Plane deformation of a piezoelectric bimaterial with two electrically conductive and charged interface cracks
Abstract
The paper considers a piezoelectric composite formed from two heterogeneous piezoelectric half-planes, on the border of which electrically conductive cracks are arbitrarily located. Consideration of such a problem is approved by the fact that modern actuators and other electronic devices are often created using thin-film electrodes located between piezoelectric layers. Such electrodes are usually made of metal powder, conductive polymers, etc. They do not change the mechanical properties of matrices. Peeling of such electrodes can lead to the appearance of electrically conductive interfacial cracks. So, if the actuator has two electrodes at the interface of piezoelectric materials and they both delaminate, then the problem of the interaction of two electrically conductive cracks arises, which is considered in this paper. The presence of an electric charge on one or both cracks is also allowed. Such a situation can occur if the electroded crack surfaces are connected to electrical sources. Representations of electrical and mechanical factors through piecewise analytical functions have been used for the solution. With their use, the problem is reduced to the problem of linear conjugation. An exact analytical solution of this problem is presented, which indicates the presence of oscillating root singularities near the crack tips. The expressions for mechanical and electrical components on the crack faces and on the parts of the interface outside the cracks are derived. In particular, quite simple analytical formulas for the stresses at the interface of materials between cracks and outside of them have been obtained. Formulas for the displacement jumps along the crack region (crack opening) have been also found. The last formulas clearly show the oscillating nature of the specified factors when approaching the crack tips. A numerical illustration of the obtained solutions is carried out. In particular, graphs of stress and crack opening dependences along the crack lengths and on their total charge have been constructed. It is shown that the effect of the total electric charge on the crack along its opening is more significant than this effect on stresses
Keywords
electrode; crack between two materials; analytical solution; piezoelectric composite
References
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