The present paper deals with theoretical and computational analysis of quasi-static, normal indentation of a transversely isotropic, linear elastic, piezoelectric half-space by a rigid spherical indenter. The contact is axisymmetric, nonconforming, monotonically advancing with load, frictionless and adhesionless. The indenter was modeled either as perfect conductor or as perfect insulator. The mechanical and electrical fields below the surface were examined. The issues of mechanical and dielectric strength due to indentation were examined using Weibull statistics of surface imperfections. The particular cases of PZT-4, PZT-5A, and indented by rigid punches having either zero electrical potential or zero electric charge were solved with finite element analysis. [S0021-8936(00)02502-2]
Issue Section:
Technical Papers
1.
Cady, W. G., 1964, Piezoelectricity, Dover, New York.
2.
Mason, W. P., 1950, Piezoelectric Crystals and Their Application to Ultrasonics, Van Nostrand, New York.
3.
Tiersten, H. F., 1969, Linear Piezoelectric Plate Vibrations, Plenum, New York.
4.
Jaffe, B., Cook, W. R., and Jaffe, H., 1971, Piezoelectric Ceramics, Academic Press, San Diego, CA.
5.
Uchino, K., 1997, Piezoelectric Actuators and Ultrasonic Motors, Kluwer, Boston.
6.
Toupin
, R. A.
, 1956
, “The Elastic Dielectric
,” J. Ration. Mech. Anal.
, 5
, pp. 849
–915
.7.
Mindlin
, R. D.
, 1972
, “Elasticity, Piezoelectricity and Crystal Lattice Dynamics
,” J. Elast.
, 2
, pp. 217
–282
.8.
Nowacki
, W.
, 1978
, “Some General Theorems of Thermo-Piezo-Electricity
,” J. Therm. Stresses
, 1
, pp. 171
–182
.9.
Newnham
, R. E.
, Skinner
, D. P.
, and Cross
, L. E.
, 1978
, “Connectivity and Piezoelectric—Pyroelectric Composites
,” Mater. Res. Bull.
, 13
, pp. 525
–536
.10.
Majorkowska-Knap
, K.
, 1987
, “Uniqueness Theorem of Linear Thermo/Piezoelectricity
,” Bull. Pol. Acad. Sci.: Tech. Sci.
, 35
, pp. 163
–177
.11.
Sneddon, I. N., 1980, Special Functions of Mathematical Physics and Chemistry, Longman, London.
12.
Ding Haojiang
, Chenbuo
, and Lian
, Gjian
, 1996
, “General Solutions for Coupled Equations for Piezoelectric Media
,” Int. J. Solids Struct.
, 33
, pp. 2283
–2298
.13.
Matysiak
, S.
, 1985
, “Axisymmetric Problem of Punch Pressing into a Piezoelectric Half Space
,” Bull. Pol. Acad. Sci.: Tech. Sci.
, 33
, pp. 25
–33
.14.
Dahan
, M.
, and Zarka
, J.
, 1977
, “Elastic Contact Between a Sphere and a Semi-infinite Transversely Isotropic Body
,” Int. J. Solids Struct.
, 13
, pp. 229
–238
.15.
Sneddon, I. N., 1966, Mixed Boundary Problems in Potential Theory, North-Holland, Amsterdam.
16.
Walton
, J. R.
, 1975
, “A Distributional Approach to Dual Integral Equations of Titchmarch Type
,” SIAM (Soc. Ind. Appl. Math.) J. Math. Anal.
, 6
, pp. 628
–643
.17.
Chen
, W.
, and Ding
, H.
, 1999
, “Indentation of a Transversely Isotropic Piezoelectric Half-Space by a Rigid Sphere
,” Acta Mech. Solid. Sin.
, 12
, pp. 114
–120
.18.
Giannakopoulos, A. E., and Suresh, S., 1999, “Theory of Indentation of Piezoelectric Materials,” Acta Mater., in press.
19.
Argon
, A. S.
, 1959
, “Distribution of Cracks on Glass Surfaces
,” Proc. R. Soc. London, Ser. A
, 250
, pp. 482
–492
.20.
Park
, S.
, and Sun
, C.-T.
, 1995
, “Fracture Criteria for Piezoelectric Ceramics
,” J. Am. Ceram. Soc.
, 78
, pp. 1475
–1480
.21.
Batdorf
, S. B.
, and Heinisch
, H. L.
, 1978
, “Weakest Link Theory Reformulated for Arbitrary Fracture Criterion
,” J. Am. Ceram. Soc.
, 61
, pp. 355
–358
.22.
Weibull
, W.
, 1951
, “A Statistical Distribution Function of Wide Applicability
,” ASME J. Appl. Mech.
, 18
, pp. 293
–297
.23.
Pohanka
, R. C.
, Rice
, R. W.
, and Walker
, B. F.
, 1976
, “Effect of Internal Stress on the Strength of BaTiO3,
” J. Am. Ceram. Soc.
, 59
, pp. 71
–74
.24.
Pohanka
, R. C.
, Freiman
, S. W.
, and Rice
, R. W.
, 1980
, “Fracture Process in Ferroic Materials
,” Ferroelectrics
, 28
, pp. 337
–342
.25.
Buessem
, W. R.
, Cross
, L. E.
, and Goswami
, A. K.
, 1966
, “Phenomenological Theory of High Permittivity in Fine Grained Barium Titanate
,” J. Am. Ceram. Soc.
, 49
, pp. 33
–36
.26.
Pisarenko
, G. G.
, Chushko
, V. M.
, and Kovalev
, S. P.
, 1985
, “Anisotropy of Fatigue Toughness of Piezoelectric Ceramics
,” J. Am. Ceram. Soc.
, 68
, pp. 259
–265
.27.
Gerson
, R.
, and Marshall
, T. C.
, 1959
, “Dielectric Breakdown of Porous Ceramics
,” J. Appl. Phys.
, 30
, pp. 1650
–1653
.28.
Yamashita
, K.
, Koumoto
, K.
, and Yanagida
, H.
, 1984
, “Analogy Between Mechanical and Dielectric Strength Distributions for BaTiO3 Ceramics
,” J. Am. Ceram. Soc.
, 67
, pp. C31–C33
C31–C33
.29.
Kishimoto
, A.
, Koumoto
, K.
, and Yanagida
, H.
, 1989
, “Mechanical and Dielectric Failure of BaTiO3 Ceramics
,” J. Mater. Sci.
, 24
, pp. 698
–702
.30.
ABAQUS, 1996, Finite Element Code, Version 5.5, Hibbit, Karlsson, and Sorensen, Pawtucket, RI.
31.
Bechmann
, R.
, 1956
, “Elastic, Piezoelectric and Dielectric Constants of Polarized Barium Titanate Ceramics and Some Applications of the Piezoelectric Equations
,” J. Acoust. Soc. Am.
, 28
, pp. 347
–350
. Copyright © 2000
by ASME
You do not currently have access to this content.
