PERIODIC PERMEABLE-CRACKS IN THERMOPIEZOELECTRIC MEDIA
热压电介质中的渗透型周期裂纹问题

In the past years, the crack problem in piezoelectric materials has received considerable attention1-7]. However, to the author's knowledge, most of the Previous theoretical analyses were focused on the cases of plane piezoelectric material without considering thermal effect. In fact, with the rapidly increasing use of piezoelectric materials in high-temperature environment, it is also important to study the heat-electric-elastic coupling problem. Although extension of the formulation of piezoelectric elasticity to the thermopiezoelectric elasticity is straightforward, it is not easy to obtain an explicit solution to thermopiezoelectric problem, due to the mathematical complexity. On this object, recently, several valuable solutions hare been presented8-14]. However, it is noted that all studies are for the case of impermeable cracks, i.e. the cracks are considered as impermeable slits and thus the electric field inside cracks is assumed to be zero. On the other hand, most of these analyses assumed that the loads are applied only along the crack faces, and as a result the crack-tip fields are obtained. But in engineering, cracks are usually filled with air or vacuum, and thus the electric field inside crack is a non-zero unknown quantity. In addition, one often is more interested in the case of remote loading. This means that one will face with a baffling Problem, i.e. how to determine the electric field inside the crack, when it is assumed that a piezoelectric medium with permeable cracks is loaded at infinity. By means of the axtended Stroh formalism, this paper presents an explicit treatment on the generalized 2D thermopiezoelectric problem of N periodic cracks in an infinite piezoelectric medium subjected to the remote mechanical-electric-thermal loading. The presented analysis has two features: one is that the cracks are considered as permeable slits across which the normal electric displacement and the tangential electric field are assumed to be continuous. The other is that the loads are applied at infinitys rather than on the crack faces. Based on these two assumptions, the field intensity factors in the medium and the electric field inside the cracks are obtained, respectively, in very explicit form. It is shown that: (i) the electric field inside cracks is linearly variable; (ii) the singularity of electric displacement is always dependeds on that of stress; (iii) all the field singularities are independent of the mphed electric electric load.