Dynamic Anti-plane Behavior Of The Interaction Between A Crack And A Circular Inclusion In A Piezoelectric Medium

Piezoelectric materials have been more and more widely used in smart matrials such as electromechanical sensors, transducers and actuators due to their strong electromechanical coupling characteristics. The objective of this paper is to provide a theoretical study on dynamic anti-plane interaction between a crack and a circular inclusion in a piezoelecctric medium. The emphasis is placed on stress intensity factors and stress concentration factors.In this paper, dynamic interaction is investigated theoretically between a crack and a circular inclusion in an infinite piezoelectric medium. The formulae are based on the method of complex variable and Green's function. The boundary conditions of the crack are assumed to be traction free and electrically permeable. Being a fundamental solution of displacement field for an infinite elastic piezoelectric medium possessing a piezoelectric circular inclusion subject to an anti-plane harmonic line force at any point, a special Green's function is constructed for the present problem. Firstly, the scattering problem of SH-wave by a circular inclusion was solved. Secondly dynamic stress intensity factors at the crack's tip and dynamic stress concentration factors at the cavity's edge are obtained with crack-division technique. Based on Green's function and employed to the method of crack-division at actual position of the crack, the crack was constructed. Thirdly, the expression of dynamic stress intensity factor was determined by intergration of Green's function. Finnaly, calculating results are plotted so as to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the geometry of the crack and the circular inclusion influence upon the dynamic stress intensity factors and dynamic stress concentration factors.