Axisymmetric indentation problem of a rigid perfect electrical insulator indenter on a functionally graded piezoelectric coating bonded to a piezoelectric substrate is investigated. The electromechanical properties of the functionally graded piezoelectric coating are assumed to vary as an exponential function along the thickness direction. The technique of the Hankel integral transform is applied to reduce the indentation problem to a singular integral equation. The numerical methods are developed and applied to compute the contact pressure for a cylindrical indenter and a spherical indenter. The effects of the material property gradient on the contact pressure, contact region, indentation depth, and electrical potential are analyzed. The numerical results are also obtained for the indentation responses of three different piezoelectric substrates.
ChenPJChenSH (2013) Partial slip contact between a rigid punch with an arbitrary tip-shape and an elastic graded solid with a finite thickness. Mechanics of Materials59: 24–35.
2.
ChenPJChenSHPengJ (2015) Sliding contact between a cylindrical punch and a graded half-plane with an arbitrary gradient direction. Journal of Applied Mechanics: Transactions of the ASME82: 041008.
3.
ChenWQ (2000) On piezoelectric contact problem for a smooth punch. International Journal of Solids and Structures37: 2331–2340.
4.
ChenWQShioyaTDingHJ (1999) The elasto-electric field for a rigid conical punch on a transversely isotropic piezoelectric half-space. Journal of Applied Mechanics66: 764–771.
5.
CivelekMB (1972) The axisymmetric contact problem for an elastic layer on a frictionless half-space. PhD Thesis, Mechanical Engineering Department, Lehigh University, Bethlehem, PA.
6.
ErdoganF (1965) Stress distribution in bonded dissimilar materials containing circular or ring-shaped cavities. Journal of Applied Mechanics32: 829–836.
7.
ErdoganFGuptaGD (1972) On the numerical solution of singular integral equations. Quarterly of Applied Mathematics29: 525–534.
8.
GiannakopoulosAE (2000) Strength analysis of spherical indentation of piezoelectric materials. Journal of Applied Mechanics47: 409–416.
9.
GiannakopoulosAESureshS (1999) Theory of indentation of piezoelectric materials. Acta Materialia47: 2153–2164.
10.
GulerMAErdoganF (2004) Contact mechanics of graded coatings. International Journal of Solids and Structures41: 3865–3889.
11.
KeLLWangYS (2006) Two-dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties. International Journal of Solids and Structures4: 5779–5798.
KeLLYangJKitipornchaiS. (2008a) Electro-mechanical frictionless contact behavior of a functionally graded piezoelectric layered half-plane under a rigid punch. International Journal of Solids and Structures45: 3313–3333.
14.
KeLLYangJKitipornchaiS. (2008b) Frictionless contact analysis of a functionally graded piezoelectric layered half-plane. Smart Materials and Structures17: 025003.
15.
LiuTJWangYSZhangCh (2008) Axisymmetric frictionless contact problem of functionally graded materials. Archive of Applied Mechanics78: 267–282.
16.
SridharSGiannakopoulosAESureshS (2000) Mechanical and electrical responses of piezoelectric solids to conical indentation. Journal of Applied Physics87: 8451–8456.
17.
SureshS (2001) Graded materials for resistance to contact deformation and damage. Science292: 2447–2451.
18.
UedaS (2008) Functionally graded piezoelectric strip with a penny-shaped crack under electromechanical loadings. European Journal of Mechanics A: Solids27: 50–60.
19.
UedaS (2010) Two parallel penny-shaped or annular cracks in a functionally graded piezoelectric strip under electric loading. Acta Mechanica210: 57–70.
20.
WangBL (2004) Circular surface electrode on a piezoelectric layer. Journal of Applied Physics95: 4267–4274.
21.
WangBLHanJC (2006) A circular indenter on a piezoelectric layer. Archive of Applied Mechanics76: 367–379.
22.
WangJHChenCQ (2011) Indentation responses of piezoelectric films ideally bonded to an elastic substrate. International Journal of Solids and Structures48: 2743–2754.
23.
WangJHChenCQLuTJ (2008) Indentation responses of piezoelectric films. Journal of the Mechanics and Physics of Solids56: 3331–3351.
24.
WuCMKahnMMoyW (1996) Piezoelectric ceramics with functionally gradients: a new application in material design. Journal of the American Ceramic Society79: 809–812.
