Analysis Of Thermal-Mechanical-Electrical Coupling Property And Crack Problems In Piezoelectric Semiconductors

As a new kind of intelligent material,piezoelectric semiconductors(PSCs)possess both piezoelectric and semiconductor properties.PSCs have thermal,mechanical,electric and other fields coupling effects,which can realize the interconversion among thermal,electrical,chemical,etc.,and mechanical energy and have attracted widespread attention both in the scientific and engineering fields.Due to the superior multi-field coupling characteristics,PSCs have a wide application prospect in nanogenerators,sensors,resonators,and other electronic devices.With consideration of the thermal effect in PSCs,this dissertation theoretically studies the thermal,mechanical,and electric coupled properties and fracture behaviors of PSCs.The main contents of this dissertation are as follows.(1)Taking one-dimensional model(1D)of PSCs as the basis and starting point,the influence of temperature on the mechanical and electrical properties of PSCs is studied to analyze the necessity of considering thermal effect in fracture problems.Considering the PSC with pyroelectric effect,the intrinsic constitutive equation contains nonlinear coupling terms of electric field and temperature gradient with carrier concentration.In this thesis,we adopt a shooting method to study the 1D model of PSCs and find the solution for the thermal-mechanical-electrical multi-field coupled nonlinear problem under the mechanical load,temperature gradient and Schottky contact boundary conditions to present the coupling behaviors of mechanical,electric,current and temperature fields.(2)Based on the assumption of small disturbance of electron concentration and temperature,the current density and heat flux density constitutive equations of PSCs are linearized.Under the frame of linearization theory,a penny-shaped crack in a threedimensional(3D)PSCs with thermal effect is studied.With the differential operator theory and Almansi’s theorem,general solutions of the extended displacements are derived.Using the Hankel transform and extended displacement discontinuity method,extended displacement discontinuity fundamental solutions of the extended displacement and extended stress are gained.Under the condition of thermally and electrically impenetrable crack,the boundary integral equations with the extended discontinuity displacements as the basic unknown quantity are established,and the numerical solutions of the extended discontinuity displacements on PSC penny crack surface are obtained by the boundary element method to obtain the extended stress intensity factors of the crack front.(3)According to the thermal and electric conduction property of the medium in crack cavity,several thermal and electrical boundary conditions on the crack surface are proposed.Based on the extended displacement discontinuity fundamental solutions,the extended discontinuity displacement boundary element method is adopted to study the penny crack problem in a 3D PSC under three different crack surface boundary conditions.These three boundary conditions are the thermally and electrically permeable,thermally and electrically impermeable and thermally and electrically semipermeable crack surface boundary conditions,respectively.The influence of the crack surface boundary conditions on the extended discontinuity displacements and the extended stress intensity factors is analyzed.(4)With consideration of the thermal effect in PSCs,a central crack problem in a two-dimensional(2D)PSC under harmonic waves is studied with the extended discontinuity displacement boundary element method.General solutions of the extended displacements for a 2D steady-state PSC are derived through the differential operator theory and Almansi’s theorem.Extended discontinuity displacement fundamental solutions of the extended displacement and extended stress are obtained with Fourier transform and the extended discontinuity displacement method.Under the condition of thermally and electrically impenetrable crack,the boundary integral equations are established and the extended discontinuity displacements on the crack surface of the crack surface and the extended stress intensity factors near the crack tip are obtained with the boundary element method,according to crack surface boundary conditions.Extended discontinuity displacements on crack surface and the extended stress intensity factors near the crack tip are obtained with the boundary element method.The effect of frequency on the extended discontinuity displacements and extended stress intensity factors crack is analyzed.(5)The extended discontinuity displacement boundary element method is used to study the cracking problem of 2D thermal-mechanical-electrical multi-field coupled functionally gradient PSCs,and obtain the general solutions of the extended displacements of the functionally gradient PSCs.The extended discontinuity displacement fundamental solutions of the extended displacements and extended stresses of the central crack problem are also obtained,and the influence of the functionally gradient parameter on the extended stress intensity factors near the crack tip is numerically analyzed.