On Publications on the Brittle Fracture Mechanics of Prestressed Materials

“…The use of piezoceramic materials necessitates developing methods to study the distribution of the mechanical and electric fields around cracks in electroelastic bodies [2, 6-8, 11-13, 15-21, 23-25]. Solutions of electroelastic equations are addressed in [7,10,25].Numerous results for prestressed bodies with cracks are presented in [5]. Guz [3][4][5] was the first to use the correspondence between the solution for transversely isotropic prestressed bodies and the solution for elastic isotropic bodies.…”

mentioning

confidence: 99%

“…Numerous results for prestressed bodies with cracks are presented in [5]. Guz [3][4][5] was the first to use the correspondence between the solution for transversely isotropic prestressed bodies and the solution for elastic isotropic bodies.…”

mentioning

confidence: 99%

“…Note that the studies [15][16][17][18][19][20][21] are also based on the ideas of [3-5] but do not give any reference to [3][4][5]. We will establish a correspondence between the solutions of two-dimensional problems for rectilinear cracks (plane strain) opened with various symmetric rigid wedges (inclusions) in an elastic isotropic plane and in an electroelastic transversely isotropic plane.…”

mentioning

confidence: 99%

“…Substituting expressions (5) into Eqs. (4), we see that these equations hold if the functions F j satisfy the equations F F j xx j j zz , ,…”

mentioning

confidence: 99%

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Wedging of piezoceramic materials

Kirilyuk

Levchuk

2010

Int Appl Mech

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The paper establishes a correspondence between the solutions for rectilinear cracks located in a piezoceramic plane at a right angle to the polarization axis and smoothly (no friction) opened with rigid wedges and the solutions for cracks in a purely elastic isotropic plane. This correspondence can be used to calculate the SIFs for cracks in a piezoceramic plane from the expressions for cracks in an elastic isotropic plane, without the need to solve the electroelastic problem. The following problems are solved as examples: opening of a semi-infinite crack with a semi-infinite rounded wedge, a truncated wedge, and a wedge of constant thickness; opening of two semi-infinite cracks with hyperbolic wedges and wedges of constant thickness Keywords: transversely isotropic electroelastic material, rectilinear crack, rigid symmetric wedge, stress intensity factor Introduction. A rigorous formulation of the wedging problem for brittle bodies was for the first time addressed in [1]. Results of stress analysis of cracked bodies are presented in [3-5, 9, 14, 22, etc.]. The use of piezoceramic materials necessitates developing methods to study the distribution of the mechanical and electric fields around cracks in electroelastic bodies [2, 6-8, 11-13, 15-21, 23-25]. Solutions of electroelastic equations are addressed in [7,10,25].Numerous results for prestressed bodies with cracks are presented in [5]. Guz [3][4][5] was the first to use the correspondence between the solution for transversely isotropic prestressed bodies and the solution for elastic isotropic bodies.We will apply his approach [3-5] to electroelastic bodies. Note that the studies [15][16][17][18][19][20][21] are also based on the ideas of [3-5] but do not give any reference to [3][4][5]. We will establish a correspondence between the solutions of two-dimensional problems for rectilinear cracks (plane strain) opened with various symmetric rigid wedges (inclusions) in an elastic isotropic plane and in an electroelastic transversely isotropic plane. It is assumed that the cracks are perpendicular to the polarization axis of the transversely isotropic electroelastic material and that the wedge and the crack are in smooth contact. We will use this correspondence to determine the stress intensity factor (SIF) K I for cracks in a piezoceramic plane from the expressions for the SIF for cracks and rigid inclusions of the same shape in an elastic isotropic plane, without the need to solve the electroelastic problem.1. Problem Formulation and Governing Equations. Consider a transversely isotropic electroelastic body with collinear cracks occupying a domain L, located normally to the polarization axis, and opened with rigid inclusions acting in a domain L L 1 Ì inside the cracks. The free portions of the cracks are not subject to mechanical loads. Assume also that there are no electric loads. The closed system of equations for an electroelastic body under plane-strain conditions with the polarization axis aligned with the Oz-axis takes the following form [2]:

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