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Indentation strength of a piezoelectric ceramic: Experiments and simulations

  • S.N. Kamble (a1), D.V. Kubair (a2) and U. Ramamurty (a1)


The spherical indentation strength of a lead zirconate titanate (PZT) piezoelectric ceramic was investigated under poled and unpoled conditions and with different electrical boundary conditions (arising through the use of insulating or conducting indenters). Experimental results show that the indentation strength of the poled PZT is higher than that of the unpoled PZT. The strength of a poled PZT under a conducting indenter is higher than that under an insulating indenter. Poling direction (with respect to the direction of indentation loading) did not significantly affect the strength of material. Complementary finite element analysis (FEA) of spherical indentation of an elastic, linearly coupled piezoelectric half-space is conducted for rationalizing the experimental observations. Simulations show marked dependency of the contact stress on the boundary conditions. In particular, contact stress redistribution in the coupled problem leads to a change in the fracture initiation, from Hertzian cracking in the unpoled material to subsurface damage initiation in poled PZT. These observations help explain the experimental ranking of strength the PZT in different material conditions or under different boundary conditions.


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1.McMeeking, R.M.: A J-integral for the analysis of electrically induced mechanical stress at cracks in elastic dielectrics. Int. J. Eng. Sci. 28, 605 (1990).
2.Pak, Y.E.: Crack extension force in a piezoelectric material. Trans. ASME J. Appl. Mech. 57, 647 (1990).
3.Shindo, Y., Ozawa, E., and Nowacki, J.P.: Singular stress and electric fields of a cracked piezoelectric strip. Appl. Electromag. Mater. 1, 77 (1990).
4.Sosa, H.A.: Plane problems in piezoelectric media with defects. Int. J. Solids Struct. 28, 491 (1991).
5.Suo, Z., Kuo, C.M., Barnett, D.M., and Willis, J.R.: Fracture mechanics for piezoelectric ceramics. J. Mech. Phys. Solids 40, 739 (1992).
6.Suo, Z.: Models for breakdown-resistant dielectric and ferroelectric ceramics. J. Mech. Phys. Solids 41, 1155 (1993).
7.Zhang, T.Y.: Effects of static electric field on the fracture behavior of piezoelectric ceramics. Acta Mech. Sin. 18, 537 (2002).
8.Zhang, T.Y. and Gao, C.F.: Fracture behaviors in piezoelectric solids. Theor. Appl. Fract. Mech. 41, 339 (2004).
9.Zarnik, M.S., Belavic, D., and Macek, S.: Evaluation of the constitutive material parameters for the numerical modeling of structures with lead–zirconate–titanate thick films. Sens. Actuators, A 136, 618 (2007).
10.Makagon, A., Kachanov, M., Kalinin, S.V., and Karapetian, E.: Indentation of spherical and conical punches into piezoelectric half-space with frictional sliding: Applications to scanning-probe microscopy. Phys. Rev. B 76, 064115 (2007).
11.Yang, F.: Analysis of the axisymmetric indentation of a semiinfinite piezoelectric material: The evaluation of the contact stiffness and the effective piezoelectric constant. J. Appl. Phys. 103, 074115 (2008).
12.Ramamurty, U. and Kumaran, M.C.: Mechanical property extraction through conical indentation of a closed-cell aluminum foam. Acta Mater. 52, 181 (2004).
13.Jana, S., Bhowmick, R., Kawamura, Y., Chattopadhyay, K., and Ramamurty, U.: Deformation morphology underneath the Vickers indent in a Zr-based bulk metallic glass. Intermetallics 12, 1097 (2004).
14.Ramachandra, S., Sudheer Kumar, P., and Ramamurty, U.: Impact energy absorption in an Al foam at low velocities. Scr. Mater. 49, 741 (2003).
15.Matysiak, S.J.: Axisymmetric problem of punch pressing into a piezoelectric half-space. Bull. Polish Acad. Techn. Sci. 33, 25 (1985).
16.Sosa, H.A. and Castro, M.A.: On concentration load at boundary of a piezoelectric half-plane. J. Mech. Phys. Solids 42, 1105 (1994).
17.Fan, H., Sze, K.Y., and Yang, W.: Two dimensional contact on a piezoelectric half-space. Int. J. Solids Struct. 33, 1305 (1996).
18.Chen, Wei-qiu: On piezoelectric contact problem for a smooth punch. Int. J. Solids Struct. 37, 2331 (2000).
19.Giannakopoulos, A.E. and Suresh, S.: Theory of indentation of piezoelectric materials. Acta Mater. 47, 2153 (1999).
20.Ramamurty, U., Sridhar, S., Giannakopulous, A.E., and Suresh, S.: Experimental study of spherical indentation on piezoelectric materials. Acta Mater. 47, 2417 (1999).
21.Sridhar, S., Giannakopoulos, A.E., Suresh, S., and Ramamurty, U.: Electric response during indentation of piezoelectric materials: A new method for materials characterization. J. Appl. Phys. 85, 380 (1999).
22.Chen, W. and Ding, H.: Indentation of a transversely isotropic piezoelectric half-space by a rigid sphere. Acta Mech. Solid. Sin. 12, 114 (1999).
23.Deluca, M., Galassi, C., and Pezzotti, G.: Residual stresses in PZT investigated by polarized Raman piezospectroscopy. Ferroelectrics Lett. 32, 31 (2005).


Indentation strength of a piezoelectric ceramic: Experiments and simulations

  • S.N. Kamble (a1), D.V. Kubair (a2) and U. Ramamurty (a1)


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