Estimating the sizes of surface cracks based on Hall element measurements of the leakage magnetic field and a dipole model of a crack

A method is proposed for estimating the sizes of surface cracks in magnetic materials. The method is based on applying a magnetic field, then determining the leakage magnetic field in the vicinity of a crack by moving a Hall element on the surface of the material along one or two scanning lines crossing the crack, and measuring the corresponding Hall voltage distribution. A dipole model of a crack is utilized, in which a surface crack is considered as being full of magnetic dipoles aligned parallel to the applied field, and whose density varies linearly along the depth of the crack. Analytical expressions are derived for the z-component of the intensity of the leakage magnetic field, and for the measured Hall voltage in the vicinity of a crack with an arbitrary cross-section along its long axis when it is perpendicular to the applied field. The crack sizes and the parameters of the distribution of magnetic dipoles along the crack depth are computed by crack inversion, which represents a regression for the Hall voltage distribution. A variable theoretical Hall voltage distribution is fitted to the measured Hall voltage distribution by minimizing the corresponding RMS error, which gives the unknown parameters at the end of the minimization. Hall voltage distributions are measured on ferromagnetic steel samples containing one artificial surface crack. Some crack inversions are performed for estimating the maximum crack depth and the crack width of cracks with rectangular and isosceles triangular cross-sections along the long crack axis. The accuracy of these crack inversions increases by utilizing either Hall voltage distributions measured along only one of the scanning lines, instead of along both scanning lines, or by using more precisely measured Hall voltage distributions. The fast and accurate estimation of the maximum crack depth and the crack width by such crack inversions could be important for pipeline inspection. Other crack inversions are performed for determining the cross-section along the long axis of the investigated cracks with satisfactory results. Received: 2 March 2001 / Accepted: 10 April 2001 / Published online: 25 July 2001     

The electric field modulation by three-dimensional crack on fused silica subsurface

The main factor of laser-induced damage is the modulation to electromagnetic field of laser by the crack on the subsurface. In this paper, a three-dimensional crack model on the exit surface is presented. Three-dimensional finite-difference time-domain (FDTD) method is employed to simulate the electric field intensity distribution in the vicinity of crack on fused silica subsurface. The roles of the crack width, depth, length and the gradient angle in the modulation to the incident light field are analyzed in detail. Results show that the crack size plays an important role in the electric modulation. With the increasing depth and width, the peak value of maximal electric field intensity appears in fused silica. However, the maximal electric field intensity tends to be a constant when the crack length reaches 1 μm. Besides, the enhancement of light intensity becomes obvious when total internal reflection occurs in fused silica. Our calculated results provide an advisable theoretical criterion to the corresponding experiment.     

Destruction of defective conductors with a current in a magnetic field

A mechanism of destruction of conductors with a crack in an external magnetic field is proposed. In this case, ponderomotive forces form a complex strained state in the crack tip, which is estimated from the equations of the linear theory of elasticity. The critical ponderomotive forces are found, which depend on the current and magnetic field parameters and induce stresses in the defect top, which are comparable with the yield strength of the material.     

Multiparadigm modeling of dynamical crack propagation in silicon using a reactive force field

We report a study of dynamic cracking in a silicon single crystal in which the ReaxFF reactive force field is used for several thousand atoms near the crack tip, while more than 100,000 atoms are described with a nonreactive force field. ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. Our results reproduce experimental observations of fracture in silicon including changes in crack dynamics for different crack orientations.     

Measurement of dynamic crack tip displacement field by speckle photography and interferometry

Speckle interferometry has been used to measure the transient displacement field around a crack due to stress wave loading. Double exposure interferograms are recorded with a pulsed ruby laser, and correlation fringes formed by spatial filtering of the developed film. A new technique is presented for reducing the noise level in spatially filtered speckle interferograms. Independent fringe patterns, obtained from one interferogram but with the filtering aperture sampling different regions of the Fourier transform plane, are digitised by a CCD camera and combined numerically. It is demonstrated that accurate analysis of fringe patterns by the Fourier transform method can be carried out, even if no carrier fringes are present. The measurements are compared with those obtained by speckle photography. Least-squares fitting of the theoretical displacement field is used to calculate the stress intensity factor at the crack tip as a function of time.     

Large scale domain switching around the tip of an impermeable stationary crack in ferroelectric ceramics driven by near-coercive electric field

It is widely accepted that the singular term plays a leading role in driving domain switching around the crack tip of ferroelectric ceramics.When an applied electric field approaches or even exceeds the coercive one,however,non-singular terms are no longer negligible and the switching of a large or global scale takes place.To analyze the large scale switching,one has to get a full asymptotic solution to the electric field in the vicinity of the crack tip.Take a double cantilever beam specimen as an example....     

Scattering of surface waves by a sub-surface crack

The scattering of Rayleigh waves by a two-dimensional sub-surface crack, which is perpendicular to the free surface of an elastic half-space, is investigated. The boundary-value problem for the scattered field is stated, and reduced to an uncoupled system of integral equations which are solved numerically. At large distances from the crack the scattered field is shown to consist of outgoing Rayleigh waves and cylindrical body waves. Graphs of the variation of the amplitude and phase of the forward and backward scattered Rayleigh waves with the frequency and the geometrical parameters of the crack are presented. The stress intensity factors at both crack tips have also been obtained.     

赫兹型微裂纹光场调制增强作用的系统研究

通过改变裂纹的倾角、宽度和深度参数,模拟了赫兹型裂纹在不同参数下对光场调制能力的不同. 模拟发现,倾斜角度为20.9°到45°之间的裂纹危害最大,倾角大于45°小于48.2°的裂纹危害也十分大,而倾斜角度为45°时的裂纹危害最小. 对于30°倾角的赫兹型裂纹,一定范围内,赫兹型裂纹深度的增加会导致其光场调制增强能力呈二次方关系增加,但宽度的增加不会使其光场调制增强作用增加. 裂纹深度和宽度的增加可以用来近似裂纹的演化过程,所以裂纹的扩展导致了其光场调制能力的增加,进而导致损伤增长速率的加快,这和e指数损伤增长规律相符. 关键词： 损伤增长 亚表面缺陷 赫兹型裂纹 光场增强     

The elastic field of general-shape 3-D cracks

We extend here the Bilby-Eshelby approach of 2-D crack representation with dislocation pileups to treat 3-dimensional cracks of general geometry. Cracks of any specified external bounding 3-D contour under general loading conditions are represented by sets of parametric Somigliana loops that satisfy total (interaction, self, and external) force equilibrium. Loop positions are solved by using a time integration scheme till equilibrium is achieved. The local Burgers vector is suitably adjusted to be proportional to the local applied surface traction on the crack. The developed method is computationally advantageous, since accurate crack stress fields are obtained with very few concentric parametric loops that adjust to the external crack shape and the local force conditions. The method is tested against known elasticity solutions for 3-D cracks and found to be convergent with an increase in the number of pileup dislocation loops. The method is applied to the determination of the stress field around a 3-D Griffith crack under general loading and a grain boundary crack before and after branching.     

The leaf venation as formed in a tensorial field

The veins of plant leaves exhibit a large variety of morphologies. They are often thought to result from their growth in a concentration scalar field. It is shown here that the topology of these patterns rather corresponds to what is expected from growth in a tensorial stress field. This is demonstrated by analogic experiments performed on crack formation in gel films where many characteristic venation patterns, of both dicotyledons and monocotyledons, were reproduced. This suggests, for the origin of the veins formation, a set of hypotheses which is new but supported by known physiological data. Received 11 March 2002 Published online 19 July 2002     

Continuum field description of crack propagation

We develop continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation which accounts for the dynamics of defects. This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching, and fragmentation.     

The dynamic analysis of a cracked Timoshenko beam by the spectral element method

The aim of this paper is to introduce a new finite spectral element of a cracked Timoshenko beam for modal and elastic wave propagation analysis. The proposed approach deals with the spectral element method. This method is suitable for analyzing wave propagation problems as well as for calculating modal parameters of the structure. In the paper, the results of the change in modal parameters due to crack appearance are presented. The influence of the crack parameters, especially of the changing location of the crack, on the wave propagation is examined. Responses obtained at different points of the beam are presented. Proper analysis of these responses allows one to indicate the crack location in a very precise way. This fact is very promising for the future work in the damage detection field.     

Effect of humidity on subcritical crack growth of indentation crack under sustained electric field in PZT ceramics

The effect of humidity on subcritical crack growth of indentation crack in lead zirconate titanate (PZT) ferroelectric ceramics under various sustained electric field has been investigated. The results showed that subcritical crack growth of indentation crack could occur in humid air of 60%RH without electric field but did not in air with RH ≤ 30%. The subcritical crack growth could occur in vacuum under a sustained electric field of E/E_C = 0.14. The incubation time decreased and the amount of the subcritical crack growth increased with increasing the humidity under the sustained field. The threshold electric field for subcritical crack growth decreased with increasing the humidity.     

悬臂方薄板振动的辐射声场及竖裂纹对其频谱的影响

在将悬臂板挠度表示为正交多项式之和的基础上，利用瑞利-里兹方法求解了悬臂板的前几阶振动模态频率及挠度．进而利用瑞利积分求解了其自由振动辐射声场的分布规律。用分区技术的瑞利-里兹方法求解了竖裂纹对悬臂板低阶模态频率的影响，并将计算结果与有限元结果作了对照。实验上用小球撞击法测定了含竖裂纹悬臂板辐射声场的频谱，谱成分与有限元结果基本符合。     

Self-consistent electric field arising on mechanical perturbation of a dielectric

The electric field arising in rock on disruption is considered. The minimum crack concentration necessary for intense radiation is determined. It is shown that the field strength at this concentration is proportional to the ratio between the statistical temperature of the dipole system and the dipole moment.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 71–74, May, 1977.     

电介质表面纵向射频电场对次级电子倍增效应的影响

基于次级电子倍增动力学模型和次级电子发射曲线,运用蒙特卡罗方法模拟电介质表面具有纵向射频电场作用下的单边次级电子倍增现象,研究次级电子倍增的表面电场敏感曲线和时间演化图像. 以一个S波段射频介质窗为例,计算次级电子在其介质表面的沉积功率. 结果表明,纵向射频电场可能加剧电介质表面的次级电子倍增效应,易于导致介质片破裂,不利于高频能量传输. 关键词： 纵向射频场 次级电子倍增效应 蒙特卡罗方法 功率沉积     

Effect of an absorbent overlay on the residual stress field induced by laser shock processing on aluminum samples

Laser shock processing (LSP) or laser shock peening is a new technique for strengthening metals. This process induces a compressive residual stress field, which increases fatigue crack initiation life and reduces fatigue crack growth rate. Specimens of 6061-T6 aluminum alloy are used in this investigation. A convergent lens is used to deliver 2.5 J, 8 ns laser pulses by a Q-switch Nd:YAG laser, operating at 10 Hz. The pulses are focused to a diameter of 1.5 mm onto aluminum samples. Density of 2500 pulses/cm² with infrared (1064 nm) radiation was used. The effect of an absorbent overlay on the residual stress field using this LSP setup and this energy level is evaluated. Residual stress distribution as a function of depth is assessed by the hole drilling method. It is observed that the overlay makes the compressive residual stress profile move to the surface. This effect is explained on the basis of the vaporization of the coat layer suppressing thermal effects on the metallic substrate. The effect of coating the specimen surface before LSP treatment may have advantages on improving wear and contact fatigue properties of this aluminum alloy.     

Calibration of the stray field gradient by a heteronuclear method and by field profiling

Heteronuclear and field-profiling stray field (STRAFI) techniques are used to calibrate the STRAFI gradient. Both methods compare very favorably indeed with the conventional method of calibration which uses a standard with a known self-diffusion constant. The distinct advantages of the techniques presented here are that the constraints on both sample purity and sample temperature that are inherent to the conventional method are completely eliminated. The accuracy of the heteronuclear method typically matches that of the conventional method with a pure sample and temperature stability to within 0.4°C. The field-profiling method is more accurate than the heteronuclear method in the form that it is presented here.     

Scatter of a plane elastic wave by a rough crack edge

The aim of this paper is to investigate the effect of roughness of the crack edge on the reliability of ultrasonic NDE (nondestructive evaluation). The rough crack face has been modeled by earlier authors as a mosaic of large triangular facets and the effect of this roughness has been simulated using the Kirchhoff approximation. We now augment this model by the rough crack edge that is a polygonal line. We then model the scattered field using the Isakovich approach, originally developed for modeling scatter from rough surfaces, also with the help of the Kirchhoff approximation.