A Study of Crack-Face Boundary Conditions for Piezoelectric Strip Cut Along Two Equal Collinear Cracks

2016 ◽  
Vol 8 (4) ◽  
pp. 573-587 ◽  
Author(s):  
R. R. Bhargava ◽  
Pooja Raj Verma
Keyword(s):  
Boundary Conditions ◽  
Crack Opening ◽  
Electric Displacement ◽  
Potential Drop ◽  
Collinear Cracks ◽  
Crack Face ◽  
Plane Shear ◽  
Fracture Parameters ◽  
Analytic Expressions ◽  
Piezoelectric Strip

AbstractA problem of two equal, semi-permeable, collinear cracks, situated normal to the edges of an infinitely long piezoelectric strip is considered. Piezoelectric strip being prescribed out-of-plane shear stress and in-plane electric-displacement. The Fourier series and integral equation methods are adopted to obtain analytical solution of the problem. Closed-form analytic expressions are derived for various fracture parameters viz. crack-sliding displacement, crack opening potential drop, field intensity factors and energy release rate. An numerical case study is considered for poled PZT–5H, BaTiO3 and PZT–6B piezoelectric ceramics to study the effect of applied electro-mechanical loadings, crack-face boundary conditions as well as inter-crack distance on fracture parameters. The obtained results are presented graphically, discussed and concluded.

Riemann–Hilbert approach-based analytical solutions for strip saturated two unequal collinear cracks in piezoelectric media

2021 ◽  
Vol 13 (4) ◽  
pp. 177-195
Author(s):  
Sandeep Singh ◽  
Kuldeep Sharma
Keyword(s):  
Analytical Solutions ◽  
Complex Potential ◽  
Crack Opening ◽  
Electric Displacement ◽  
Potential Functions ◽  
Collinear Cracks ◽  
Crack Face ◽  
Piezoelectric Media ◽  
Fracture Parameters ◽  
Poling Direction

The objective of the work is to derive analytical solutions based on the Riemann–Hilbert (R–H) approach for semipermeable strip saturated two unequal collinear cracks in arbitrary polarized piezoelectric media. We particularly consider the influence of far field electromechanical loadings, poling direction and different crack-face boundary conditions. The problem is mathematically formulated into a set of non-homogeneous R–H problems in terms of complex potential functions (related to field components) using complex variable and extended Stroh formalism approach. After solving these equations, explicit solutions are obtained for the involved unknown complex potential functions and hence, the stress and electric displacement components at any point within the domain. Furthermore, after employing standard limiting conditions, explicit expressions for some conventional fracture parameters such as saturated zone lengths (in terms of nonlinear equations), local stress intensity factors and crack opening displacement are obtained. Numerical studies are presented for the PZT-4H material to analyze the effects of prescribed electromechanical loadings, inter-cracks distance, crack-face conditions and poling direction on the defined fracture parameters.

Nonlinear analysis of a crack in 2D piezoelectric semiconductors with exact electric boundary conditions

2020 ◽  
pp. 1045389X2096316
Author(s):  
MingHao Zhao ◽  
XinFei Li ◽  
Chunsheng Lu ◽  
QiaoYun Zhang
Keyword(s):  
Boundary Condition ◽  
Intensity Factor ◽  
Boundary Conditions ◽  
Crack Opening ◽  
Electric Displacement ◽  
Opening Displacement ◽  
Crack Face ◽  
Electric Boundary Condition ◽  
Electric Displacement Intensity Factor ◽  
Piezoelectric Semiconductors

In this paper, taking the exact electric boundary conditions into account, we propose a double iteration method to analyze a crack problem in a two-dimensional piezoelectric semiconductor. The method consists of a nested loop process with internal and outside circulations. In the former, the electric field and electron density in governing equations are constantly modified with the fixed boundary conditions on crack face and the crack opening displacement; while in the latter, the boundary conditions on crack face and the crack opening displacement are modified. Such a method is verified by numerically analyzing a crack with an impermeable electric boundary condition. It is shown that the electric boundary condition on crack face largely affects the electric displacement intensity factor near a crack tip in piezoelectric semiconductors. Under exact crack boundary conditions, the variation tendency of the electric displacement intensity factor versus crack size is quite different from that under an impermeable boundary condition. Thus, exact crack boundary conditions should be adopted in analysis of crack problems in a piezoelectric semiconductor.

Fracture Analysis of Piezoceramic CT-Specimen for Different Types of Crack Face Boundary Conditions

2015 ◽  
Vol 725-726 ◽  
pp. 949-954
Author(s):  
Ilia V. Ivashov ◽  
Artem S. Semenov
Keyword(s):  
Boundary Conditions ◽  
Piezoelectric Materials ◽  
Compact Tension ◽  
Fracture Criteria ◽  
Lifetime Estimation ◽  
Crack Face ◽  
Fracture Parameters ◽  
Different Types ◽  
Electromechanical Loading ◽  
The Moment

At the moment a problem of fracture and lifetime estimation for piezoelectric materials is not completely solved. The paper considers fundamentals of linear fracture electromechanics, fracture parameters and fracture criteria. The main difference from linear mechanics is crack face boundary conditions taking into account relative permeability of media inside the crack gap and coulomb traction. Different types of crack face boundary conditions and their numerical implementation are described. The paper presents results of finite element modeling of fracture toughness experiments on the compact tension specimens under combined electromechanical loading. Different types of crack face boundary conditions were tested and comparison of fracture parameters and fracture criteria was carried out.

Accurate fracture analysis of electrically permeable/impermeable cracks in one-dimensional hexagonal piezoelectric quasicrystal junction

2019 ◽  
Vol 24 (12) ◽  
pp. 4032-4050 ◽  
Author(s):  
Zhenting Yang ◽  
Xiong Yu ◽  
Wang Xu ◽  
Chenghui Xu ◽  
Zhenhuan Zhou ◽  
...  
Keyword(s):  
Electric Displacement ◽  
Fracture Analysis ◽  
The Finite Element Method ◽  
Crack Face ◽  
Impermeable Crack ◽  
One Dimensional ◽  
Fracture Parameters ◽  
Small Set ◽  
Singular Domain ◽  
Good Agreement

An accurate fracture analysis of a multi-material junction of one-dimensional hexagonal quasicrystals with piezoelectric effect is performed by using Hamiltonian mechanics incorporated in the finite element method. Two idealized electrical assumptions, including electrically permeable and impermeable crack-face conditions, are considered. In the Hamiltonian system, the analytical solutions to the multi-material piezoelectric quasicrystal around the crack tip (singular domain) are obtained and expressed in terms of symplectic eigensolutions. Therefore, the large number of nodal unknowns in the singular domain is reduced into a small set of undetermined coefficients of the symplectic series. The unknowns in the non-singular domain remain unchanged. Explicit expressions of phonon stresses, phason stresses, and electric displacement in the singular domain and newly defined fracture parameters are achieved simultaneously. Comparisons are presented to verify the proposed approach and very good agreement is reported. The key influencing parameters of the crack are discussed in detail. The effects of electrical assumptions and positions of the crack on the fracture parameters are discussed in detail.

scholarly journals Nearly Circular Connections of Elastic Half Spaces

1987 ◽  
Vol 54 (3) ◽  
pp. 627-634 ◽  
Author(s):  
Huajian Gao ◽  
James R. Rice
Keyword(s):  
Boundary Conditions ◽  
Perturbation Technique ◽  
Harmonic Wave ◽  
Crack Opening ◽  
Circular Crack ◽  
Weight Functions ◽  
Wave Form ◽  
Opening Displacement ◽  
Crack Face ◽  
Conditions At Infinity

In this paper we solve the elasticity problem of two elastic half spaces that are joined together over a region that does not differ much from a circle, i.e., the problem of an external planar crack leaving a nearly circular uncracked connection. The method we use is based on the perturbation technique developed by Rice (1985) for solving the elastic field of a crack whose front deviates slightly from some reference geometry. Quantities such as crack opening displacement and stress intensity factor are derived in detail to the first order of accuracy in the deviation of the shape of the connection from a circle. In addition, some results such as the crack face weight functions and Green’s functions for a perfectly circular connection are also discussed under various boundary conditions at infinity. The formulae derived are used to study the configurational stability problem for quasistatic growth of an external circular crack. The results, derived when the crack front is perturbed from circular in a harmonic wave form and is subjected to axisymmetric loading, suggest that a perturbation of wavenumber higher than one is configurationally stable under all boundary conditions at infinity. The perturbation with wavenumber equal to one, which corresponds to a translational shift of the geometric center of the circular connection, turns out to be configurationally stable if any rotation in the remote field is suppressed and configurationally unstable if there is no such restraint.

Transient Dynamic Analysis of Cracked Multifield Solids with Consideration of Crack-Face Contact and Semi-Permeable Electric/Magnetic Boundary Conditions

2014 ◽  
Vol 618 ◽  
pp. 123-150
Author(s):  
Michael Wünsche ◽  
Andrés Sáez ◽  
Felipe García-Sánchez ◽  
Chuan Zeng Zhang ◽  
Jose Domínguez
Keyword(s):  
Intensity Factor ◽  
Boundary Conditions ◽  
Electric Displacement ◽  
Dynamic Crack ◽  
Intensity Factors ◽  
Crack Face ◽  
Transient Dynamic ◽  
Electric Displacement Intensity Factor ◽  
Non Linear ◽  
Crack Face Contact

Boundary element method (BEM) formulations for transient dynamic crack analysis intwo-dimensional (2D) multifield materials are reviwed in this paper. Both homogeneous and lin-ear piezoelectric as well as magnetoelectroelastic material models are considered. Special attentionis paid to properly modeling the non-linear crack-face contact and semi-permeable electric/magneticboundary conditions. Implementation of the corresponding time-domain BEM(TDBEM) is discussedin detail. The proposed TDBEM uses a Galerkin-method for the spatial discretization, whilst thecollocation method is considered for the temporal discretization. Iterative solution algorithms aredeveloped to compute the non-linear crack-face boundary conditions. Crack-tip elements that ac-count for the square-root local behavior of the crack opening displacements (CODs) at the crack-tipsare implemented. In this way, stress intensity factors (SIF), electric displacement intensity factor(EDIF) and magnetic induction intensity factor (MIIF) may be accurately evaluated from the nu-merically computed CODs at the closest nodes to the crack-tips. Numerical examples involving sta-tionary cracks in piezoelectric and magnetoelectroelastic solids under different combined (mechani-cal/electric/magnetic) impact loadings are investigated, in order to illustrate the effectiveness of theproposed approach and characterize the influence of the semi-permeable crack-face boundary condi-tions on the dynamic field intensity factors.

scholarly journals Analysis of Mode I Conducting Crack in Piezo-Electro-Magneto-Elastic Layer

2013 ◽  
Vol 18 (1) ◽  
pp. 153-176
Author(s):  
B. Rogowski
Keyword(s):  
Boundary Conditions ◽  
Electric Displacement ◽  
Hankel Transform ◽  
Fredholm Integral Equations ◽  
Intensity Factors ◽  
Permeable Crack ◽  
Crack Face ◽  
Field Intensity Factors ◽  
Dielectric Crack ◽  
Thickness Field

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto - electrically dielectric crack embedded in a magnetoelectroelastic layer is investigated. The prescribed displacement, electric potential and magnetic potential boundary conditions on the layer surfaces are adopted. Applying the Hankel transform technique, the boundary - value problem is reduced to solving three coupling Fredholm integral equations of second kind. These equations are solved exactly. The corresponding semi - permeable crack - face magnetoelectric boundary conditions are adopted and the electric displacement and magnetic induction of crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings, the dielectric permittivity and magnetic permeability of crack interior, and the ratio of the crack length and the layer thickness. Field intensity factors are obtained as explicit expressions.

Effects of Mixed-Mode and Crack Surface Convection in Rapid Crack Growth in Coupled Thermoelastic Solids

1999 ◽  
Vol 67 (1) ◽  
pp. 59-65 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Boundary Conditions ◽  
Crack Growth ◽  
Crack Surface ◽  
Thermal Response ◽  
Crack Face ◽  
Plane Shear ◽  
Displacement Boundary ◽  
Mode Ii Loading ◽  
Surface Convection ◽  
Line Loads

Two Green’s function problems for rapid two-dimensional steady-state crack growth governed by fully coupled (dynamic) linear thermoelasticity are analyzed. In Problem A, normal and in-plane shear line loads move on the insulated surfaces of a semi-infinite crack growing at a subcritical speed. Problem B involves only normal line loads, but crack surface convection is allowed. Problem A involves, therefore, mixed traction/displacement boundary conditions, while Problem B also exhibits mixed thermal boundary conditions. Robust asymptotic forms based on exact solutions for related problems reduce Problems A and B to coupled sets of integral equations. Both sets exhibit both Cauchy and Abel operators, but are solved exactly. The solutions show that Mode II loading couples the tangential crack face separation and discontinuity in crack-face temperature changes, while crack surface convection enhances thermal response, especially at large distances. [S0021-8936(00)03101-9]

Semi-Permeable Cracks in Magnetoelectroelastic Solids under Impact Loading

2011 ◽  
Vol 488-489 ◽  
pp. 751-754 ◽  
Author(s):  
Michael Wünsche ◽  
Andrés Sáez ◽  
Chuan Zeng Zhang ◽  
Felipe García-Sánchez
Keyword(s):  
Boundary Conditions ◽  
Boundary Integral Equations ◽  
Domain Boundary ◽  
Crack Opening ◽  
Iterative Algorithms ◽  
Boundary Integral ◽  
Dynamic Crack ◽  
Permeable Crack ◽  
Crack Face ◽  
Magnetoelectroelastic Solids

In this paper, transient dynamic crack analysis in two-dimensional, linear magnetoelectroelastic solids by considering different electrical and magnetical crack-face boundary conditions is presented. For this purpose, a time-domain boundary element method (TDBEM) using dynamic fundamental solutions is developed. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is applied to compute the discrete boundary data and the generalized crack-opening-displacements. Iterative algorithms are implemented to deal with the non-linear electrical and magnetical semi-permeable crack-face boundary conditions.

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