Theoretical Analysis Of Fracture Mechanics In Thermopiezoelectric Materials Based On Continuous Dislocation Model

Thermopiezoelectric ceramics, as a typical smart material, are widely used assensors, transducers and actuators in intelligent systems due to their pronouncedpiezoelectric, dielectric and pyroelectric properties. However, these materials are brittleand susceptible to cracking. It is of vital importance to investigate thethermoelectroelastic fields as a result of the presence of defects, such as crack andinclusions in thermal environments. The requirements of structural strength, reliabilityand lifetime of these intelligent systems call for a better understanding of the fracturemechanics of thermopiezoelectric materials. The problems of crack, crack branching,interface crack and thermoelectric boundary conditions of crack surfaces areinvestigated based on the extended Stroh formalism, Green’s function method andsingular integral equation technique in this paper. The main research contents andconclusions are as follows:A partial contact zone model is developed for the stress and electric displacementfields due to the obstruction of a uniform heat flux in thermopiezoelectric materials inthe charpters two and three. The crack is assumed electrically impermeable andelectrically permeable, respectively. Green’s function method is used to reduce theproblem to a set of singular integral equations which are solved in closed-form. Whenthe crack is assumed to be traction free, the crack opening displacement is found to benegative over one half of the crack unless a sufficiently large far field tensile stress issuperposed. The problem is reformulated assuming a contact zone at one crack tip. Theextent of this zone, the stress and electric displacement intensity factors at each crack tipare obtained as functions of the applied mechanical stress and heat flux. The resultshows that the electric displacement intensity is not only singular at both crack tips, butalso at contact zone tip for the electrically impermeable crack. For the electricallypermeable, the singularity only exists at the crack tips.Solutions are presented for an electrically impermeable crack branching out of thecrack plane in a thermopiezoelectric medium under thermo-electro-mechanical loadsbased on Stroh formalism in charpter four. Explicit Green’s functions for the interactionof a crack and a thermopiezoelectric dislocation (i.e., a thermal dislocation, amechanical dislocation and an electric dipole located at the same point) are developed.The problem then can be expressed in terms of coupled singular integral equations forthe thermopiezoelectric dislocation density functions associated with a branched crack. Some essential fracture mechanics parameters, such as stress and electric displacementintensity factors, and energy release rate at the branched crack tip are obtained.Numerical results are presented for the effect of applied thermal flux loads and electricfield on the crack propagation path.It is well known that there is oscillation singularity near the interface crack tip,which is physically unreasonable. A modified interface dislocation model is developedto remove such oscillation singularity for interface fracture in charpter five. The Diracdelta function in the fundamental solution of interface dislocation is explained bylocally-distributed continuous function. The oscillation singularity at the crack tip ofrinterface fracture is eliminated. Then the problem is reduced to the solution of a systemof singular integral equations. The critical interfacial fracture mechanics parameters,such as the stress intensity factor, the mode mixity and the energy release rates forparticular materials group of the isotropic solids are obtained. Finally, the modifiedinterface dislocation model is extended to the thermopiezoelectric bimaterials interfacecrack problem.The applicability and effect of the crack surfaces thermoelectric boundaryconditions in thermopiezoelectric fracture mechanics problem are discussed by usingthe finite thickness notch approach in charpter six. The notch in these materials is full ofair (or vacuum). The stress and electric displacement intensity factors at the notch tips,and thermal flux and electric displacement inside the notch are derived in closed-form.The numerical results are compared with the ideal crack solutions. It is found that theelectrically impermeable crack boundary condition assumption is a reasonable one, andthe thermal conductivity of air or vacuum inside the crack must be considered.