Study On The Nonlinear Medium Crack Problem Of The Thermopiezoelectric Strip

Fracture mechanics mainly studies the strength of the cracked body and the law of crack growth under the action of external load,which can provide theoretical guidance for the reliability and life of materials and structures.In this thesis,the thermoelectroelastic fields of the crack tip in the thermopiezoelectric strip or the functionally graded thermopiezoelectric strip under uniform heat flux and electromechanical loading are researched.The main achievements are given as follows:(1)The problem of a cracked thermopiezoelectric strip subjected to uniform heat flux and electromechanical loading is investigated.An extended dielectric crack model is proposed to capture the effects of the physical properties of crack interior on crack-tip thermoelectroelastic fields.Making use of the Fourier transform technique,the thermoelectroelastic problem is transformed to solve the system of the second kind Fredholm integral equations.The Lobatto-Chebyshev collocation method is used to form a nonlinear system of algebraic equations,which is solved by elaborating an algorithm.The crack-tip thermoelectroelastic fields are determined by using the approximate solutions.Numerical results are carried out to show the variations of the fracture parameters of concern on applied thermoelectromechanical loadings,the physical properties of the dielectric inside the crack and the geometries of the cracked thermopiezoelectric strip.Some comparisons with the experimental results are reported to reveal the effectiveness of the extended dielectric crack model.(2)Based on an extended dieletric crack model,the problem of a functionally graded thermopiezoelectric strip under uniform heat flux and electromechanical loading is studied.Applying the Fourier transform technique,the thermoelectroelastic problem is transformed to solve the system of the integral equations.A nonlinear system of algebraic equations obtained by using LobattoChebyshev collocation method,which is solved by elaborating an algorithm.The numerical results show that the crack growth in a functionally graded thermopiezoelectric strip is caused by the interaction of applied thermoelectromechanical loadings,the physical properties of the dielectric inside the crack and the geometries of the cracked thermopiezoelectric strip.The above studies are based on the extended dielectric crack model,and the effectiveness is revealed.The theory of fracture mechanics for piezoelectric solids has been developed by using the obtained results.A new model for better simulating the crack problem under complex conditions.