Coulomb traction on a penny-shaped crack in a three dimensional piezoelectric body

Abstract

The axisymmetric problem of a penny-shaped crack embedded in an infinite three-dimensional (3D) piezoelectric body is considered. A general formulation of Coulomb traction on the crack surfaces can be obtained based on thermodynamical considerations of electromechanical systems. Three-dimensional electroelastic solutions are derived by the classical complex potential theory when Coulomb traction is taken into account and the poling direction of piezoelectric body is perpendicular to the crack surfaces. Numerical results show that the magnitude of Coulomb tractions can be large, especially when a large electric field in connection with a small mechanical load is applied. Unlike the traditional traction-free crack model, Coulomb tractions induced by an applied electric field influence the Mode I stress intensity factor for a penny-shaped crack in 3D piezoelectric body. Moreover, compared to the current model, the traditional traction-free crack model always overestimates the effect of the applied electric load on the field intensity factors and energy release rates, which has consequences for 3D piezoelectric fracture mechanics.

Effects of electric field and pressure on the shrinkage behaviors of cylindrical pore in piezoelectric materials

“…In this paper, an analytical method is presented to solve the effect of piezoelectric parameter and electric potential field on the shrinkage rate and the healing time of a cylindrical pore in stressed piezoelectric grains. Some significant conclusions are taken as follows: The electric potential field exerted on the boundary interface of cylindrical hollow piezoelectric grain under a given pressure will influence the characteristics of pore shrinkage rate, and the influence becomes larger as the pore in piezoelectric grain become smaller. The hydrostatic pressure exerted on the boundary interface of piezoelectric grain can enhances the shrinkage rate of pore in the piezoelectric grain. The shrinkage rate of cylindrical pore in piezoelectric grain gradually increases as the electric field exerted on the boundary interface of piezoelectric grain increases. The finally healing size of cylindrical pore in piezoelectric grain is larger than that of cylindrical pore in non-piezoelectric grain when other calculation parameters are fixed, but the healing times for shrinking into a stable small size from the initial pore are identical for two different grains. It will be interesting that the traction-free condition in equation (4) is replaced by the Coulombic traction on the surface of pores in further investigations on the present problem, due to Li and Chen (2008) and Li et al. (2011) had demonstrated that the Coulombic traction on the surface of pores is significant and leads to the non–traction-free boundary condition on the surface of pore in piezoelectric materials. …”

“…(4) The finally healing size of cylindrical pore in piezoelectric grain is larger than that of cylindrical pore in non-piezoelectric grain when other calculation parameters are fixed, but the healing times for shrinking into a stable small size from the initial pore are identical for two different grains. (5) It will be interesting that the traction-free condition in equation (4) is replaced by the Coulombic traction on the surface of pores in further investigations on the present problem, due to Li and Chen (2008) and Li et al (2011) had demonstrated that the Coulombic traction on the surface of pores is significant and leads to the non-traction-free boundary condition on the surface of pore in piezoelectric materials.…”

“…Various methods to research failure modes induced by those initial defects in piezoelectric material have been given in the study by Gerber et al. (2005), Liu et al. (2011), Zheng et al.…”

Effects of crack surface electrostatic tractions on the fracture behaviour of magnetoelectric composite materials

“…The electrostatic tractions acting upon crack faces should be introduced in piezoelectric medium fracture evaluation together with the electrically semi-permeable crack model, especially when the mechanical loads is not too large and the electric displacement loads is not too small (Ricoeur and Kuna, 2009). The axisymmetric problem of a penny-shaped crack embedded in an infinite three-dimensional piezoelectric body is considered by Li et al (2011). The effect of electrostatic tractions on the fracture behavior of a piezoelectric material under mechanical and/or electric loading is analyzed by Xie et al (2014) and Zhang and Wang (2014b).…”

Impact of Torsional Load on a Penny-Shaped Crack in an Elastic Layer Sandwiched Between Two Elastic Half-Space

“…The contact problem for an open penny-shaped crack under normally tension-compression wave has been analysed by Menshykov et al [21]. Li et al [22] solved the problem of Coulomb traction on a penny-shaped crack in a three dimensional piezoelectric body. Dovzhik [23] considered the problem of fracture of a half-space compressed along a penny-shaped crack located at a short distance from the surface and Lee [24] discussed the problem of pennyshaped crack in a plate of finite thickness subjected to a uniform shearing stress.…”