A mode III crack in a piezoelectric semiconductor of crystals with 6mm symmetry

Abstract

A finite mode III crack in a piezoelectric semiconductor of 6 mm crystals is analyzed. Fourier transform is employed to reduce the mixed boundary value problem to a pair of dual-integral equations. Numerical solution of these equations yields coupled electromechanical fields, the intensity factor and the energy release rate near the crack tip. Numerical results are presented graphically to show the fracture behavior which is affected by the semiconduction.

Piezoelectric-conductor iterative method for analysis of cracks in piezoelectric semiconductors via the finite element method

“…In the steady state, the governing equations for linear n-type piezoelectric semiconductors without body force and free of electric charge are given by Hu et al [21] The constitutive equations for a two-dimensional n-type piezoelectric semiconductor with the polarization direction along the y-direction can be given in the form [3,4] where u, v, φ, and n are elastic displacements in the x-and y-directions, electric potential, and carrier density, respectively, which are sometimes called extended displacements; ij c , ij e , and ij ε are the elastic, piezoelectric and dielectric constants, respectively; q and 0 n are the electric charge of an electron and the initial carrier density, respectively; ij µ and ij d are the electron mobility and carrier diffusion, respectively.…”

“…Yang [20] considered a semi-infinite crack in piezoelectric semiconductors of 6-mm symmetry and found that the fields were affected by the semiconductor and have certain qualitative differences from those in a non-conducting piezoelectric dielectric. Hu et al [21] analyzed a finite mode III crack in a piezoelectric semiconductor with 6-mm crystals and presented numerical results to show the fracture behavior affected by the semiconductor. Sladek et al [22] analyzed the anti-plane crack problem in bounded domains under transient loading conditions.…”

Electric Current Dependent Fracture in GaN Piezoelectric Semiconductor Ceramics

“…An oxy Cartesian coordinate system was set up, with the origin point o at a sample center and the x and y being symmetrical axes, as illustrated in Figure 3 . For a plane problem of PSCs with an N -type semiconductor property, the linearized equilibrium equations were given by Hu et al [ 15 ], that is where σ ij are the stress components ( i , j = x , y ), D i and J i are the components of electric displacement vector and electrical current, respectively, q is the elementary charge, and Δ n is the variation of carrier density.…”

“…For example, Yang [ 14 ] considered a semi-infinite crack and found out that there are certain differences in fracture behavior of PSC from insulating piezoelectric materials, and furthermore, obtained an analytical solution for both stress and electric fields near a crack. Hu [ 15 ] analyzed the singularities of physics fields at a type-III crack tip in PSC, and presented that the fracture behavior is closely related to the semiconductor properties. Sladek et al [ 16 ] and Lu et al [ 17 ] investigated the dynamic anti-plane crack in functional graded PSC, derived local integral equations that involve one order lower derivatives than the original partial differential equations, and finally, built up a system of ordinary differential equations for the involved nodal unknown quantities.…”

Carrier distribution and electromechanical fields in a free piezoelectric semiconductor rod

“…This theory has been used to study some of the applications mentioned above: the inclusion problem for composites (Yang et al, 2006), the fracture of piezoelectric semiconductors (Hu et al, 2007;Sladek et al, 2014a;2014b), the electromechanical energy conversion in these materials (Li et al, 2015), the vibrations of plates (Wauer and Suherman, 1997), and to develop low-dimensional theories of piezoelectric semiconductor plates and shells (Yang and Zhou, 2005;. Researchers have also developed more general and fully nonlinear theories (de Lorenzi and Tiersten, 1975;McCarthy and Tiersten, 1978;Maugin and Daher, 1986).…”