scholarly journals Fracture Analysis of Griffith Interface Crack in Fine-Grained Piezoelectric Coating/Substrate under Thermal Loading

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Shuaishuai Hu ◽  
Jiansheng Liu ◽  
Junlin Li
Keyword(s):  
Intensity Factor ◽  
Interface Crack ◽  
Thermal Loading ◽  
Integral Transformation ◽  
Electric Displacement ◽  
Singular Integral Equations ◽  
External Loading ◽  
Principle Of Superposition ◽  
Fine Grained ◽  
Electric Displacement Intensity Factor

Coating often plays a role in monitoring and protecting substrates in engineering applications. Interface cracks between the coating and the substrate can lead to crack growth under the action of external loading and will cause device failure. In this paper, the behavior of a fine-grained piezoelectric coating/substrate with a Griffith interface crack under steady-state thermal loading is studied. The temperature field, displacement field, and electric field of the coupling of thermal and electromechanical problems are constructed via integral transformation and the principle of superposition. Thus, problems are transformed into a system of singular integral equations, and the expressions of thermal intensity factor, thermal stress intensity factor, and electric displacement intensity factor are obtained. We used a numerical calculation and a system of singular equations to obtain the relationship of strength factor with material parameters, coating thickness, and crack size.

scholarly journals Research on Multiple Griffith Cracks at the Interface of Fine-Grained Piezoelectric Coating/Substrate

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Shuaishuai Hu ◽  
Jiansheng Liu ◽  
Junlin Li
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Singular Integral ◽  
Release Rate ◽  
Electric Displacement ◽  
Singular Integral Equations ◽  
Interface Cracks ◽  
Fine Grained ◽  
Piezoelectric Structure ◽  
Bimaterial Structure

The behavior of a fine-grained piezoelectric coating/substrate with multiple Griffith interface cracks under electromechanical loads is investigated. In this work, double coupled singular integral equations are proposed to solve the fracture problems. Both the singular integral equation and single-valued conditions are simplified into an algebraic equation and solved by numerical calculation. Thereby, the intensity factors of electric displacement and stress obtained are used to obtain the expression of the energy release rate. Furthermore, numerical results of the energy release rate with material parameters are demonstrated. Based on the obtained results, it could be concluded that the energy release rate is closely related to the size of the interface cracks and the mechanical-electrical loading. For a bimaterial structure, the fine-grained piezoelectric structure exhibited better material performance compared to the large one.

scholarly journals Antiplane Fracture Problem of Three Nanocracks Emanating from an Electrically Permeable Hexagonal Nanohole in One-Dimensional Hexagonal Piezoelectric Quasicrystals

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Dongsheng Yang ◽  
Guanting Liu
Keyword(s):  
Stress Intensity ◽  
Intensity Factor ◽  
Boundary Conditions ◽  
Energy Release Rate ◽  
Release Rate ◽  
Surface Effect ◽  
Electric Displacement ◽  
One Dimensional ◽  
Phonon Field ◽  
Electric Displacement Intensity Factor

Based on the Gurtin-Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping, the electrically permeable boundary condition with surface effect is established, and the antiplane fracture problem of three nanocracks emanating from a hexagonal nanohole in one-dimensional hexagonal piezoelectric quasicrystals with surface effect is studied. The exact solutions of the stress intensity factor of the phonon field and the phason field, the electric displacement intensity factor, and the energy release rate are obtained under the two electrically permeable and the electrically impermeable boundary conditions. The numerical examples show the influence of surface effect on the stress intensity factors of the phonon field and the phason field, the electric displacement intensity factor, and the energy release rate under the two boundary conditions. It can be seen that the surface effect leads to the coupling of the phonon field, phason field, and electric field, and with the decrease of cavity size, the influence of surface effect is more obvious.

Anti-plane fracture problem of three nano-cracks emanating from a magnetoelectrically permeable regular triangle nano-hole in magnetoelectroelastic materials

2020 ◽  
pp. 2150127
Author(s):  
Dongsheng Yang ◽  
Guanting Liu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Release Rate ◽  
Magnetic Induction ◽  
Surface Effect ◽  
Electric Displacement ◽  
Magnetoelectroelastic Materials ◽  
Electric Displacement Intensity Factor ◽  
Magnetic Induction Intensity

Based on the Gurtin–Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping, the anti-plane fracture problem of three nano-cracks emanating from a magnetoelectrically permeable triangle nano-hole in magnetoelectroelastic materials with surface effect is studied. The exact solutions of the stress intensity factor, the electric displacement intensity factor, the magnetic induction intensity factor, and the energy release rate are obtained under the boundary conditions of magnetoelectrically permeable and impermeable. The numerical examples show the influence of surface effect on the stress intensity factor, the electric displacement intensity factor, the magnetic induction intensity factor, and the energy release rate under two different boundary conditions. It can be seen that the surface effect leads to the coupling of stress, electric and magnetic field, and with the increase of cavity size, the influence of surface effect begins to decrease until it tends to classical elasticity theory.

The Interface Crack Problem of Bonded Piezoelectric and Elastic Half-Space Under Transient Electromechanical Loads

2002 ◽  
Vol 69 (3) ◽  
pp. 244-253 ◽  
Author(s):  
S. A. Meguid ◽  
X. Zhao
Keyword(s):  
Boundary Condition ◽  
Intensity Factor ◽  
Boundary Conditions ◽  
Half Space ◽  
Interface Crack ◽  
Singular Integral ◽  
Crack Problem ◽  
Elastic Half Space ◽  
Electric Displacement Intensity Factor ◽  
Impermeable Boundary

The interface crack problem of bonded piezoelectric and elastic half-space under transient electromechanical loads is considered. Both the permeable and impermeable boundary conditions are examined and discussed. Based on the use of integral transform techniques, the problem is reduced either to a singular integral equation for the permeable boundary condition or to two coupled singular integral equations for the impermeable boundary condition, which can be solved using Chebyshev polynomial expansions. Numerical results are provided to show the effect of the applied electric fields, the electric boundary conditions along the crack faces and a free surface on the resulting dynamic stress intensity factor and electric displacement intensity factor.

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.

Effects of Maxwell Stress on Interfacial Crack Between Two Dissimilar Piezoelectric Solids

2014 ◽  
Vol 81 (10) ◽  
Author(s):  
Yi-Ze Wang
Keyword(s):  
Intensity Factor ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Maxwell Stress ◽  
Electric Load ◽  
Piezoelectric Composites ◽  
Fracture Characteristics ◽  
Electric Displacement Intensity Factor ◽  
Piezoelectric Solids ◽  
Remote Stress

In this study, the effects of the Maxwell stress on the interfacial crack between two dissimilar piezoelectric solids are investigated. With the Stroh form and Muskhelishvili theory, the explicit expressions of generalized stresses are presented and the closed forms of the stress and electric displacement intensity factors are derived. Results show that the generalized stress field has singularities and oscillatory properties near the crack tip and the Maxwell stress has influences on the fracture characteristics. For the piezoelectric composites with the Maxwell stress, the normalized stress intensity factor KI* can be changed by both the remote stress and electric load. Such phenomenon cannot be found for the piezoelectric system without the Maxwell stress. Furthermore, the electric displacement intensity factor is more sensitive to the electric load than that to the remote stress.

Fracture Analysis of Magnetoelectroelastic Composite Materials

2007 ◽  
Vol 348-349 ◽  
pp. 69-72 ◽  
Author(s):  
R. Rojas-Díaz ◽  
Felipe García-Sánchez ◽  
Andrés Sáez ◽  
Chuan Zeng Zhang
Keyword(s):  
Intensity Factor ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Electric Displacement ◽  
External Boundary ◽  
Loading Conditions ◽  
Magnetoelectroelastic Materials ◽  
Electric Displacement Intensity Factor ◽  
Total Energy Release Rate

This paper presents a crack analysis of linear magnetoelectroelastic materials subjected to static loading conditions. To this end, an efficient boundary element method (BEM) is developed. Unlike many previous investigations published in literature, two-dimensional (2-D) linear magnetoelectroelastic materials possessing fully coupled piezoelectric, piezomagnetic and magnetoelectric effects are considered in this paper. A combination of the displacement BEM and the traction BEM is used in the present formulation. The displacement BEM is applied for the external boundary of the cracked solid, while the traction BEM is used for the crack-faces. A regularization technique is implemented to compute the strongly singular and hypersingular boundary integrals in the BEM. The electric displacement intensity factor (EDIF), the magnetic induction intensity factor (MIIF), the stress intensity factors (SIF), the mechanical strain energy release rate (MSERR) and the total energy release rate (TERR) are evaluated directly from the computed nodal values at discontinuous quarter point elements placed next to the crack tip. The accuracy of the BEM is verified by analytical solutions known in literature. Results are presented for a branched crack in a bending specimen subjected to combined magnetic-electric-mechanical loading conditions.

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.

The Interface Crack

1977 ◽  
Vol 44 (4) ◽  
pp. 631-636 ◽  
Author(s):  
Maria Comninou
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Interface Crack ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Open Crack ◽  
Intensity Factors ◽  
Frictionless Contact ◽  
Crack Faces

It is known that oscillatory singularities appear in problems involving interface cracks that are assumed to have open tips. An unsatisfactory aspect of the oscillatory singularities is that they lead to overlapping of the crack faces. The interface crack in a tension field, originally treated by England among others, is thus reconsidered on the basis that the crack is not completely open and that its faces are in frictionless contact near the tips. The formulation leads to a pair of coupled singular integral equations. The singularities, no longer oscillatory, exhibit some unusual features and indicate that the spreading of the interface crack in a tension field is intimately connected with failure in shear. A new stress-intensity factor is obtained and compared to the stress-intensity factors for the completely open crack.

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