Dynamic Anti-plane Behaviors Of An Semi-infinite Piezoelectric Medium With An Circular Cavity And An Crack Near The Surface

It is well known that the coupling behavior of piezoelectric materials has led to their wide applications in smart materials. When subjected to mechanical and electrical loads in service, these piezoelectric materials can fail prematurely owing to defects, e.g. cracks, holes, inhomogeneities, etc, arising in the manufacturing process. It is of great importance to study dynamic behavior of piezoelectric materials with subsurface defects, and of great valuable reference to design and manufacture sensors or actuators.The scattering of SH-wave, which is caused by a circular cavity and a crack near the surface in a piezoelectric medium, is studied in this paper in the field of linearly elastic dynamics. The methods of Green's function, complex variables and multi-polar coordinates are employed here. Firstly, a suitable Green's function is constructed, which is an essential solution for the elastic field and electric field about a semi-infinite piezoelectric medium with a circular cavity while bearing anti-plane time-harmonic line force at an arbitrary point. Secondly, by using the technique of crack-division, the crack is constructed as follows. Shear stresses are applied at the location where the crack will appear, which have the same values and opposite direction with the stresses produced for the reason of SH-wave scattering by a subsurface circular cavity. Thus, expressions of displacement and electric potential are established while both of a subsurface crack and a subsurface circular cavity are existent. Therefore, the analytic expressions of dynamic stresses concentration factor around the circular cavity and dynamic stress intensity factor at the crack tip are obtained. Finally, numerical results are given and plotted to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material, the incident angle of SH-wave, the depth of the circular cavity and the position and orientation of the crack influence upon the dynamic stresses concentration factor and dynamic stress intensity factor.