Penny shaped crack in a three-dimensional piezoelectric strip under in-plane normal loadings

Summary The singular mechanical and electric fields in a three-dimensional piezoelectric ceramic strip containing a penny shaped crack under in-plane normal mechanical and electrical loadings based on the continuous electric boundary conditions on the crack surface are considered here. The potential theory and Hankel transforms are used to obtain a system of dual integral equations, which is then expressed as a Fredholm integral equation. All sorts of field intensity factors of Mode I are given, and numerical values for PZT-6B piezoelectric ceramic are graphically shown.     

A magneto-electro-elastic material with a penny-shaped crack subjected to temperature loading

Summary The analysis of intensity factors for a penny-shaped crack under thermal, mechanical, electrical and magnetic boundary conditions becomes a very important topic in fracture mechanics. An exact solution is derived for the problem of a penny-shaped crack in a magneto-electro-thermo-elastic material in a temperature field. The problem is analyzed within the framework of the theory of linear magneto-electro-thermo-elasticity. The coupling features of transversely isotropic magneto-electro-thermo-elastic solids are governed by a system of partial differential equations with respect to the elastic displacements, the electric potential, the magnetic potential and the temperature field. The heat conduction equation and equilibrium equations for an infinite magneto-electro-thermo-elastic media are solved by means of the Hankel integral transform. The mathematical formulations for the crack conditions are derived as a set of dual integral equations, which, in turn, are reduced to Abel's integral equation. Solution of Abel's integral equation is applied to derive the elastic, electric and magnetic fields as well as field intensity factors. The intensity factors of thermal stress, electric displacement and magnetic induction are derived explicitly for approximate (impermeable or permeable) and exact (a notch of finite thickness crack) conditions. Due to its explicitness, the solution is remarkable and should be of great interest in the magneto-electro-thermo-elastic material analysis and design.     

Simultaneous measurements of RF electric and magnetic nearfields-theoretical considerations

Theoretical considerations for the design of an isotropic combined electric and magnetic radio-frequency field probe are presented. The probe is intended for simultaneous measurements of hazardous electric and magnetic fields under near-field conditions in the frequency range from 10 MHz to 300 MHz. The probe consists of six dipoles and six loops placed on all six sides of a small cube, thus providing a well defined electrical center due to the symmetry. Other significant advantages are improvement of the isotropicity, reduction of the detection errors associated with asymmetrical waveforms, and reduction of the electric field coupling to the magnetic field sensors. Theoretical findings are in agreement with the measured results of a constructed experimental probe     

Electromagnetic control of convective heat transfer during electron beam evaporation: model experiments

The present paper aims to demonstrate that melt-flow during electron beam evaporation can be effectively controlled by using external magnetic fields to considerably reduce the convective heat transfer. We discuss the various effects of a static magnetic field, a static field combined with an applied electrical current, and a rotating magnetic field. We perform model experiments using GaInSn in eutectic composition as a test liquid. The liquid metal is heated locally at its free surface by an electric resistance heater. The results of the measurements are compared to prediction of numerical simulations.     

Coil Probe Dimension and Uncertainties During Measurements of Nonuniform ELF Magnetic Fields

Comparisons are made between the calculated average magnetic flux density for single-axis and three-axis circular coil probes and the calculated magnetic flux density at the center of the probes. The results, which are determined as suming a dipole magnetic field, provide information on the uncertainty associated with measurements of nonuniform extremely low frequency (ELF) magnetic fields produced by some electrical appliances and other electrical equipment.     

Linear electro-elastic fracture mechanics of piezoelectric materials

The concepts of linear elastic fracture mechanics, generalized to treat piezoelectric effects, are employed to study the influence of the electrical fields on the fracture behavior of piezoelectric materials. The method of distributed dislocations and electric dipoles, already existing in the literature, is used to calculate the electro-elastic fields and the energy-release rate for a finite crack embedded in an infinite piezoelectric medium which is subjected to both mechanical and electric loads. The energy-release rate expressions show that the electric fields generally tend to slow the crack growth. It is shown that the stress intensity factor criterion and the energy-release rate criterion differ when the energetics of the electric field is taken into account. The study of crack tip singular stress field yields a possible explanation for experimentally observed crack skewing in the presence of a strong electric field.     

Effect of displacement current in magneto–electro-elastic plates subjected to dynamic loading

Dynamic response of moderately thick magneto?Celectro-elastic plate using magnetic vector potential in finite element formulation is presented in this paper. Dynamic loading generate time varying electric and magnetic fields in magneto?Celectro-elastic continuum. Displacement current is associated with the generation of magnetic field due to time varying electric field. The non-conservative electric field is represented using electric scalar potential and magnetic vector potentials. Studies are carried out for CCCC, CCFC, CFFC and FCFC boundary conditions of the plate excited with time-harmonic mechanical excitation, the frequency range being chosen based on the critical frequency of the plate analyzed. The magnetic flux density in longitudinal x-direction is not affected by the electric displacement current for all the boundary conditions. The longitudinal y-direction and transverse direction components of magnetic flux density are showing variations for FCFC boundary condition when displacement current is accounted. The effect of displacement current is significant when two opposite edges of the plate are clamped.     

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.     

Theory of Nondestructive Testing in the Electrical Degradation of Semiconductor Devices

The electric field strength has been determined at which electromagnetic field oscillations arise in metal–insulator–metal structures on account of defects. The radius of curvature at the crest of a microridge on a metal electrode can be determined by electrophysical methods. Formulas are derived for the mechanical and electrical fields around microscopic and macroscopic defects, as well as surface-tension energies.     

含界面边裂纹压电材料反平面问题的应力强度因子

研究了含界面边裂纹的不同压电介质组成的复合材料在反平面荷载和平面内电场作用下的电弹场,得到了级数形式的基本解和应力强度因子,最后用边界配置法求解了应力强度因子.结果表明,在外加剪切荷载的作用下,应力强度因子与外加电场无关.     

NUMERICAL ANALYSIS OF CRACK PROPAGATION IN PIEZOELECTRIC CERAMICS

The formulation of an isoparametric displacement – electric potential finite element method that accounts for the electro-mechanical coupling effect of piezoelectric materials is briefly presented in this paper. The crack propagation behaviour and the elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and mechanical – electrical mixed loads are investigated using this electro-mechanical finite element method. From the numerical results, it can be seen that crack propagation along the crack plane direction will be impeded and the crack will tend to propagate at an angle of about 84° to the crack plane under a negative electric field on the basis of the maximum stress criterion. The physical explanation of the phenomena is presented in this paper and it is shown that the mechanical strain energy release rate is not a good criterion for predicting crack propagation in the case where the ratio of the electric field to the mechanical load becomes large.     

Low-frequency transient electric and magnetic fields coupling to child body

Much of the research related to residential electric and magnetic field exposure focuses on cancer risk for children. But until now only little knowledge about coupling of external transient electric and magnetic fields with the child's body at low frequency transients existed. In this study, current densities, in the frequency range from 50 Hz up to 100 kHz, induced by external electric and magnetic fields to child and adult human body, were investigated, as in residential areas, electric and magnetic fields become denser in this frequency band. For the calculations of induced fields and current density, the ellipsoidal body models are used. Current density induced by the external magnetic field (1 microT) and external electric field (1 V/m) is estimated. The results of this study show that the transient electric and magnetic fields would induce higher current density in the child body than power frequency fields with similar field strength.     

Current understanding of the origin of equiaxed grains in pure metals during ultrasonic solidification and a comparison of grain formation processes with low frequency vibration,pulsed magnetic and electric-current pulse techniques

The formation of fine,non-dendritic equiaxed grains throughout a casting without the addition of refiners(i.e.independent of alloy chemistry),is made possible by using ultrasonic,magnetic or pulsed magnetic and electric current pulse techniques.The dominant mechanisms proposed for the grain refinement produced during the application of an external field are cavitation phenomena assisted nucleation or fragmentation of dendrites(ultrasonic field),wall crystals arising from the cold surface of the mould(electric current pulse,magnetic and pulsed magnetic fields).In all these cases fluid flow provides an additional contribution(e.g.reduced temperature gradients,growth rate and remelting of dendrites)to maintaining an equiaxed grain structure.The origin of equiaxed grains under an external field also depends on the casting conditions(volume and shape of casting)and the type of alloy other than the mechanisms specific to a particular technique.The current work aims to provide a detailed understanding of the various factors and mechanisms that influence the grain refinement achieved during the solidification of pure metals(magnesium and zinc)subjected to Ultra Sonic Treatment(UST).The role of the temperature range of UST application,time duration and an unpreheated sonotrode are examined with respect to the origin,evolution of equiaxed grain structure,morphology and the columnar to equiaxed transition.The origin of grains was analysed from three fundamental aspects that contribute to refinement(i)heterogeneous nucleation(ii)fragmentation of existing dendrites and(iii)grains produced from the colder surfaces(arising from mould walls or vibrating surfaces as wall crystals).A comparison of UST refinement with mechanical,low-frequency vibration,electric current pulse and magnetic field solidification of pure metals has also been provided to highlight the importance of the cold surfaces(sonotrode and mould wall)in influencing grain refinement.     

Efficiency of excitation of piezoceramic transducers at antiresonance frequency

The efficiency of piezoceramic transducers excited at both the resonance and antiresonance frequency was investigated. Losses in piezoceramics are phenomenologically considered to have three coupled mechanisms: dielectric, mechanical, and piezoelectric losses. Expressions for the resonance and antiresonance quality factors, which ultimately determine transducer efficiency, have been received on the basis of complex material constants for both stiffened and unstiffened vibration modes. Comparison of electric and mechanical fields, thermal and electrical losses of power supply, and their distribution in the transducer volume have been made. For a given constant mechanical displacement of the transducer top, the required electric voltage applied to the transducer at the antiresonance frequency is proportional to the resonance quality factor, but the changes in the intrinsic electric and mechanical field characteristics in the common case are not too essential. The requirements on the piezoceramic parameters, types of transducer vibration, and especially on the factor of piezoelectric losses in a range of physically valid values were established to provide maximal quality factors at the antiresonance frequency.     

磁电弹双材料条中螺位错与界面边裂纹的相互作用

研究半无限长磁电弹双材料条中螺位错与界面边裂纹的相互作用。基于镜像原理和保角变换方法,得到了弹性场、电场和磁场的解析解,给出了应力、电位移、磁感应强度、应力强度因子以及像力的显函表达式。以压电-压磁双材料条形介质为例,分析了应力场、电位移和磁感应强度的分布特性,讨论了几何参数、压电和压磁效应对应力强度因子和像力的影响。     

Influence of the electric current waveform on the dynamic response of the electrified composites

The influence of the electric current waveform (DC, AC and pulsed currents) on the dynamic electromagnetic, thermal, and impact response of the composite plate is studied. The analysis includes solving Maxwell’s equations in the electrified composite plate to determine an electric-current induced magnetic field and heat transfer equation to estimate the electric-current-induced heating. In addition, the dynamic mechanical response of the electrified composite plate subjected to impact and various electromagnetic loads (DC, AC, pulsed electric currents and a constant magnetic field) is analyzed by solving a coupled system of equations of motion and Maxwell’s equations in the composite plate. The results show that the dynamic response of the plate is highly dependent on the characteristics of the electromagnetic field, and the pulsed electromagnetic fields are most effective in reducing vibrations caused by the application of dynamic mechanical loads.     

压电材料中反平面渗透裂纹的解

用复变函数的保角映射法,采用可渗透边界条件,研究了含裂纹的无限大压电材料在平面内电场和反平面荷载作用下的耦合场,得到了精确的解和场强度因子以及能量释放率。结果表明,电场强度在裂尖没有奇异性,应变、应力、电位移具有1/2阶的奇异性,能量释放率总是正的。     

Magnetic field enhancement in electromagnetic forming systems using anisotropic materials

Electromagnetic Forming (EMF) is a type of high rate forming which exploits pulsed power techniques to create high intensive pulsed magnetic fields to rapidly reshape metal parts. This technique is sometimes called magnetic pulse forming. In this technique, a metal work-piece is pushed to a die and formed by a pressure created using an intensive, transient magnetic field. This magnetic field is produced by passing a pulse of electric current through a forming coil in a pulsed power circuit. Application of field shapers has been proposed to enhance the magnetic fields and consequently to increase the applied magnetic pressure at some desired regions. In this paper, 3D Finite element simulations have been applied to study the magnetic field distribution during an electromagnetic forming process with anisotropic material. Anisotropic magnetic material is described using a permeability tensor. Elements of this tensor are obtained from different magnetization curves dependent on the direction of the magnetic field. It has been shown that application of anisotropic materials with appropriate lamination directions can result in an enhancement of the magnetic field at desired points as well as in better overall efficiencies.     

Numerical analysis for piezoelectric crack under varied boundary conditions by optimized hybrid element method

In this article, a piezoelectric hybrid element is presented and optimized by penalty equilibrium approach, and special crack surface element is suggested for exactly implementing the boundary conditions on crack surface. An iteration technique is used to treat one of the electric boundary conditions. Then, a piezoelectric material with crack is numerically studied by the optimized hybrid element method, and the results are compared with the analytical solutions. The stress and the electrical displacement fields with different crack surface conditions are studied, and the influence to those fields arisen by the far field mechanical and electric loading is also studied.