Loss of specular reflection due to nonlinear crack-face interaction

The interaction between rough crack faces is modeled by nonlinear relations between the crack-face tractions and the crack-opening displacements. These relations account for crack closure and for the related resistance to crack-face sliding. The relations are used to investigate reflection and transmission of an incident pulse by an infinite flaw plane. The problem statement is reduced to a set of inhomogeneous nonlinear ordinary differential equations for the displacement discontinuities, [u] and [v], across the flaw plane. These equations have been solved numerically. The reflection and transmission of an incident pulse by a crack with interacting crack faces. Both incident longitudinal and transverse waves have been considered. The loss of specular reflection as compared to a perfect (traction-free) crack is exhibited by specific examples.     

Ultrasonic diffraction technique for characterization of fatigue cracks

This paper describes an ultrasonic diffraction technique for characterizing fatigue cracks. The angular field of energy scattered from a crack tip was computed. Using the theoretically predicted and experimentally verified optimum range of angles, we measured the crack profiles by the ultrasonic diffraction technique. Ultrasonic measurements agreed very well with direct destructive measurements. In addition, fatigue crack closure was detected and information on crack surfaces was obtained.Oak Ridge National Laboratory; Oak Ridge National Laboratory is operated by Union Carbide Corporation under contract W-7405-eng-26 with the U.S. Department of Energy.     

Ill-posed and well-posed problems in inverse elastodynamic scattering for nondestructive evaluation

The practical significance of ill-posedness in a data reduction problem is reviewed. Inverse elastodynamic scattering is shown to be ill-posed in general, although suitably restricted problems may be well-posed. These results underscore the need to analyze carefully the errors of data reduction problems in NDE, and to focus attention on final results of an NDE exercise, rather than on intermediate steps.     

Probe characterization in ac field measurements of surface crack depth

In the ac field method of crack depth measurement by the Crack Microgauge, the area of the loop formed in the probe gives rise to an induced voltage, which can introduce errors into the depth measurement. In this paper, a method for measuring the probe area is given, and the quality of the probe is thereby characterized. The underlying theory was given previously, and it is applied here to the probe characterization problem. The probe area is determined by two voltage measurements taken on an artificial rectangular flaw machined in an arbitrary metal. By measurements on several such specimens with the same probe, it is confirmed that the area so obtained is a characteristic of the probe and is independent of the specimen material. Thereafter, measurements on various rectangular flaws with probes of different characteristic area were taken, and very good agreement between predicted and real depths was achieved. Both theory and experiments show that probe characterization is of particular importance when this method is used to measure surface crack depths in metals of low permeability such as aluminum.     

Kirchhoff Approximation Revisited—Some New Results for Scattering in Isotropic and Anisotropic Elastic Solids

Through a series of numerical studies that compare the Kirchhoff approximation to more exact scattering theories, it is demonstrated that the Kirchhoff approximation can accurately predict the pulse–echo peak-to-peak responses of spherical pores and circular cracks in isotropic media over a very wide range of cases that extend well beyond the limits normally associated with this approximation. The reason for this good agreement is shown to lie in the ability of the Kirchhoff approximation to model accurately the very early time response of the flaw. It is also shown that in the Kirchhoff approximation the pulse–echo response of an arbitrary traction-free scatterer in an isotropic elastic solid is identical to the same response obtained using a scalar (fluid) scattering model. This leads to simple analytical expressions for the pulse–echo far-field scattering amplitude of some canonical geometries (circular cracks, spherical voids, cylindrical holes) and to simplified numerical expressions for more general scatterers. For general anisotropic volumetric flaws in a anisotropic elastic solid, it is shown that a high-frequency asymptotic evaluation of the Kirchhoff approximation yields an explicit analytical expression for the pulse–echo leading-edge response of the flaw. Explicit expressions are also given for the pitch–catch response of an elliptical-shaped flat crack in a general anisotropic solid.     

Effects of sinusoidal crack-face perturbations on scattering of elastic waves

The scattering of a plane longitudinal wave from a two-dimensional crack, with a sinusoidal surface perturbation whose amplitude and wavelength are much smaller than the length of the crack, is investigated. The amplitude of the cylindrical body waves in the far field are calculated from a Kirchhoff approximation that utilizes the solution to the reflection from the sinusoidal surface profile of a semiinfinite solid. The results are compared to those for a flat crack, and conditions for significant differences of the amplitude as a function of the angle of observation are discussed. Characteristic changes in the scattered field produced by profiles with different amplitudes and periods are explained.     

Concrete crack depth meter using nonlinear ADC

This paper introduces the design and construction of an electronic hybrid signal processing meter that develops an output voltage proportional to the depth of a concrete crack. The circuit employs multiplication, squaring, and square-rooting functions by means of a special nonlinear ADC and counting scheme.     

Separation and characterization of stress levels and texture in metal sheet and plate: I. Principles and preliminary experiment

An approach is proposed for obtaining separate measures of stress anisotropy and texture in metal sheet or plate. The approach is based on the propagation characteristics ofSH _n modes of ultrasonic waves. Experimental work has established that differences betweenSH ₀ modes with orthogonal directions of propagation provide a measure of stress anisotropy that is insensitive to texture, with the restriction that the pseudosymmetry of the polycrystalline matrix of the sheet or plate is orthorhombic or higher. In the present work, it is argued that the differences between elastic constants associated with orthogonal directions of propagation of higher order modes should provide a meaningful measure of texture. The only requirement is that the texture be sufficiently well developed so that the following inequality is obeyed: C₄₄–C₅₅>0.002 with =1/2 (C₄₄+C₅₅). HereC₄₄ andC₅₅ are the effective shear moduli for planes normal to the sheet or plate surface and at right angles to each other. They are measurable by observing the differences between the phase velocities of theSH ₀ and theSH _n>0 modes in the principal directions. By using Electromagnetic Acoustic Transducers (EMATs), the phase velocities can be deduced from the frequencies at which an SH mode of fixed wavelength is optimally excited. This approach has the advantage of being independent of specimen geometry and dimensions other than thickness.This article is a work performed under the auspices of the U.S. Department of Energy.     

XFEM‐based crack detection scheme using a genetic algorithm

A new computational tool is developed for the accurate detection and identification of cracks in structures, to be used in conjunction with non‐destructive testing of specimens. It is based on the solution of an inverse problem. Based on some measurements, typically along part of the boundary of the structure, that describe the response of the structure to vibration in a chosen frequency or a combination of frequencies, the goal is to estimate whether the structure contains a crack, and if so, to find the parameters (location, size, orientation and shape) of the crack that produces a response closest to the given measurement data in some chosen norm. The inverse problem is solved using a genetic algorithm (GA). The GA optimization process requires the solution of a very large amount of forward problems. The latter are solved via the extended finite element method (XFEM). This enables one to employ the same regular mesh for all the forward problems. Performance of the method is demonstrated via a number of numerical examples involving a cracked flat membrane. Various computational aspects of the method are discussed, including the a priori estimation of the ill‐posedness of the crack identification problem. Copyright © 2007 John Wiley & Sons, Ltd.     

大粗糙度起伏下一维海面声散射建模与分析

针对起伏海面高频声散射计算问题,提出了一种改进的基尔霍夫(Kirchhoff)近似方法。该方法考虑了海面的阴影区和亮区之间的多次散射声场,可对小入射角下大粗糙度起伏海面的散射声场进行计算。以一维余弦和高斯谱海面散射声场的有限元计算结果为标准解验证了所提方法的准确性和适用性。利用该方法计算了一维余弦海面的散射强度,分析了不同入射声波频率和角度下海面散射强度的分布情况,并解释了Bragg散射的产生机理,同时讨论了不同海面均方根高度和相关长度情况下高斯谱海面散射强度的变化规律。     

Measurement Models and Scattering Models for Predicting the Ultrasonic Pulse-Echo Response From Side-Drilled Holes

A side-drilled hole (SDH) is a commonly used reference reflector in ultrasonic nondestructive evaluation. In this paper, we will develop reciprocity-based measurement models along with scattering models that allow us to predict the ultrasonic response from a SDH in a pulse-echo immersion setup. Two measurement models will be derived, one suitable for large SDHs where variations of the incident fields over the cross section area of the SDH are considered, and a second model which neglects those variations. Two scattering models are also used along with these measurement models. These include an explicit model based on the Kirchhoff approximation, as well as an exact model obtained using the separation of variables method. Examples of the model-based received waveforms and peak-to-peak voltage responses are presented for a number of SDHs of different sizes and compared with experimentally determined SDH responses.     

Time domain Born approximation

The time domain Born approximation for ultrasonic scattering from volume flaws in an elastic medium is described. Results are given both for the direct and the inverse problem. The time domain picture leads to simple intuitive formulas, which we illustrate by means of several simple examples. Particular emphasis is given to the front surface echo and its use in reconstructing the properties of the flaw.     

Ultrasonic characteristics of graphite/epoxy composite material subjected to fatigue and impacts

Fiber-reinforced composites, because of their superior specific strengths and stiffnesses, are used in many aircraft components. However, in this application these composites are subjected not only to fatigue loading, but to occasionally high velocity impact due to the bird injection, hail, dust, and rain. Thus, it is important to evaluate the residual life and degradation due to combined fatigue and impact loadings. Unidirectional graphite epoxy composites (MA8276-Tiger) which are used in the aerospace industry were impacted by a free falling weight at energy levels of 0.567j, 1.134j, and 1.571j [impact energy toughness (j/cm³); 0.12, 0.24, 0.34], respectively. The subsequent changes/degradation in elastic moduli, strength, toughness, and fatigue properties were measured after different number of impacts. It was found that for all energy levels these properties vary linearly with the number of impacts. Furthermore, attenuation changes is not a good ultrasonic parameter for degradation estimation, since it does not incorporate the micro- and macrocracks beyond the impact point. However, these micro- and macrocracks have significant effect on the mechanical properties. In contrast to the attenuation, the stress wave factor, which indicates the efficiency of wave propagation along the specimen, correlates very well with degradation, and it can be used effectively to measure the residual strength after impact. Ultrasonic characteristic on specimens subjected to combined fatigue and impact were also studied. Based on these experiments, it is concluded that the loss in fatigue residual life due to impact loads may be predicted by measuring the effects of the impact load on attenuation and stress wave factor. It was found that the reduction in fatigue life is proportional to sudden changes in attenuation and stress wave factor. Damage accumulation models based on Coffin-Manson equation, was suggested for impact and combined fatigue and impact. It was found that residual properties and fatigue life can be estimated from these models.     

An improved crack tracking algorithm with self-correction ability of the crack path and its application in a continuum damage model

In this paper, a new procedure for predicting the crack propagation and fracture behavior in quasi-brittle materials is presented based on continuum damage mechanics. Several crack tracking algorithms are widely used for failure analysis, among which the local tracking algorithm is very simple and easy to implement with low computational cost. However, in the prediction of crack growth with the traditional local tracking algorithm, it can be often seen that the sharp changes in the crack path such as U-turns can occur. An improved local tracking algorithm with self-correction ability of the crack path is proposed to overcome these difficulties of the traditional crack tracking algorithms. A continuum damage model, in addition to the present crack tracking algorithm, can greatly enhance the performance of failure prediction in quasi-brittle materials. The present approach has the advantages that it can well predict the crack propagation path and can avoid mesh size and mesh bias dependence without the embedment of discontinuities or nodal enrichment. The present model is incorporated into ANSYS by the ANSYS Parameter Design Language to simulate the initiation and propagation of the discrete crack in engineering applications. The numerical results by this model are compared with the ones by the extended finite element method and experiments, and good agreements are achieved.     

Ultrasonic evaluation of geometrical and surface parameters of rough defects in solids

Ultrasonic measurements from rough cracks were carried out using both broad-band and narrow-band methods. An analysis is suggested to determine parameters of the crack quantitatively such as size, shape, rms surface roughness, and distribution function of the surface roughness. Ultrasonic measurements of the parameters compare very well with the actual parameters of the defect.     

Electromagnetic crack detection in ferritic steel

The detection and sizing of fatigue cracks in ferritic materials, especially in offshore structures, is of major importance. This paper describes an eddy current system to detect such cracks, operating in an offshore environment with a search probe to electronic instrument separation of up to 600 m. An analysis of the various factors influencing the search coil behavior is given in terms of a mutually coupled primary and secondary electrical circuit; the component values of which are influenced by the coil design, induced electrical currents in the material, and any defects it contains. It is further shown that, with proper coil parameters, the phase variation in the phase angle of the coil complex impedance can be kept almost constant compared with the rapid variation occurring during lift-off. This behavior can be exploited in the instrumentation to give a clear vector display indication of the crack presence on less than ideal surfaces.     

Relationships between crack opening displacement,alloy variables,and crack detection sensitivity

Alloy grain size is known to influence both the propagation path and the closure stress of surface fatigue cracks in many alloys. The general trend is for the path to be more tortuous and the closure stress to be larger, the larger the grain size. By use of Ti Al-4V and Al 7075-T6, the effects of grain size on the nondestructive detection of surface cracks which might arise from closure stress and path irregularity variables were evaluated. Titanium specimens were inspected using an acoustic harmonic generation technique, and it was discovered that the major source of harmonic signals was grain sized crystallographic cracks. Harmonic signals were larger during fatigue in an 8-µm compared to a 4-µm grain sized alloy, as there were more grain sized cracks in the large grain material. Crack closure was found to be extremely important in determining the reflected acoustic amplitude obtained in inspecting small (100–1000 µm) cracks in Al 7075-T6 using a critical angle technique. Average received amplitudes were an order of magnitude smaller for cracks at zero load than for those opened by a tensile stress. The scatter in the reflected amplitude was also large, apparently as the result of variations in the degree of the closure from crack to crack. For the 7075 material, the important effect of larger grain size was to increase the irregularity of the crack path, making the small cracks more visible acoustically at azimuthal angles not normal to the crack plane.     

Analysis of ultrasonic wave scattering for characterization of defects in solids: I. Spherical inclusions and reciprocity

This paper, as part of a series on elastic wave scattering, presents results of measurements and calculations on scattering of ultrasonic waves by a solid spherical inclusion (tungsten carbide) embedded in titanium alloy by the diffusion bonding process. Both direct scattering and mode-converted scattering angular distributions are reported for shear and compressional incident waves. The consequences upon the signals when transmitter and receiver were interchanged are explored in a reciprocity rule.     

Ultrasonic leaky interface waves for composite-metal adhesive bond characterization

Highly stressed or damaged regions in aircraft structures are increasingly being reinforced by adhesively bonding an overlay of a unidirectional boron fiber-epoxy composite to the aircraft metallic substrate. While conventional C-scan ultrasonics can be used to detect disbonding of the overlay, nondestructive methods are also required to detect weak adhesive bonding. This paper describes a preliminary experimental investigation of the existence of ultrasonic leaky interface waves between overlays and 2024-T351 aluminum alloy and D6ac steel substrates, and their possible use for detection of weak bonds. The approach used was to excite these leaky waves using Rayleigh waves generated by a laser line-source on the substrate. The existence of the leaky waves, traveling normal to the composite fibers, between boron-epoxy overlays and either an aluminum or steel substrate, was confirmed by observations of the quasishear pulses leaked to the top of the overlay, and of the Rayleigh wave transmitted to the free surface beyond the overlay. When quantitative measurements were possible, measured values of the complex interface wave speed agreed satisfactorily with predicted values. This paper also demonstrates one case for which leaky interface waves are sensitive to weak bonding caused by the presence of a contaminant on the substrate surface prior to bonding: application of a low-concentration aqueous solution of hydraulic oil to the aluminum substrate prior to bonding of the overlay caused a marked increase, over that for the well-bonded case, in the observed amplitude of the quasi-shear pulses leaked to the top of the overlay by decay of the interface wave. More experiments are needed to establish whether leaky interface waves are sensitive to bond condition for various other combinations of substrate, overlay and contaminant.     

Comparison between piezoelectric method and ultrasonic signal analysis for crack detection in type II multilayer ceramic capacitors

In this paper we present a comparison between two non-destructive techniques for crack detection in MLCCs. First, if a type II MLCC is biased with a DC field, the capacitor becomes temporarily ‘poled’ and can act as a transducer. This is induced by a residual piezoelectric effect used in the impedance spectroscopy method. Second, we used a scanning ultrasonic system working in the 10–100 MHz frequency bandwidth. To understand the ultrasonic signature, we used time-of-flight (TOF) detection with short-time Fourier transform (STFT) analysis to determine the depth and nature of defects with high accuracy. An application of digital signal processing to the characterization of defects is presented for a lot of MLCCs with cracks defects. For comparison, the same lot was tested with the piezoelectric method. The two techniques are closely correlated. © 1998 John Wiley & Sons, Ltd.