Flexural Stress Concentration Near a Hyperboloidal Neck in a Transversely Isotropic Piezoceramic Cylinder

The exact solution is found to the three-dimensional electroelastic problem for a transversely isotropic piezoceramic body with a spheroidal cavity. The solutions of static electroelastic problems are represented in terms of harmonic functions. The case of stretching the piezoceramic medium at a right angle to the spheroid axis of symmetry is analyzed numerically. The dependence of the stress concentration factor on the geometry of the spheroid and the electromechanical characteristics of the material is studied.Piezoceramic materials are widely used in various industries. Structural members made of such materials may contain voids, inclusions, delaminations, and other defects, which are detrimental to mechanical and electric strength. This is the reason why the stress-strain state of piezoceramic bodies needs further analysis.The authors of [1-3, 7-11, etc.] studied the stress concentration near different types of heterogeneities. The papers [1, 7] set forth a method of solving three-dimensional electroelastic problems for a piezoceramic layer. There, boundary-value problems were reduced to systems of singular integro-differential equations solved using mechanical quadratures. The paper [6] studies the axisymmetric electroelastic field near a spheroidal cavity in a piezoceramic body and uses the general electroelastic solution expressed in terms of harmonic functions [5]. Nonaxisymmetric problems for such bodies have not yet been investigated because of severe mathematical difficulties.In the present paper, we will solve the general electroelastic problem for a piezoceramic body with a spheroidal cavity. The solution will be used to study the stress concentration near the cavity in the case where the piezoceramic medium is stretched at a right angle to the spheroid axis of symmetry.

Stress state of a transversely isotropic piezoceramic body with a spheroidal cavity

Podil'chuk

Myasoedova

2004

Electroelastic State of a Prolate Piezoceramic Spheroid with Two Electrodes

Podil'chuk

Neznakina

2005

The electroelastic problem for a transversely isotropic prolate ceramic spheroid is solved explicitly. The spheroid surface is free from external forces. The case is considered where the piezoceramic body is subjected to a given potential difference between electrodes partially covering the surface at the vertices. The normal component of electric-flux density is equal to zero on the noneletroded portion of the surface. Plots of normal stresses in the symmetry plane of the piezoceramic body are given Piezoceramic materials are finding ever-widening application in various industries, which requires further in-depth study of the deformation of piezoceramic bodies subjected to mechanical and electric loads. Significant results have been obtained on the influence of the piezoelectric effect on the static and dynamic deformation of piezoceramic bodies [1-3, 5-6].Here we will find the explicit solution to the electroelastic problem for a transversely isotropic prolate ceramic spheroid. The spheroid surface is free from external forces. We will consider the case where the piezoceramic body is subjected to a given potential difference between electrodes partially covering the body at the vertices. The normal component of electric-flux density is equal to zero on the noneletroded portion of the surface. We will also determine the stresses in the symmetry plane of the spheroid.

On the stress state of a piezoceramic body with a flat crack under symmetric loads

Kirilyuk

2005

A static-equilibrium problem is solved for an electroelastic transversely isotropic medium with a flat crack of arbitrary shape located in the plane of isotropy. The medium is subjected to symmetric mechanical and electric loads. A relationship is established between the stress intensity factor (SIF) and electric-displacement intensity factor (EDIF) for an infinite piezoceramic body and the SIF for a purely elastic material with a crack of the same shape. This allows us to find the SIF and EDIF for an electroelastic material directly from the corresponding elastic problem, not solving electroelastic problems. As an example, the SIF and EDIF are determined for an elliptical crack in a piezoceramic body assuming linear behavior of the stresses and the normal electric displacement on the crack surface Keywords: piezoelectricity, flat crack, elliptical crack, stress intensity factor, electric-displacement intensity factorIntroduction. The wide use of piezoelectric ceramic materials, which are highly brittle, in various transducers (based on the coupling of mechanical and electric fields) necessitates a careful study into the concentration of mechanical and electric fields in electroelastic bodies with imperfections such as cavities, inclusions, and cracks. However, the solution of three-dimensional problems of electroelasticity involves severe mathematical difficulties since the original system of equations describing the electrostressed state of a body consists of complicated coupled differential equations [1,4]. This is why plane problems of electroelasticity have recently been studied in more detail. Noteworthy are the papers [2,11,14,17,18] that address the two-dimensional electroelastic state around a single cavity, inclusion, and crack and the interaction of concentrators of electric and mechanical fields. Three-dimensional problems of electroelasticity for an infinite medium with cavities, inclusions, and cracks are solved in [5-7, 9, 10, 13, 15, 16]. The papers [5,15,16] propose approaches to finding the general solutions of coupled equations of electroelasticity for a transversely isotropic body. The exact solutions of electroelastic problems for spheroidal and hyperboloidal cavities and inclusions have been found in [6,13]. The electrostressed state and stress intensity factors (SIFs) and electric-displacement intensity factors (EDIFs) for an infinite medium with penny-shaped and elliptic cracks are studied in [1, 9, 10] and [7, 15, 16], respectively.