Analysis Of Fracture Problem In Two Dimensional Piezoelectric Semiconductors

Piezoelectric semiconductors are materials which have the properties of both piezoelectrics and semiconductors.Because this kind of material is very sensitive to defects such as cracks,so it is necessary to analyze the fracture of piezoelectric semiconductors.Because of the particularity of the governing equations in piezoelectric semiconductors,obtaining an analytical solution for fracture in piezoelectric semiconductors is more difficult as in other materials,such as elastic,piezoelectric,and magnetoelectroelastic media,so in this paper we analyzed cracks in two-dimensional n-type piezoelectric semiconductors via boundary integral equation method and boundary element method.The main works of this paper are listed in the following:(1)Based on the governing equations of two-dimensional n-type piezoelectricsemiconductors,the general solution is obtained,and the fundamental solutionsfor a line crack under uniformly distributed extended displacementdiscontinuities on the crack surface are derived via Fourier transform,in whichthe extended displacement discontinuity denotes the displacement discontinuitiesalong the normal and tangential directions,electric potential discontinuity,electron density discontinuity,respectively.By using the obtained fundamentalsolutions,the extended displacement discontinuity boundary element method fora line crack in two-dimensional n-type piezoelectric semiconductors that is underextended loadings is developed to calculate the extended displacementdiscontinuities on the crack surface and the extended stress intensity factors atcrack tip.(2)The extended displacement discontinuities method is extended to study cracks intwo-dimensional n-type thermal piezoelectric semiconductors.The fundamentalsolutions for a line crack under uniformly distributed extended displacementdiscontinuities on the crack faces are derived.Based on the obtainedfundamental solutions,an extended displacement discontinuity boundaryelement method is developed.The extended displacement discontinuity on thecrack surface and the stress intensity factor,heat flux intensity factor at the cracktip are calculated under different combined loadings.(3)Considering the media in the crack cavity and the real boundary condition,underthe semi-permeable boundary condition,employing the iterative computations,the related numerical results are derived.