Anti-plane deformation of a composite piezoceramic space with interphase crack

Фильштинский, Л. А.; Fil'shtinskii, M. L.

doi:10.1007/bf02700683

Cited by 8 publications

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“…Relations (1)- (3) imply that the displacement u 3 and electric potential tO are harmonic functions. Therefore, the fields under investigation admit the following complex representations [3]:…”

Section: 4mentioning

confidence: 99%

Distinctive features of physical fields near the edge of a composite piezoceramic wedge (antiplane deformation)

Фильштинский¹

1999

Mater Sci

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We consider a composition in the form of a wedge made of two different conjugate piezoceramic or anisotropic piezopassive wedges and study the distinctive features of the behavior of physical fields in the vicinity of the edge of this composite wedge under homogeneous boundary conditions imposed on its external faces. The problem is solved by the method of complex representations of the components of electroelastic fields for two principal types of mechanical and electrical boundary conditions. The results of numerical computations are also presented.1. We consider a composite piezoceramic wedge (dihedral angle) in a Cartesian coordinate system Ox 1 x2x 3. The edge of the wedge coincides with the x3-axis and, for its opening angle, we have tx = t~l + ix2 (Fig. 1). The wedge is formed by two smaller wedges made of different piezoactive (piezopassive) materials. We assume that the conditions of ideal mechanical and electrical contact hold along the interface of materials. The homogeneous boundary conditions imposed on the external faces OA and OB are specified in what follows. We restrict ourselves to the case of antiplane deformation of the composite wedge in the plane x I Ox 2 and investigate the distinctive features of the conjugate electroelastic fields near the edge of the wedge. For piezopassive isotropic media, a similar problem was studied in [ 1 ]. X2 BO xl ,4 Fig. 1. Computational scheme.The antiplane deformation of a piezoceramic body is described by the following relations:the material equations ~x m "

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Section: 4mentioning

confidence: 99%

Distinctive features of physical fields near the edge of a composite piezoceramic wedge (antiplane deformation)

Фильштинский¹

1999

Mater Sci

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“…for both electrically permeable and impermeable assumptions on the crack faces. The papers by Fil'shtinskii and Fil'shtinskii, Hou and Mei are devoted to the consideration of anti‐plane interface crack problem for a piezoelectric compound subjected to piecewise uniform anti‐plane mechanical loading combined with in‐plane electric loading at infinity, and also a line loading at an arbitrary point.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the integral equation approach, the anti-plane problems of a crack situated at the interface between piezoelectric layers or between a piezoelectric layer and an elastic layer were considered in the works by Narita and Shindo, [1] Soh et al, [2] Kwon and Lee, [3] Li and Tang, [4,5] Wang and Sun, [6] Feng et al [7] for both electrically permeable and impermeable assumptions on the crack faces. The papers by Fil'shtinskii and Fil'shtinskii, [8] Hou and Mei [9] are devoted to the consideration of anti-plane interface crack problem for a piezoelectric compound subjected to piecewise uniform anti-plane mechanical loading combined with in-plane electric loading at infinity, and also a line loading at an arbitrary point.The anti-plane problem of three collinear interface cracks between dissimilar transversely isotropic piezoelectric materials subjected to electromechanical loadings was analyzed by Choi and Shin [10] and Choi and Chung. [11] Narita and Shindo [12] and Kwon and Lee [13] analyzed the problem of a three-layer structure constructed of a piezoelectric and two elastic strips cracked at…”

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confidence: 99%

Bond zone model for a conductive crack at the interface of piezoelectric materials under anti‐plane mechanical and in‐plane electric loadings

et al. 2019

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An electrically conductive crack between two semi‐infinite piezoelectric spaces under the action of anti‐plane mechanical loading and in‐plane electrical field parallel to the crack faces is considered. An exact analytical solution of this problem is found and the oscillating singularity is revealed at the crack tips. A new model, which is free from oscillation, is also developed for a conductive interface crack. This model is based on the introduction of a mechanically bonded zone at the conducting crack tip characterizing by zero crack faces displacement jump. The most reasonable length of this zone is found from the condition of a smooth crack closing. The validity confirmation of the bond zone model is given by means of description of conductive crack formation process. Some recommendations concerning the use of suggested model for the study of finite and infinite sized bodies with electrically conducting interface cracks are formulated.

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“…There is a constant shear load X 3 = -Pl (X l = X 2 = 0) along the fiber x t = Xto, x 2 = x20 > 0, -,,o < x 3 < o0 that is continuously distributed, or an electric charge of intensityp2, and at infinity the components of the stress tensor (Yi3 and the electric field intensity vector E m are zero. Under these conditions the compound space is in a state of antiplanar strain, all the field quantities being expressible in terms of four analytic functions ~r)(z) (v, r = 1, 2) as follows [2]:…”

mentioning

confidence: 99%

“…Then the solution, which we shall call the Green's function, is determined by the following relations [2]: The other constants and the functions ~)(z) are defined in (2). The stress intensity factors and the electric field intensity at the vertices of the interphase crack can be computed from the formulas…”

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confidence: 99%

Fundamental two-dimensional solutions of electroelasticity for compound piezoceramic bodies

Фильштинский¹

1998

J Math Sci

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We construct fundamental solutions of the two-dimensional equations of electroelasticity for antiplanar strain of a piezoceramic space with an interphase defect. We study the orders of the powers of the singularities at the vertices of the defect for two cases: an interphase crack and a stiff fiber continuously joined to the upper halfspace which has flaked off the lower half-space. The solution is constructed in closed form. Bibliography: 4 titles. Kosmodamianskii et al. [ 1 ] have constructed the Green's function for a piezoceramic half-plane with elliptic holes. In the present paper we use fundamental solutions of the corresponding equations of electroelasticity in constructing integral representations of the solutions of boundary-value problems.We consider an antiplanar strain of a compound piezoceramic space under concentrated forces. Suppose the space is composed of two inhomogeneous piezoceramic half-spaces (polarized along the x3-axis ) continuously conjoined along the plane x 2 = 0 and is referred to Cartesian axes OXlX2X 3 . There is a constant shear load X 3 = -Pl (X l = X 2 = 0) along the fiber x t = Xto, x 2 = x20 > 0, -,,o < x 3 < o0 that is continuously distributed, or an electric charge of intensityp2, and at infinity the components of the stress tensor (Yi3 and the electric field intensity vector E m are zero. Under these conditions the compound space is in a state of antiplanar strain, all the field quantities being expressible in terms of four analytic functions ~r)(z) (v, r = 1, 2) as follows [2]: u~r) = Re fl(r)(z), r = Re f(r)(z), Elr)-iE~r) =-F~2r)(z),are respectively the electric potential and components of the vectors of elastic displacement and cp, u 3 and D,, electric induction; c44 =c~, el5 and ell =eSt are the shear modulus measured with zero electric field, the piezomodulus, and the dielectric permittivity measured at zero strain [3]; the subscripts 1 and 2 refer to quantities defined in the upper and lower half-spaces.The solution of this problem (the fundamental solution for a compound space) has the form [2] 2 ~(l) ~'(t) (D~)(z) A(v ') Xtxv,~ ~_m = + _ , Imz>__0(v=l, 2);

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Anti-plane deformation of a composite piezoceramic space with interphase crack

Cited by 8 publications

References 0 publications

Distinctive features of physical fields near the edge of a composite piezoceramic wedge (antiplane deformation)

Distinctive features of physical fields near the edge of a composite piezoceramic wedge (antiplane deformation)

Bond zone model for a conductive crack at the interface of piezoelectric materials under anti‐plane mechanical and in‐plane electric loadings

Fundamental two-dimensional solutions of electroelasticity for compound piezoceramic bodies

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