Distribution of electric field and energy flux around the cracks on the surfaces of Nd-doped phosphate glasses

We simulate and calculate numerically the electromagnetic field and energy flux around a surface crack of an Nd-doped phosphate laser glass by using the finite-difference time-domain method. Because of a strong interference between the incident wave and the total internal reflections from the crack and the glass surface, the electric field is redistributed and enhanced. The results show that the electric-field distribution and corresponding energy flux component depend sensitively on the light polarization and crack geometry, such as orientation and depth. The polarization of the incident laser beam relative to the crack surfaces will determine the profile of the electric field around the crack. Under TE wave incidence, the energy flux peak is always inside the glass. But under TM wave incidence, the energy flux peak will be located inside the glass or inside the air gap. For both incident modes, the light intensification factor increases with the crack depth, especially for energy flux along the surface. Because cracks on the polished surfaces are the same as the roots extending down, the probability for much larger intensification occurring is high. The results suggest that the surface laser-damage threshold of Nd-doped phosphate may decrease dramatically with subsurface damage.     

Investigation of an interface crack with a contact zone in a piezoelectric bimaterial under limited permeable electric boundary conditions

Summary The plane strain problem for an interface crack between two bonded piezoelectric semi-infinite planes under remote electromechanical loading is considered. Mechanically frictionless and electrically permeable contact zones are assumed at the crack tips and the remaining part of the crack is considered as electrically limited permeable with a certain permeability of the crack medium. Patron’s way of modelling limited permeable conditions is used. By means of integral transforms the problem is reduced to a nonlinear system of singular integral equations. An iterative scheme together with discretization and utilization of Gauss-Chebishev quadrature rule is applied for the solution of this system. Distributions of the electric displacement along the crack region as well as the stress and electric intensity factors and the energy release rate are found for different electromechanical loads and crack permeabilities. Calculations are performed for an artificial contact zone length, however the way of an easier determination of the associated values for the real contact zone length is shown. As a particular case of the obtained solution the crack in a homogeneous piezoelectric media is considered. The results of the calculations are compared to the corresponding results obtained earlier by means of Hao and Shen’s way of modelling the crack permeability. Even though the electric displacements obtained in the respective framework of these models differ essentially, it appears that the fracture mechanical parameters are in good agreement with each other.     

Extension of winding function theory for nonuniform air gap in electric machinery

This paper extends the winding function theory for nonuniform air gap in rotating electric machinery. It shows that the winding function differs from that used in the symmetrical case, although several papers employ the uniform air-gap winding function to study electric motor performance under fault conditions. The extended theory will be particularly helpful in the study of squirrel-cage induction motors with a nonuniform air gap such as that caused by eccentricity of the rotor and stator.     

Crack growth in ferroelectric ceramics under electric loading

Summary A crack with growth in ferroelectric ceramics under purely electric loading is analyzed. The crack tip stress intensity factor for the growing crack under small scale conditions is evaluated by employing the model of nonlinear domain switching. The electrical fracture toughness is obtained from the result of the stress intensity factor. It is shown that the ferroelectric material can be either toughened or weakened as the crack grows. Fatigue crack growth in a ferroelectric material under cyclic electric loading is also examined. The incremental fatigue crack growth under cyclic electric loading is obtained numerically. The fatigue crack growth rate is affected strongly by the electrical nonlinear behavior. It is found that the curve of fatigue crack growth rate versus electric field intensity factor is linear on the log-log plot at intermediate values of the electric field intensity factor.     

Steady propagate crack in a transverse isotropic piezoelectric material considering the permittivity of the medium in the crack gap

This paper derives an exact solution of the steady propagated crack in a transverse isotropic piezoelectric material plane. In order to consider the medium in the crack gap, two cases have been studied. In the first case, the permittivity of the medium in the crack gap _a is far less than that of piezoelectric materials _m. Therefore, the electric induction in the gap (Pak, 1990; Suo et al., 1992) is neglected. In the second case, the permittivity of the medium in the crack gap is comparable with that of piezoelectric material. This electric induction is considered. This result shows that the consideration of the induction has reduced the electric displacement intensity factor k ₄. Due to the influence of the dynamic effect, the elastic constants have become smaller as the dynamic anisotropy case. It must be pointed out that only the small speed of steady propagated crack is considered. Therefore, according to Sosa et al. (1999, 2001), the magnetic effect is neglected.     

Fracture of electrostrictive solids subjected to combined mechanical and electric loads

Based on the complex variable method, this paper studies the effects of electric fields on the fracture of an electrostrictive solid under combined mechanical and electrical loads at infinity. The electric field inside a deformed crack is first determined by using the semi-permeable crack model. Then, the complex potentials and the intensity factors of stresses are presented, respectively, in concise and closed forms. Numerical results are also obtained to discuss the effects of applied electric and/or mechanical loads on the induced electric fields inside the crack and the stress intensity factors when the interior of the deformed crack and the surrounding space at infinity are filled with different gases.     

Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium

In this paper, the influence of the electric boundary conditions on cracks in piezoelectric components shall be studied. Several electric boundary conditions have been proposed in the literature. Here, influence of the permeability of the crack on electric and mechanical fields near the crack tip is considered. Cracks of lower permeability lead to stronger electric singularities. Furthermore, the influence on the stress intensity factors and energy release rate will be discussed. Finally, an experiment with piezoceramic CT specimens, which was performed by Park and Sun, will be evaluated taking into account the permeability of the crack.     

Left-handed metamaterials based on only modified circular electric resonators

Abstract

The novel design of a single-sided left-handed metamaterial (LHM) based only on modified circular electric resonators (MCERs) is presented experimentally and numerically in this letter. A capacitive gap is introduced in the middle arm of the electric resonator. Through adjusting the geometrical dimensions properly, the two frequency bands corresponding to negative permittivity and permeability overlap, which is validated by the parametric retrieval algorithm and equivalent circuit analysis. Furthermore, a dual-band LHM is achieved by combining two kinds of MCERs within the same unit cell. Compared to previous composite structures, the MCERs have the advantages of simple pattern, flexible design and fabricating three-dimensional LHMs readily.     

Suspended and localized single nanostructure growth across a nanogap by an electric field

Direct growth of a suspended single nanostructure (SSN) at a specific location is presented. The SSN is grown across a metallic nanoscale gap by migration in air at room temperature. The nanogap is fabricated by industrial standard optical lithography and anisotropic wet chemical silicon etching. A DC current bias, 1 nA, is applied across the metallic gap to induce nanoscale migration of Zn or ZnO. The history of the voltage drop across the gap as a function of time clearly indicates the moment when migration begins. The shape of SSNs grown across the nanogap by the migration is asymmetric at each electrode due to the asymmetric electric field distribution within the nanogap. An SSN can be used as the platform for two-terminal active or passive nanoscale electronics in optoelectronics, radio frequency (RF) resonators, and chemical/biological sensors.     

Influence of the solid dielectric surface structure on the electric field at an air-barrier boundary

The distribution of electric field in air near a solid dielectric plate has been calculated using a model that takes into account the degree of roughness of the dielectric surface. Calculations performed for pyroceram show that the electric field strength at the vertices of juts on the dielectric surface can be 2.5ÌæÌ3.5 times (depending on the degree of surface roughness) greater than the values in the air gap. At the same time, the field strength in hollows is about ten times weaker than that at the juts. The obtained results agree with experimentally observed [1] changes in the intensity of discharge processes at a dielectric surface with increasing degree of roughness.     

在脉冲电流作用下钢中裂纹的愈合

对含有人工预置贯穿裂纹的钢进行脉冲电流处理．在光学显微镜和扫描电镜下观察了处理前后钢样品中裂纹和组织的变化．结果表明，脉冲电流处理可以使裂纹的局部在固态下愈合．愈合是在极短时间内发生的，不影响材料不含裂纹部分的原有结构．在电流通过裂纹时产生的较高温度使其有比较大的膨胀量，周围温度较低基体的约束导致向着裂纹内的压缩，从而使裂纹面上的原子重新成键接合．     

Insights into process innovation through ultrasonically agitated concentric flow dielectric streams for dry wire electric discharge machining

Application of gaseous dielectric in place of liquid dielectric for wire electric discharge machining (WEDM), popularly known as dry wire electric discharge machining (DWEDM), offers technological solutions to some environmental and metallurgical issues pertaining to process. However, conventional side jet stream of dielectric in dry WEDM renders ineffective debris removal from sparking gap to cause unwanted arcing. Moreover, side thrust on the wire surface tends to induce wire vibrations and results into uneven geometrical profiles. To harness full potential of DWEDM technology, it is imperative to improve cutting characteristics of process by minimizing the adverse impacts of side jet stream of dielectric. In this research work, the authors have conceptualized and demonstrated the idea of using concentric flow pattern of gaseous dielectric as a novel technological solution to limitations of DWEDM process by introducing ultrasonic-agitated concentric dry wire electric discharge machining (UCDWEDM). Experiments have been performed on Ti–6Al–4V material. Ultrasonically agitated pressurized air streams were supplied through indigenously developed concentric and side flow nozzles mounted on experimental set up. The experimental results showed that concentric flow mode of dielectric supply has outperformed the conventional side flow mode with 42% higher CV, 22% lower SR, and 8% lesser KW. Process mechanism of UCDWEDM is based on high velocity of air in concentric flow and ultrasonic-agitation in spark gap and suggested that UCDWEDM has potential to replace conventional dielectric supply system in DWEDM.     

Fatigue crack growth driven by electric fields in piezoelectric ceramics and its governing fracture parameters

Fatigue crack growth test for piezoelectric ceramics was performed under cyclic electric loading. Double cantilever beam specimen, which was made of two different piezoelectric ceramics, with a through notch was used. The specimens were, varying the amplitude and the mean value, subjected to various cyclic electric fields. It was found that crack growth behavior is greatly dependent on the amplitude and mean value of cyclic electric field and materials. Crack growth rate decreased as electric field increased and finally stopped. Crack growths under the positive, the negative and the shifted electric field were very slow compared to that under fully reversed electric field. However, threshold for the crack propagation did not depend greatly on materials. Then, as possible governing fracture parameters, CED and electric displacement intensity factor were chosen based on the results of electromechanical finite element analysis within linear framework and their closed form equations were also obtained considering the influences of electric boundary conditions inside the notch. Finally, the parameters were correlated with crack growth rate measured experimentally by employing Paris law type equation.     

On approach of crack tip energy release rate for a semi-permeable crack when electromechanical loads become very large

This paper presents an investigation on the approach of the crack tip energy release rate (ERR) for a semi-permeable crack full with air/vacuum or Silicon oil when the electromechanical loads become very large. Numerical results for a central semi-permeable crack, respectively, in seven kinds of piezoelectric ceramics are compared with those for a central impermeable crack when the mechanical loads vary from 50 to 100 MPa and the electric loads are fixed to be 1 MV/m, 0, and –1 MV/m, respectively, within the range of practical interest. It is verified that McMeekings statement (2004): as the electromechanical loads become very large, the crack tip ERR approaches the values associated with an impermeable crack is actually valid under very large mechanical and positive electric loads. However, under very large mechanical and negative electric loads, the approach is quite different showing large discrepancies between the calculated values for the semi-permeable crack and those for an impermeable crack in all seven kinds of piezoelectric ceramics. This means that his statement is not valid when the electric loads are negative even though the mechanical loads still remain very large although, mathematically, McMeekings statement is correct if McMeekings statement: very large is replaced by infinitely large. Moreover, under purely mechanical loads his statement is uncertain, depending on which kind of piezoelectric ceramic is used. It is concluded that, generally speaking, the crack tip ERR for a semi-permeable crack does not approach the values associated with an impermeable crack, depending on the direction of the electric loads with respect to the poling axis. Physically, this is because of the inherent piezoelectric effect that yields the surface charges distributed on the crack surfaces for a semi-permeable crack under the mechanical loads, whereas on the surfaces of an impermeable crack the unphysical charge-free condition leads to incorrect estimations: the applied mechanical loads do not yield any surface charges on the crack surfaces. The influence of the permittivity of medium inside the semi-permeable crack gap on McMeekings statement is discussed too. It is found that Silicon oil yields larger discrepancies than air from those for an impermeable crack.     

Stress analysis in a cracked infinite electrostrictive plate with local saturation electric fields

Based on the electric circular saturation zone near an ideal crack tip, the approximate complete solution for electric and stress field in a cracked electrostrictive plate under general loading at infinity is carried out. The SIFs are then obtained. We find that the stress distributions in front of the crack tip can be divided into four different regions. The fracture behavior is closely related to these distributions.     

Crack detection by the electric method: Uniqueness and~approximation

Let U be a bounded domain in the boundary ∂ U of which is a closed nonself-intersecting curve. Let ω be a hole (a crack) in the interior of U the boundary of which is a closed nonself-intersecting curve. Let U and ω be star-shaped. It is shown that the problem of finding a harmonic function u and its domain , subject to given Cauchy conditions on an open subset of ∂ U and to the condition ∂ u/∂n=0 on ∂ω has at most one solution. This uniqueness result shows that an insulating crack (e.g. one made up of air) can be identified by the electric method. The problem of determining ∂ω is an ill-posed problem; it is here regularized using finite dimensional approximations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of electric boundary conditions on crack energy density and its derivatives for piezoelectric material

This paper deals with crack energy density (hereafter CED) as a possible fracture parameter in piezoelectricity under arbitrary electric boundary conditions on a notch-like crack surface. The definitions of CED and its derivatives are given first under exact boundary condition. Next, their path independent integrals are also derived and their approximate expressions are discussed under some restrictions on the crack surfaces. It is found that electrical terms along the notch-like crack surface do not vanish unlike in the case of impermeable crack. Then, we introduce evaluation methods of CED, and, with the help of the results of finite element analyses (FEA), we closely examine how electric boundary conditions along the notch surface and initial notch width influence CED and its derivatives. It is shown from the FEA results that because of the difficulties of computing path integral terms along the notch-like crack tip in the path independent expressions, the evaluation by the definitions of CED and its derivatives is preferable and more convenient than the evaluation of their path independent expressions. It is also found that all the parameters are significantly affected by both permittivity inside the electric inclusion and root radius of the notch. Finally, the possibility of mechanical CED as a governing fracture parameter is discussed.     

Fracture of pre-cracked thin metallic conductors due to electric current induced electromagnetic force

We investigated propagation of a sharp crack in a thin metallic conductor with an edge crack due to electric current induced electromagnetic forces. Finite element method (FEM) simulations showed mode I crack opening in the edge-cracked conductor due to the aforementioned (i.e., self-induced) electromagnetic forces. Mode I stress intensity factor due to the self-induced electromagnetic forces, \(K_{\mathrm{IE},}\) was evaluated numerically as \(K_{\mathrm{IE}}=\upmu l^{2}j^{2}(\uppi a)^{0.5}f(a/w)\), where \(\upmu \) is the magnetic permeability, l is the length of the conductor, a is the crack length, j is the current density, w is the width of the sample and f(a / w) is a geometric factor. Effect of dynamic electric current loading on edge-cracked conductor, incorporating the effects of induced currents, was also studied numerically, and dynamic stress intensity factor, \(K_{\mathrm{IE,d}}\), was observed to vary as \(K_{\mathrm{IE,d}} \sim f_{d}(a/w)j^{2}(\uppi a)^{1.5}\). Consistent with the FEM simulation, experiments conducted using \(12\,\upmu \hbox {m}\) thick Al foil with an edge crack showed propagation of sharp crack due to the self-induced electromagnetic forces at pulsed current densities of \(\ge \) \(1.85\times 10^{9}\,\hbox {A/m}^{2}\) for \(a/w = 0.5\). Further, effects of current density, pulse-width and ambient temperature on the fracture behavior of the Al foil were observed experimentally and corroborated with FEM simulations.     

Transient response of a functionally graded piezoelectric strip with a penny-shaped crack under electric time-dependent loading

Summary The dynamic fracture problem for a functionally graded piezoelectric material (FGPM) strip containing a penny-shaped crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the strip vary continuously along the thickness direction of the strip, and that the strip is under time-dependent electric load. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the crack location and the material nonhomogeneity.     

Microstructure and stray electric fields at surface cracks in ferroelectrics

Ferroelectric perovskites are widely used in transducer, memory and optical applications due to their attractive electromechanical and optical properties. In these brittle materials, reliability and failure of devices is dominated by the behavior of cracks. The electromechanical coupling causes cracks to interact strongly with both mechanical as well as electrical fields. Additionally, cracks and domain patterns interact strongly with each other. Hence, an understanding of the electromechanics of cracks requires an accounting of all these interactions. In this work, we apply a real-space phase-field method to compute the stresses, domain patterns, and stray electric fields in the vicinity of a stationary crack, defined here as a geometric feature that causes large but bounded stress. We investigate the effects of charge compensation on the crack face, crack orientation with respect to the crystal lattice, and applied far-field stress and electric fields.