A damped forward EMI model for a horizontally stratified earth

If a magnetic dipole is placed above the surface of the earth, the Electromagnetic Induction (EMI) effect, encoded in Maxwell's equations, causes eddy currents in the soil which, on their turn, induce response electromagnetic fields. The magnetic field can be measured in geophysical surveys to determine the conductivity profile of the ground in a non-destructive manner. The forward model used in the inversion of experimental data usually consists of a set of horizontal homogeneous layers. A frequently used analytical model, proposed by McNeill, does not include the interaction between the eddy currents, and therefore fails for larger conductivities. In this paper we construct a new forward, analytical, model to estimate the magnetic field caused by a horizontally stratified earth but which approximates the interaction between eddy currents. This makes it valid for a broader range of parameters than the current state of the art. Furthermore, the error with the (numerically obtainable) exact result is substantially decreased. We also calculate the vertical sensitivity ("depth of exploration") of the model and observe that it is in good agreement with the values obtained from the exact model.Comment: Accepted for publication in Exploration Geophysic

Simulation study of the localization of a near-surface crack using an air-coupled ultrasonic sensor array

The importance of Non-Destructive Testing (NDT) to check the integrity of materials in different fields of industry has increased significantly in recent years. Actually, industry demands NDT methods that allow fast (preferably non-contact) detection and localization of early-stage defects with easy-to-interpret results, so that even a non-expert field worker can carry out the testing. The main challenge is to combine as many of these requirements in one single technique. The concept of acoustic cameras, developed for low frequency NDT, meets most of the above mentioned requirements. These cameras make use of an array of microphones to visualize noise sources by estimating the Direction Of Arrival (DOA) of the impinging sound waves. Until now, however, because of limitations in frequency range and lack of integrated nonlinear post-processing, acoustic camera systems have never been used for the localization of incipient damage. The goal of the current paper is to numerically investigate the capabilities of locating incipient damage by measuring the nonlinear airborne emission of the defect using a non-contact ultrasonic sensor array. We will consider a simple case of a sample with a single near-surface crack and prove that after efficient excitation of the defect sample, the nonlinear defect responses can be detected by a uniform linear sensor array. These responses are then used to determine the location of the defect by means of three different DOA algorithms. The results obtained in this study can be considered as a first step towards the development of a nonlinear ultrasonic camera system, comprising the ultrasonic sensor array as hardware and nonlinear post-processing and source localization software.status: publishe

Recent advances in the ultrasonic polar scan method for characterizing (degraded) fiber reinforced plastics

The ultrasonic polar scan (UPS) technique originated in the 1980's as a sophisticated method for inspecting composites. However, it is only in recent times that the true capabilities and strengths of the UPS methodology have been evidenced through experiment and simulation. Nowadays, the UPS method exists in different versions which led to several novel applications in the field of material inspection and characterization. This contribution gives an overview of our recent advances

2D modeling of acoustic waves in solids with frictional cracks

Contact acoustic nonlinearity underlies modern nondestructive testing methods that use nonlinear ultrasound to detect cracks, delamination, debondings, welding defects, imperfect gluing, etc. Since the nonlinear response of a sample highly depends on the actual configuration of internal contacts (called cracks for brevity), numerical modeling is most suitable. In this communication, we present a numerical toolbox for modeling vibrations or acoustic wave propagation in solids containing cracks of known geometry. With the help of our numerical tool, the user can calculate the nonlinear time-dependent distributions of stress, strain, displacement, etc., in a sample with known excitation sources and compare the results to actual measurements. The final objective would be to estimate geometric and physical parameters of defects using this comparison. Description of contact acoustic nonlinearity requires the junction of two classical disciplines: acoustics and contact mechanics. The numerical tool also contains two components: a unit for solving the elasticity equations in the bulk volume and a unit that provides the appropriate boundary conditions imposed at the internal defect boundaries in the material. The solid mechanics unit can be programmed using available finite element software that accepts internal boundaries and user-supplied boundary conditions. We have used COMSOL® whose features provide an interface to an external crack model programmed in MATLAB®. The crack model is created using physics-based theoretical considerations. The presence of cracks invokes two major mechanisms of nonlinearity: asymmetric reaction of a crack on normal compression/tension, and friction-induced hysteresis activated by shearing action. On the other hand, an internal contact can evolve in one of several regimes, such as contact loss, stick, and sliding. The crack model has to take into account these phenomena to provide the load-displacement relationships for any value of the drive parameters. The basic friction model is Coulomb's friction law written for loads. Obviously, this model does not have the desired properties, since, for instance, in the sliding regime, when the tangential load exceeds the threshold defined by the normal one, the tangential displacement remains undefined. Therefore we use another concept, based on the Coulomb friction law as well, that includes the account for roughness and therefore results in appearance of an additional contact regime of partial slip, when some parts of the contact zone slip and some do not. This situation is successfully dealt with by using the previously developed method of memory diagrams. In this method, the hysteretic load-displacement solution is constructed with the help of an internal system function (memory diagram) that contains all memory information. This displacement-driven solution can be easily extended onto two other contact regimes (contact loss and total sliding) and is finally computed for any combination of normal and tangential displacement values and their time dependencies. Memory diagrams have to be maintained at each discretization point on the crack surface and updated following the applied displacement field. In this communication, we present an example of wave propagation in a sample of known geometry and quantitatively illustrate its nonlinear behavior (e.g. compute the field of secondary nonlinear sources). Our results may be of interest for researchers working in experimental nondestructive testing, nonlinear acoustics, or dealing with vibrations of loaded contacts, nonlinear metamaterials, imaging techniques including nonlinear vibrometry, thermography, etc

Time-of-flight recorded pulsed ultrasonic polar scan for elasticity characterization of composites

In its orginal configuration, the pulsed ultasonic polarscan (P-UPS) mainly focussed on elastic material characterization through the inversion of amplitude landscape measurements. However, for several materials, special attention is required as minima in the transmission amplitudes do not exactly coincide with critical angles calculated from the Christoffel equations. Consequently, other means to extract the information on elastic moduli from P-UPS measurements are being investigated. In the present paper, we report on the use of time-of-flight ultrasonic polarscan (TOF-UPS) simulations as a new means of material characterization. Previous TOF inversions, although successful, were based on bulk wave approximations, which are not longer valid for thin materials. Our first inversion results on numerical cases demonstrate the usefulness of the new developed technique and highlight the added value compared to the bulk wave approximation

Matching spectroscopy with the ultrasonic polar scan for advanced NDT of composites

The Pulsed Ultrasonic Polar Scan (P-UPS) is a powerful technique for characterizing anisotropic materials like fiber reinforced plastics. A time-domain analysis of the ultrasonic signals yields amplitude and time-of-flight polar diagrams that provide a fingerprint of the local stiffness properties. Though, this simple analysis ignores a lot of information contained in the ultrasonic signals. In this study, we propose to use the P-UPS technique in combination with the spectroscopic analysis of broadband pulses, to obtain plane wave transmission spectra for all in-plane polar angles. This allows us to combine on one hand the strengths of the P-UPS technique, that does not require a priori knowledge about the sample anisotropy, and on the other hand the frequency-domain analysis that utilizes information contained in the broadband pulses

Towards a phased array based ultrasonic polar scan : simulation study and comparison with plane wave results

The ever-increasing use of composite materials in the industry has resulted in the need for new, intricate approaches to not only properly characterize their anisotropic mechanical properties (i.e., the visco-elastic tensor), but also to detect various types of internal flaws. Both goals can be achieved by the Ultrasonic Polar Scan (UPS). During an UPS experiment, a material spot is insonified at many oblique incidence angles Ψ(θ,φ), with θ the vertical incident angle and φ the inplane polar angle, after which the reflected or transmitted ultrasound signal is recorded. The resulting dataset provides an integral view of the angle-dependent reflection (R) and transmission (T) scatter coefficients, and can be employed to infer the material properties. Although the current UPS scanner provides highly accurate experimental data, it is impractical for in-situ measurements. In order to create a more compact and practical measuring device, we propose the use of a hemispherical phased array, consisting of small piezoelectric elements, to generate a broadband, quasi plane wave signal. It will be shown, based on simulations, that a circular phased array concept allows for the determination of the reflection coefficients in θ − f space, from which the dispersion curves can be immediately inferred. Comparison of these results with the plane wave theoretical results show an excellent agreement

Linear and nonlinear guided wave imaging of impact damage in CFRP using a probabilistic approach

The amount and variety of composite structures that need to be inspected for the presence of impact damage has grown significantly in the last few decades. In this paper, an application of a probabilistic ultrasonic guided wave imaging technique for impact damage detection in carbon fiber-reinforced polymers (CFRP) is presented. On the one hand, a linear, baseline-dependent, technique utilizing the well-known correlation-based RAPID method and an array of piezoelectric transducers is applied to detect impact-induced damage in plate-like composite structures. Furthermore, a baseline-independent nonlinear extension of the standard RAPID method is proposed, and its performance is demonstrated both numerically and experimentally. Compared to the conventional RAPID, the baseline-free version suffers from a somewhat lower imaging quality. However, this drawback is compensated by the fact that no damage-free (intact) baseline is necessary for successful imaging of damage

Visualization of delaminations in composite structures using a baseline-free, sparse array imaging technique based on nonlinear Lamb wave propagation

Environmental factors such as temperature and humidity influence the efficacy of defect imaging procedures based on the identification of changes between an intact state and the current state of a sample/component/structure in the presence of a defect. In this paper, we focus on the Reconstruction Algorithm for Probabilistic Inspection of Damage (RAPID) and propose a nonlinear Lamb wave version of RAPID to visualize a delamination in a composite structure without having to know anything about the intact state, i.e. a baseline free RAPID. Once the optimal frequency selection of Lamb waves in a pitch-catch configuration mode is performed, low and high excitation amplitude signal responses within a sparse array at that frequency are evaluated along each transducer-receiver path by analyzing a set of damage sensitive parameters: the correlation coefficient, the energy of the scaling subtracted signal, and the and the third harmonic ratio. Processing of this information leads to a corresponding probabilistic damage map of the area within the sparse array. The obtained results from a validation experiment demonstrate the capability of this nonlinear variant of RAPID for the identification of a delamination in a composite structur