .

[5]  Sergei V. Kalinin,et al.  Quantitative Probing of Electromechanical Phenomena on the Nanoscale By Piezoelectric Nanoindentation , 2006 .

[6]  X. Tan,et al.  Indentation-induced domain switching in Pb(Mg1/3Nb2/3)O3–PbTiO3 crystal , 2001 .

[7]  A. E. Giannakopoulos,et al.  Strength Analysis of Spherical Indentation of Piezoelectric Materials , 2000 .

[8]  S. Cheng,et al.  Micro‐Indentation‐Induced Domain Switching in Tetragonal Barium Titanate , 2008 .

[9]  Fuqian Yang.  Electromechanical interaction of linear piezoelectric materials with a surface electrode , 2004 .

[10]  S. El-Borgi,et al.  Flexoelectric properties of ferroelectrics and the nanoindentation size-effect , 2011 .

[11]  K. Okazaki,et al.  Finite element simulation of equal channel angular extrusion , 2005 .

[12]  K. Nickel,et al.  Raman spectroscopy for the investigation of indentation-induced domain texturing in lead zirconate titanate piezoceramics , 2010 .

[13]  J. H. Wang,et al.  Indentation responses of piezoelectric films , 2008 .

[14]  Subra Suresh,et al.  THEORY OF INDENTATION OF PIEZOELECTRIC MATERIALS , 1999 .

[15]  U. Ramamurty,et al.  Indentation strength of a piezoelectric ceramic: Experiments and simulations , 2009 .

[16]  E. Soergel,et al.  Determination of the effective coercive field of ferroelectrics by piezoresponse force microscopy , 2011 .

[17]  Sergei V. Kalinin,et al.  Relationship between direct and converse piezoelectric effect in a nanoscale electromechanical contact , 2007 .

[18]  Haojiang,et al.  INDENTATION OF A TRANSVERSELY ISOTROPIC PIEZOELECTRIC HALF-SPACE BY A RIGID SPHERE , 1999 .

[19]  Zhong Lin Wang,et al.  Piezoelectric Characterization of Individual Zinc Oxide Nanobelt Probed by Piezoresponse Force Microscope , 2004 .

[20]  K. Hsia,et al.  Fracture and domain switching by indentation in barium titanate single crystals , 2001 .