Abstract: A three dimensional (3D) hybrid method combining the classical finite element (FE) method with the semi-analytical finite element (SAFE) technique is developed. This hybrid method is employed to study the interaction of guided waves with non-axisymmetric damages in cylinders. The near field surrounding the damage is analysed with the 3D FE method. The solution is expanded into sums of guided modes on both inlet and outlet cross-sections. Such eigenmode expansions enable separation into ingoing and outgoing waves, i.e., incident, reflected and transmitted waves. Using the SAFE method, elastic guided modes are then computed at the aforementioned cross-sections thus reducing the analysis to two dimensions (2D). The amplitudes of the incident modes are imposed, whereas those of the scattered modes are determined by solving the global system of the 3D hybrid FE-SAFE model. In this paper, a formula is proposed for the calculation of eigenforces and modal power flows from eigendisplacements and SAFE matrices. This has the advantage of simplifying the post-process of load eigenvectors in hybrid FE-SAFE methods. Results obtained for a vertical free-end cylinder are in good agreement with those published in the literature. Moreover, first results of the interaction of the fundamental compressional, flexural and torsional Pochhammer–Chree modes with non-axisymmetric vertical cracks are obtained and discussed. Then, the interactions of the fundamental compressional mode with oblique free-ends and cracks are briefly addressed. The power balance is shown to be satisfied with a good accuracy.
Abstract: The aim of this work is to study the fundamental Lamb modes interaction with defects in isotropic plates. For these experimental investigations, symmetrical notches with various depths milled in aluminum plates are considered. Moreover, the incident Lamb wave of a specific mode is generated by means of two identical thin piezoceramic transducers placed at the opposite sides of the plate. The waves scattered by the notch are recorded with conventional transducers located on the plate surface in front and behind the defect. The selection of the A0 or the S0 modes is obtained by exciting the transducers with anti-phased or in-phased signals, respectively. Furthermore, a calibration process is investigated to correct errors caused by the presence of the receiver between the emitters and the defects. The power reflection and transmission coefficients are then obtained and the power balance is verified. Finally, these measurements are compared successfully with those obtained by a numerical method using the finite-element modeling described in a previous work.
Abstract: The aim of this work is to predict the propagation of the fundamental Lamb modes in an isotropic structure containing discontinuities in a simple and a fast way. The key point is to decompose the symmetrical notch into two elementary abrupt changes in the plate section. The power reflection and transmission coefficients are computed, using two techniques, with the help of the finite element and the well-known average power flow equation. In the first technique, the through-thickness displacements and stresses are used while in the second technique only the normal or tangential displacement at a given location on the plate surface is used. An equality relation between the direct and the inverse abrupt changes of the plate section is given, which allows computing the power reflection and transmission coefficients for a symmetrical notch from those obtained from one elementary damage. Finally, aluminum plates with different notches depths are tested. Experimental and numerical results are in good agreement.
Abstract: The interaction of the fundamental Lamb modes with asymmetrical discontinuities in isotropic plates is studied numerically and experimentally. Three kinds of discontinuities that enable mode conversions are considered: steps down, steps up and asymmetrical notches. The anti-symmetrical and symmetrical Lamb modes contributions are separated by means of the simple arithmetic operations of addition and subtraction. The power reflection and transmission coefficients are then computed with the well-known average power flow equation described in a previous work. Furthermore, the asymmetrical notch is reconstructed from the superposition of a step down and a step up. It is shown that it allows directly the determination of all power coefficients of the reflected, the transmitted and the multiple converted Lamb modes contrarily to the finite element model. Finally, an experimental device is realized to test aluminum plates with different notch depths. Good agreement is found between experimental and numerical results.
Abstract: The aim of this work is to study the fundamental compressional (L(0,1)) Pochhammer-Chree mode interaction with non-axisymmetric damages in cylinders. To this end, experimental and numerical investigations of non-axisymmetric vertical cracks are considered. A non-contact magnetostrictive device is used for experimental investigations. Magnetotrictive transducers are used to generate and receive compressional guided waves. These are enabled by using an axisymmetric and longitudinal magnetic polarising field. In the used experimental configuration, the emitter is located before the damage whereas the receiver is positioned between the emitter and the damage. Both, the incident and the reflected signals are acquired by the same receiver which allows a direct calculation of the reflected power flow. Different vertical cracks with various depths milled in steel cylinders are considered. The power flows are compared with those obtained by a three dimensional numerical method. This numerical method is based on a hybrid three dimensional (3D) approach combining the classical finite element (FE) method with the semi-analytical finite element (SAFE) technique. The near field surrounding the damage is analysed with the 3D FE method whereas transparent conditions are applied to the wave guide sections for the far field analysis. These transparent conditions are based on modal expansions on cross-sections. The SAFE technique is used to compute the eigenmodes. Eigenforces and modal power flows are post-processed on a straightforward way. First, the hybrid method is validated with published results in the litterature obtained for a free-end cylinder. Finally, numerical and experimental results are compared and good agreement is found.
Abstract: Repair of structures in concrete is still a challenge, especially when access and environment offer a difficult context such as the case of wharves. Concerning the repair of concrete for marine structures, European standards give the requirements in predefined and standardised conditions. However, repair of wharves is performed in harsh conditions such as access, humidity and operator position. These conditions do not enable the direct application of standards. By accounting for these requirements, the repair technique consists in rebuilding the concrete cover and in some cases using protective coating for some beams. In this paper, we focus on the concrete repair techniques. The aim of MAREO project (French project of the National competitive cluster in Civil Engineering and Eco-Building) is to compare several repair techniques carried out in the most complex area for repair: the tidal zone. The project deals with initial performance, sustainability, cost of durability and concrete properties monitoring by destructive testing (DT) and non destructive testing (NDT) techniques. The studied NDT techniques are: impact-echo, surface waves, multi-offset radar, and capacitive method. Both, beams placed in natural exposure and slabs specimens placed in accelerated conditions in laboratory are considered. For all the beams, the contaminated concrete was removed using high-velocity water jets (hydro-demolition). The selected techniques are wet shotcrete, dry shotcrete, formed concrete and manual repair. This paper focuses on the ability of NDT techniques to evaluate the changes of properties related to the chloride ingress in concrete both on site and in laboratory accelerated conditions. The interest of each technique and its sensitivity to several physical factors are highlighted. The need of NDT-combination is illustrated.
Abstract: The interaction of guided waves with non-axisymmetric damages in cylinders is studied. A three dimensional hybrid method involving the classical Finite Element Method (FEM) and the Semi-Analytical Finite Element (SAFE) technique is developed. The damage and its near field are analysed with the standard FEM. Then, eigenmode expansions of the solutions at both inlet and outlet cross-sections of the FEM region are performed. The far field is investigated by using eigenmode expansions based on SAFE method, which is used to determine the elastic guided modes for both inlet and outlet cross-sections of the volume. The amplitudes of the incident modes are fixed. The amplitudes of the scattered modes are determined by solving the global system of the hybrid FEM-SAFE model. The average power flow is directly derived from SAFE matrices. A comparison with results found in the literature for the free-end cylinder is performed with success. Then, a few results of the fundamental longitudinal Pochhammer-Chree mode interaction with non-axisymmetric cracks are obtained and discussed. The power balance is shown to be satisfied with a good accuracy.
Abstract: The interactions of the fundamental Lamb modes with discontinuities in an isotropic structure will be presented and analyzed in a simple and a fast way. The key point is to decompose the symmetrical or asymmetrical notch into two elementary steps. The fundamental anti-symmetrical and symmetrical Lamb modes contributions are separated by means of the simple arithmetic operations of addition and subtraction. The power reflection and transmission coefficients are then computed with the well-known average power flow equation described in a previous work [NDT&E international, Vol. 41, 2008, p.1-9]. Using these coefficients, the symmetrical notch can be constructed from one elementary symmetrical step while the asymmetrical notch is constructed from the superposition of asymmetrical down- and up- steps. Mode conversions phenomena are observed and analyzed for the asymmetrical steps and notches case. Finally, an experimental device is realized to test aluminum plates with different notch depths. Good agreement is found between experimental and numerical results.
Abstract: The aim of this work was to study the fundamental Lamb modes interaction with defects in isotropic plates. For these experimental investigations, symmetric notches with various depths milled in aluminum plates were considered. Moreover, the incident Lamb wave of a specific mode was generated by means of two identical thin piezoceramic transducers placed at the opposite sides of the plate. The waves scattered by the notch were recorded with conventional transducers located on the plate surface in front and behind the defect. The selection of the A0 or the S0 modes was
obtained by exciting the piezoceramic transducers with in-anti-phased or in-phased signals, respectively. Furthermore, a calibration process was investigated to correct errors caused by the presence of the receiver between the emitters and the defects. The power reflection and transmission coefficients were then obtained and the power balance, which takes into account
the physical phenomena of interaction, was verified. Measurement results showed that the A0 mode was more sensitive than the S0 mode to the considered defects. Finally, these measurements were compared successfully with those obtained by a hybrid method involving the finite-element modeling and the modal decomposition method developed in a previous work.
Abstract: In order to improve transport safety in aircrafts by a fast and efficient way, a possible solution is
to embed a system of piezoelectric transducers that generates ultrasonic Lamb waves in the structure. Indeed, the interaction of Lamb waves with damage enables its detection. However,
due to the properties of Lamb waves, the understanding of these interaction phenomena
is complex. Therefore, the problem of Lamb modes interaction with a sharp change of
section in a plate is analysed in this paper with the help of a new hybrid method based on the
finite element method and the normal mode analysis.
Abstract: Environmental and operational conditions cause corrosions and fatigue damage in cables used in civil engineering. For their non-destructive testing, an appropriate method might be to employ guided ultrasonic waves since they can interrogate the entire section of cables for long distances. Cables are typically made of a central wire and several peripheral helical wires. Due to the complexity of such a geometry, only cylindrical waveguides are considered. The present work is dedicated to a numerical study of the interaction of guided waves with non-axisymmetric cracks in an infinite cylinder. The numerical computations are based on a hybrid method involving the Finite Element Method (FEM) and the Semi-Analytical Finite Element (SAFE) technique. The classical FEM is used to analyse the crack and its near field. Then, eigenmode expansions of the solutions at both inlet and outlet cross-sections of the FEM region are performed. The SAFE technique is used to determine the elastic guided modes for both inlet and outlet cross-sections of the volume. The amplitudes of the incident modes are enforced while the amplitudes of the scattered modes are determined by solving the global system of the hybrid FEM-SAFE model. Obtained results for the free-end cylinder compare favourably with results found in the literature. The interaction of the fundamental longitudinal Pochhammer-Chree mode with non-axisymmetric cracks are predicted and discussed.
Abstract: The scattering of the fundamental Lamb modes from discontinuities in isotropic plates is studied. Both finite element method and modal analysis are used to quantify power coefficients of the scattered waves from symmetrical and asymmetrical notches, down- and up- steps. Mode conversions phenomena are only observed for the asymmetrical steps and notches case. The A0 and S0 modes are separated by means of simple arithmetic operations (addition and subtraction). The power coefficients are then computed with the well-known average power flow using temporal signals acquired on the plate surfaces. A method to determine the reflection, the transmission and the mode conversion power coefficients from a notch by superimposing power coefficients from down- and up- steps is described. The limits of this method to analyse crack-like defects are studied. An experimental device is realized to test the interaction of a selected fundamental Lamb mode with different notch depths in aluminum plates. Experimental measurements are in good agreement with numerical computations.
Abstract: The Non Destructive Testing is more and more used in aeronautics field. Among the various techniques available, Integrated Health Monitoring (IHM) systems based on Lamb waves offer a convenient method for quick and continuous inspection of plate structures. This work is devoted to the understanding of the physical interaction of Lamb waves with damages encountered in aluminum structures. These damages can be of different kinds. For example, this study deals with symmetric and asymmetric thickness variations and notches. First, one single mode is launched, either fundamental anti-symmetric mode (A0), or fundamental symmetric mode (S0), in order to simplify physics interpretation of interactions. Moreover, to analyze the Lamb modes issued from the interaction with the damage, a hybrid method (FEM – analytic) giving the power reflection and
transmission coefficients of Lamb waves, is developed. At the reception, the modes are separated with a simple technique based on the addition and the subtraction of the displacements computed in the opposite sides of the structure. This work shows that it is often possible to understand and quantify the interaction of a Lamb mode with a complex damage only from elementary damages.
Second, an IHM experimental system is proposed. The selection of a Lamb wave at the emission is provided with two piezoelectric sensors placed at the two opposite faces of the structure. Experimental results are in good keeping with numerical results and allow conceiving an optimal system.
