热压电介质中的渗透型周期裂纹问题

PERIODIC PERMEABLE-CRACKS IN THERMOPIEZOELECTRIC MEDIA

利用Ｓｔｒｏｈ公式，研究了合共线周期裂纹热的压电介质的广义二维问题．该工作有两个特征：一是裂纹被建模为具有渗透表面的缝隙，并假设为跨越上下表面时，电场的切向分量和电位移的法向分量是连续的；另一个特征是，机一电载荷和热载荷被假设作用在无限远处，而不是在裂纹表面．基于这两个假设，我们获得了有关场强因子，以及裂纹内电场的相当简洁的表达式．结果表明：①在裂纹内电场是线性变化的，②电位移的奇异性总是取决于应力的奇异ｓ性，③所有场的奇异性与所加的电载荷无关．

In the past years, the crack problem in piezoelectric materials has received considerable attention[1-7]. 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 presented[8-14]. 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.