This paper presents an analytical method to describe the effect of electric field on the shrinkage rate and healing history of a cylindrical pore in piezoelectric grain under hydrostatic pressure. Based on the thermal dynamic potential theory of piezoelectric elastic solid, the coupled influence of the surface energy of pore, the interface energy of piezoelectric grain, and the elastic energy and electric potential stored in the piezoelectric grain dominates the shrinkage rate and healing history of the pore. Utilizing the excess chemical potential in an axisymmetric piezoelectric grain with a cylindrical pore, the govern equation of thermodynamic for the piezoelectric grain with a cylindrical pore is established. Then, an analytical expression for the govern equation is given to predict the shrinkage rate and healing time of a cylindrical pore in piezoelectric grain. Results show that the effect of electric field on the shrinkage rate and healing history of a pore in piezoelectric grain is obviously different from the effect of hydrostatic pressure applied on the interface of the piezoelectric grain, and the finally shrinkage size of pore in piezoelectric grain is larger than that of the pore in non-piezoelectric grain when other calculation parameters are fixed.
HuangPLiZSunJ (2001) Finite element analysis of the splitting and cylinderization processes of damage microcracks. Modelling and Simulation in Material Science and Engineering9: 193–206.
5.
HuangPLiZSunJ (2002) Shrinkage and splitting of microcracks under pressure simulated by the finite-element method. Metallurgics and Materials Transactions A33: 1117–1124.
6.
HuangPSunJLiZ (2003) Evolution of penny-shaped microcracks by interface migration. International Journal of Solids and Structures40: 1959–1972.
7.
GerberPKügelerCEllerkmannU, (2005) Effects of ferroelectric fatigue on the piezoelectric properties (d33) of tetragonal lead zirconate titanate thin films. Applied Physics Letters86: 1–2.
8.
GuptaTK (1975) Crack healing in thermally shocked MgO. Journal of the American Ceramic Society58: 143–148.
9.
GurtinME (1996) Generalized Ginzburg–Landau and Cahn–Hilliard equations based on a microforce balance. Physics D: Nonlinear Phenomena92: 178–192.
10.
LeeJKCourtneyTH (1989) Two-dimensional finite difference analysis of shape instabilities in plates. Metallurgical Transactions A20: 1385–1394.
11.
LiQChenYH (2008) Why traction-free? Piezoelectric crack and Coulombic traction. Archive of Applied Mechanics78: 559–573.
12.
LiQKunaM (2012) Evaluation of electromechanical fracture behavior by configurational forces in cracked ferroelectric polycrystals. Computational Materials Science57: 94–101.
13.
LiQRicoeurAKunaM (2011) Coulomb traction on a penny-shaped crack in a three dimensional piezoelectric body. Archive of Applied Mechanics81: 685–700.
14.
LiuYWangXWangH, (2011) Effects of electric and mechanical loads on the morphological evolution of a pore in piezoelectric films. Applied Mathematical Modelling35: 972–980.
15.
LiuYWangXLiZ (2010) Scale effect on the shrinkage characteristics of a spherical pore in stressed grain. Metallurgical and Materials Transactions A42: 2011–2017.
16.
MengFWangHWangX, (2010) Elliptically delaminated buckling near the surface of piezoelectric laminated shells under electric and thermal loads. Composite Structures92: 684–690.
17.
MaQ (1998) Non-linear capillary shape evolution of rod morphologies via interfacial diffusion. Acta Metallurgica46: 1669–1681.
18.
MahadevanMBradleyR (1999) Phase field model of surface electromigration in single crystal metal thin films. Physics D: Nonlinear Phenomena126: 201–213.
19.
Müller WolfgangHHauckT (2008) Simple methods for the durability assessment of microelectronic solders. Mechanics of Advanced Materials and Structures15: 485–498.
20.
PowersJDGlaeserAM (1992) High-temperature healing of cracklike flaws in Mg- and Ca-ion-implanted sapphire. Journal of the American Ceramic Society75: 2547–2558.
21.
ReddyJN (1997) On laminate composite plates with integrated sensors and Actuators. Enginnering Structures21: 568–593.
22.
RiceJRChuangTJ (1981) Energy variations in diffusive poregrowth. Journal of the American Ceramic Society64: 46–53.
23.
ShengGGWangX (2009) Studies on dynamic behavior of functionally graded cylindrical shells with PZT layers under moving loads. Journal of Sound and Vibration323: 772–789.
24.
ShengGGWangX (2010a) Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells. Applied Mathematical Modelling34: 2630–2643.
25.
ShengGGWangX (2010b) Response and control of functionally graded laminated piezoelectric shells under thermal shock and moving loadings. Composite Structures93: 132–141.
26.
SunJ (2002) A model for shrinkage of a spherical pore in the center of a grain: Influence of lattice diffusion. Journal of Materials Engineering and Performance11: 322–331.
27.
TakahashiTUenoFNishiguchiK (1988) A numerical analysis of the pore shrinkage process controlled by surface-diffusion. Acta Metallurgica36: 3007–3018.
28.
WangHLiZ (2004a) Stability and shrinkage of a pore in stressed grain. Journal of Applied Physics95: 6026–6031.
29.
WangHLiZ (2004b) The three-dimensional analysis for diffusive shrinkage of a grain-boundary pore in stressed solid. Journal of Materials Science39: 3425–3432.
30.
YangYWZhangL (2006) Optimal excitation of a rectangular plate resting on an elastic foundation by a piezoelectric actuator. Smart Materials and Structures15: 1063–1078.
31.
YangYWHuYH (2008) Electromechanical impedance modeling of PZT transducers for health monitoring of cylindrical shell structures. Smart Materials and Structures17: 1–11.
32.
YangYWXuJFSohCK (2005) Generic impedance-based model for structure–piezoceramic interacting system. Journal of Aerospace Engineering18: 93–101.
33.
YaoFAndoKKChuMC (2000) Crack-healing behavior: High temperature and fatigue strength of SiC-reinforced silicon nitride composite. Journal of Materials Sciences Letters19: 1081–1085.
34.
YuHHSuoZ (1999) An axisymmetric model of pore–grain boundary separation. Journal of the Mechanics and Physics of Solids47: 1131–1155.
35.
YuNYLiQ (2013) Failure theory via the concept of material configurational forces associated with the M-integral. International Journal of Solids and Structures50: 4320–4332.
36.
ZhangYJHanJTLiuJ, (2004) In situ observation of the micro-hole healing process. Key Engineering Materials274–276: 817–822.
37.
ZhengLYLiGRYinQR, (2006) Phase transition and failure at high temperature of bismuth-layered piezoelectric ceramics. Journal of American Ceramic Society89: 1317–1320.
