Numerical Analysis Of Exact Crack Model Of Two-dimensional Piezoelectric Semiconductor

Piezoelectric semiconductors both possess a piezoelectric effect and a semiconductor property,due to excellent multi-field coupling properties,they are widely used in piezoelectric electronic devices.However,cracks and other defects unavoidable exist when piezoelectric semiconductors being produced,so it is important to study crack problems in piezoelectric semiconductors.Based on the exact electric boundary condition across crack face in two dimensional piezoelectric semiconductor,an exact crack model of piezoelectric semiconductor is established,and a finite element method with a double iterative process is used to solve the exact crack model.Influences of the external boundary condition,contact type between metal and piezoelectric semiconductors and crack size on the stress intensity factor,electric displacement intensity factor and electric flux density intensity factor of piezoelectric semiconductor are numerically analyzed.The main contents of this thesis are as follows:1)Considering the real electric boundary condition across crack face,an exact crack model of piezoelectric semiconductor is established,the exact crack model contains a region without crack cavity and a crack cavity region.According to continuous conditions on the interface of two regions and the non-homogeneous control equation of piezoelectric semiconductors,a double iterative process is introduced to the finite element method to solve this complex nonlinear problem with the PDE module of COMSOL Multiphysics.Based on the small perturbation theory of the carrier concentration,the constitutive equation of piezoelectric semiconductor is linearized.The electric displacement,displacement discontinuous,potential discontinuous,carrier concentration discontinuous across crack face and stress,electric displacement and electric current density fields near crack tip are obtained by using the above double iterative method.Effects of crack face boundary conditions,applied loads,contact types and crack size on the electric displacementand the stress intensity factor,electric displacement intensity factor and electric current density factor are discussed.2)Based on the strict nonlinear constitutive relation of piezoelectric semiconductors,the exact crack model of piezoelectric semiconductors is solved by using the proposed double iterative algorithm in 1).The effects of the applied stress,applied electric field,initial carrier concentration,metal-piezoelectric semiconductor contact type on crack surface displacement and crack tip stress intensity factor,potential shift strength factor and current density factor are discussed.