Surface effect on two nanocracks emanating from an electrically semi-permeable regular 2n-polygon nanohole in one-dimensional hexagonal piezoelectric quasicrystals under anti-plane shear

2021 ◽  
Author(s):  
Zhilin Wu ◽  
Guanting Liu ◽  
Dongsheng Yang
Keyword(s):  
Stress Intensity ◽  
Intensity Factor ◽  
Surface Effect ◽  
Mechanical Load ◽  
Electric Displacement ◽  
Relative Size ◽  
Size Change ◽  
One Dimensional ◽  
Phonon Field ◽  
Electric Displacement Intensity Factor

In this paper, the conformal mapping from a regular 2[Formula: see text]-polygon hole with two collinear asymmetric cracks into a circle is constructed. Based on the Gurtin–Murdoch surface/ interface model and complex potential theory, two collinear asymmetric nanocracks emanating from an electrically semi-permeable regular 2[Formula: see text]-polygon nanohole embedded in an infinite one-dimensional hexagonal piezoelectric quasicrystals with surface effect are investigated. The size-dependent stress intensity factors of phonon field and phason field, electric displacement intensity factor at the nanocrack tip are derived for electrically semi-permeable boundary condition. Numerical examples are illustrated to show that the size of the hole, mechanical load, electric load, cracks relative size change with stress intensity factor of phonon field and electric displacement intensity factor. Also analyzed the change of the electric displacement intensity factor with different electric permeability at the nanocrack tip and the dimensionless intensity factor with [Formula: see text].

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.

Analytical Solution of the Star-Shaped Crack in One-Dimensional Hexagonal Quasicrystals

2013 ◽  
Vol 838-841 ◽  
pp. 2254-2261
Author(s):  
Lu Guan ◽  
Zhu Chen
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Analytical Solution ◽  
Conformal Mapping ◽  
Complex Analysis ◽  
Crack Tip ◽  
One Dimensional ◽  
Shaped Crack ◽  
Shear Problem

With the use of complex analysis, and by introducing adequate conformal mapping, the anti-shear problem of the star-shaped crack in One-dimensional Hexagonal Quasicrystals was studied. An analytical solution to the crack tip stress intensity factor is found.

The Antiplane Shearing Problem of Circular Holes with 2k Periodic Cracks in One-Dimensional Hexagonal Quasicrystals

2014 ◽  
Vol 915-916 ◽  
pp. 1086-1095
Author(s):  
Lu Guan ◽  
Zhu Chen
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Conformal Mapping ◽  
Complex Analysis ◽  
Analytic Solution ◽  
Crack Tip ◽  
One Dimensional ◽  
Circular Holes ◽  
Periodic Cracks

Using the method of complex analysis and by constructing conformal mapping, the study investigated the antiplane shearing problem of circular holes with 2k periodic cracks in one-dimensional hexagonal quasicrystals. Wherefrom we simulated the problem of antiplane shearing in circular holes of cross-cracks, single-cracks, symmetrical double-cracks, symmetrical four-cracks, as well as periodic straight cracks, and provided an analytic solution to the crack tip stress intensity factor (SIF).

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.

Stress Intensity Factor of Interface Crack in the Cermet Cladding Material Structure under Steady Mechanical-Thermal Coupled Loads

2016 ◽  
Vol 723 ◽  
pp. 394-399
Author(s):  
Jun Ru Yang ◽  
Yu Rong Chi ◽  
Ming Lan Wang ◽  
Ran Zhu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Interface Crack ◽  
Mechanical Load ◽  
Theoretical Models ◽  
Material Structure ◽  
The Finite Element Method ◽  
Coupled Loads ◽  
Cladding Material

In the paper, the crack parallel to and lying on the interface in the hard cermet cladding material structure is taken as the study object. Theoretical models of the stress intensity factor (SIF) of the interface crack under steady mechanical-thermal coupled loads are built. Based on which the interface crack SIFs in the cermet cladding material of 5Cr2Ni08C/Q235 under the same loads are analyzed with the finite element method. The crack SIF change laws under the coupled loads are obtained. KI increases with the increase of the temperature, the mechanical load and the crack length respectively. The absolute values of KII have the same change laws. And KI corresponding to the coupled loads is bigger than that to the single load. The research results are very important to develop the interface crack propagation theory. And they will also improve the optimization designs of the hard cladding material parts, and expand their applications.

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.

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