Modelling the attenuation in the ATHENA finite elements code for the ultrasonic testing of austenitic stainless steel welds

Multipass welds made in austenitic stainless steel, in the primary circuit of nuclear power plants with pressurized water reactors, are characterized by an anisotropic and heterogeneous structure that disturbs the ultrasonic propagation and makes ultrasonic non-destructive testing difficult. The ATHENA 2D finite element simulation code was developed to help understand the various physical phenomena at play. In this paper, we shall describe the attenuation model implemented in this code to give an account of wave scattering phenomenon through polycrystalline materials. This model is in particular based on the optimization of two tensors that characterize this material on the basis of experimental values of ultrasonic velocities attenuation coefficients. Three experimental configurations, two of which are representative of the industrial welds assessment case, are studied in view of validating the model through comparison with the simulation results. We shall thus provide a quantitative proof that taking into account the attenuation in the ATHENA code dramatically improves the results in terms of the amplitude of the echoes. The association of the code and detailed characterization of a weld’s structure constitutes a remarkable breakthrough in the interpretation of the ultrasonic testing on this type of component.     

Defect imaging with elastic waves in inhomogeneous-anisotropic materials with composite geometries

Imaging of defects in composite structures plays an important role in non-destructive testing (NDT) with elastic waves, i.e., ultrasound. Traditionally the imaging of such defects is performed using the synthetic aperture focusing technique (SAFT) algorithm assuming homogeneous isotropic materials. However, if parts of the structure are inhomogeneous and/or anisotropic, this algorithm fail to produce correct results that are needed in order to asses the lifetime of the part under test. Here we present a modification of this algorithm which enables a correct imaging of defects in inhomogeneous and/or anisotropic composite structures, whence it is termed InASAFT. The InASAFT is based on the exact modelling of the structure in order to account for the true nature of the elastic wave propagation using travel time ray tracing techniques. The algorithm is validated upon several numerical and real life examples yielding satisfactory results for imaging of cracks. The modified algorithm suffers, though, from the same difficulties encountered in the SAFT algorithm, namely “ghost” images and eventual lack of clear focused images. However, these artifacts can be identified using a forward wave propagation analysis of the structure.     

Wave guide imaging through Time Domain Topological Energy

Time Domain Topological Energy (TDTE), uses the reflected ultrasonic field recorded by an array of transducers placed on the boundary of the inspected medium. Two numerical determinations (forward and adjoint problems) of the acoustical field inside a reference medium are necessary to compute an image. Topological Energy is defined as a variation of topological sensitivity or gradient and comes from the field of mathematical optimisation. Recent developments for Non-Destructive Testing have shown the analogy with Time Reversal concepts. Time Reversal mirrors have been employed for various applications in a wide number of situations including wave guides where very good re-focalization performances have been obtained with a reduced number of transducers instead of an array of transducers. Moreover recent works have enlightened that the reverberation properties of a wave guide allow to re-focalize using Time Reversal with only one transducer. For TDTE imaging a single transducer placed at one end of a wave guide has been modelled. The boundaries of the wave guide create virtual sources that can be understood as a virtual array of transducers. Numerical and experimental results are presented using TDTE and a single transducer in a wave guide for targets and conditions of increasing complexity.     

A semi-analytical model for predicting multiple propagating axially symmetric modes in cylindrical waveguides

A semi-analytical model for multiple mode axially symmetric wave propagation in finite solid cylindrical waveguides is presented. The model is designed as a tool for predicting and interpreting experimental signals. The model is based on a common experimental configuration and considers the excitation, propagation and reception of the ultrasonic signal in the waveguide. The Pochhammer-Chree solution for an infinite cylinder is the basis for the model. Extensions are made to enable comparison to experimental results. Comparisons with experiment are performed in the time, frequency and joint-time frequency domain for both narrow band and broad band excitation of the piezo-electric transducer.     

Ultrasonic material characterization using large-aperture PVDF receivers

This work describes the use of a large-aperture PVDF receiver in the measurement of liquid density and composite material elastic constants. The density measurement of several liquids is obtained with accuracy of 0.2% using a conventional NDE emitter transducer and a 70-mm-diameter, 52-μm P(VDF-TrFE) membrane with gold electrodes. The determination of the elastic constants is based on the phase velocity measurement. Diffraction can lead to errors around 1% in velocity measurement when using alternatively the conventional pair of ultrasonic transducers (1-MHz frequency and 19-mm-diameter) operating in through-transmission mode, separated by a distance of 100 mm. This effect is negligible when using a pair of 10-MHz, 19-mm-diameter transducers. Nevertheless, the dispersion at 10 MHz can result in errors of about 0.5%, when measuring the velocity in composite materials. The use of an 80-mm diameter, 52-μm-thick PVDF membrane receiver practically eliminates the diffraction effects in phase velocity measurement. The elastic constants of a carbon fiber reinforced polymer were determined and compared with the values obtained by a tensile test.     

The detectability of kissing bonds in adhesive joints using ultrasonic techniques

This paper concerns a study of the detectability of dry contact kissing bonds in adhesive joints using three ultrasonic inspection techniques. Conventional normal incidence longitudinal and shear wave inspection were conducted on dry contact kissing bonds using a standard damped ultrasonic transducer and an electro-magnetic acoustic transducer (EMAT) respectively. The detectability of the dry contact kissing bonds was assessed by calculating the reflection coefficient of the imperfect interface at varying loads for a number of surface roughnesses. A high power ultrasonic method was also employed to determine the non-linear behavior of the adhesive interface. The non-linearity of the interface was determined by the ratio of the amplitudes of the first harmonic and fundamental frequencies of the transmitted waveform. It was found that the high power technique showed the greatest sensitivity to these kissing bonds at low contact pressures, however at high loads conventional longitudinal wave testing was more sensitive. It was also noted that a combination of two or more techniques could provide enhanced information about the kissing bond compared to a single technique alone.     

Non-contact sound velocities and attenuation measurements of several ceramics at elevated temperatures

Laser ultrasonic technique has been employed to carry out the sound velocities and attenuation measurements as a function of temperature in alumina, two kinds of silicon nitride and partially stabilized zirconia (PSZ) samples. Accuracy of the laser technique used has been checked in terms of the diffraction effect and reproducibility of the results. Results of attenuation at room temperature have been compared with quartz transducer technique. In PSZ, velocity behavior has become non-linear and also, a peak in attenuation has been observed around 500 degrees C. In one of the silicon nitride sample, which uses glassy sintering agent, attenuation has shown a sharp peak around 950 degrees C. Interestingly, when the experiment was repeated from 800 to 1000 degrees C, this anomalous attenuation peak has disappeared, leaving a background increasing towards higher temperatures.     

Attenuation coefficient estimation using experimental diffraction corrections with multiple interface reflections

The ultrasonic attenuation coefficient of a fluid or solid is an acoustic parameter routinely estimated for the purpose of materials characterization and defect/disease detection. This paper describes a broadband attenuation coefficient estimation technique that combines two established estimation approaches. The key elements of these two approaches are: (1) the use of magnitude spectrum ratios of front surface, first back surface, and second back surface reflections from interfaces of materials with plate-like geometries, and (2) the use of an experimental diffraction correction approach to avoid diffraction losses. The combined estimation approach simplifies the attenuation coefficient estimation process by eliminating the need to explicitly make diffraction corrections or calculate reflection/transmission coefficients. The approach yields estimates of the attenuation coefficient, reflection coefficient, and material density. Models, experimental procedures, and signal analysis procedures, which support implementation of the approach, are presented. Attenuation coefficient and reflection coefficient estimates are presented for water and solid samples with estimates based on measurements made with multiple transducers.     

Ultrasonic wave propagation in heterogeneous solid media: theoretical analysis and experimental validation

This research deals with the ultrasonic characterization of thermal damage in concrete. This damage leads to the appearance of microcracks which then evolve in terms of volume rate and size in the material. The scattering of ultrasonic waves from the inclusions is present in this type of medium. The propagation of the longitudinal wave in the heterogeneous media is studied via a homogenization model that integrates the multiple scattering of waves. The model allows us to determine the phase velocity and the attenuation according to the elements which make the medium. Simulations adapted to the concrete are developed in order to test the responses of the model. These behaviors are validated by an experimental study: the measurements of phase velocity and attenuation are performed in immersion, with a comparison method, on a frequency domain which ranges from 160 kHz to 1.3 MHz. The analysis of different theoretical and experimental results obtained on cement-based media leads to the model validation, on the phase velocity behavior, in the case of a damage simulated by expanded polystyrene spheres in granular media. The application to the case of a thermally damaged concrete shows a good qualitative agreement for the changes in velocity and attenuation.     

Schlieren photography to study sound interaction with highly absorbing materials

Strong absorption of sound is often caused by the conversion of sound energy into heat. When this happens, it is not possible to study the interaction of sound with the absorbing material by means of reflected sound characteristics, because there is no reflected sound. Detecting for example the distance that sound travels in a strongly absorbing material, can be done by heat detection systems. However, the presence of temperature detectors in such materials interferes with the sound field and is therefore not really suitable. Infrared measurements are a possible option. Another option is the use of Schlieren photography for simultaneous visualization of sound and heat. This technique is briefly outlined with a 3 MHz sound beam incident on a highly absorbing sponge.     

Ultrasonic field modeling for immersed components using Gaussian beam superposition

The Gaussian beam (GB) superposition approach can be applied to model ultrasound propagation in complex-structured materials and components. In this article, progress made in extending and applying the Gaussian beam superposition technique to model the beam fields generated by transducers with flat and focused rectangular apertures as well as with circular focused apertures is addressed. The refraction of transducer beam fields through curved surfaces is illustrated by calculation results for beam fields generated in curved components during immersion testing. In particular, the following developments are put forward: (i) the use of individually determined sets of GBs to model transducer beam fields with a number of less than ten beams; (ii) the application of the GB representation of rectangular transducers to focusing probes, as well as to the problem of transmission through interfaces; and (iii) computationally efficient transient modeling by superposition of ‘temporally limited’ GBs.     

A concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids

This paper presents a concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids. The formalism is capable of resolving completely the numerical instability problems associated with transfer matrix method, thereby obviating the extensive reformulation in its modified versions based on delta operator technique. In contrast to the earlier reflection matrix formalisms, all scattering matrices are obtained in a direct manner without invoking wave-propagator or scatterer operator concepts. Both local and global reflection and transmission matrices corresponding to scatterings in two and more layers are derived. The derivation of global scattering matrices in terms of the local ones is carried out concisely based on physical arguments to provide better insights into scattering mechanism. Another formulation which is even more succinct is also devised for obtaining the global scattering matrices directly from eigensolutions. The resultant expressions and algorithm are terse, efficient and convenient for implementation.     

Effect of anisotropy on acoustoelastic birefringence in wood

The ultrasonic velocity of shear waves propagating through radial direction of a wood plate specimen, transversely to the loading direction, was measured. By rotating an ultrasonic sensor, the oscillation direction of the shear waves was varied with respect to the wood plate axis and loading direction. The relationship between shear wave velocity and oscillation direction was examined to discuss the effect of anisotropy on the acoustoelastic birefringence in wood. The results obtained were summarized as follows. When the oscillation direction of the shear wave corresponded to the tangential direction of the wood specimen regardless of the stress direction, shear wave velocity decreased markedly and the relationship between shear wave velocity and rotation angle tended to become discontinuous. That is, when the shear waves oscillated in the anisotropic axis of the wood, the shear wave velocity peaked unlike in the case of oscillation in the stress direction. In an isotropic material (acrylic, aluminum 5052), on the contrary, when the shear waves oscillated in the stress direction of the specimen, the shear wave velocity peaked regardless of the main-axis direction of the specimen. On the basis of the discussion of these results, the ultrasonic shear wave propagating in wood under stress is confirmed to be polarized in the anisotropic axis of the wood.     

Reflection of structural waves at a solid/liquid interface

This paper investigates the reflection characteristics of structural or guided waves in rods at a solid/liquid interface. Structural waves, whose wavelengths are much larger than the diameter of the rod, are described in a first approximation by classical one-dimensional wave theory. The reflection characteristics of such waves at a solid/liquid (melting) interface has been reported by two different ultrasonic measurement techniques: first, measuring the fast regression rate of a melting interface during the burning of metal rod samples in an oxygen-enriched environment, and second, monitoring the propagation of the solid/liquid interface during the slow melting and solidification of a rod sample in a furnace. The second work clearly shows that the major reflection occurs from the solid/liquid interface and not the liquid/gas interface as predicted by plane longitudinal wave reflectivity theory. The present work confirms this observation by reporting on the results of some specially designed experiments to identify the main interface of reflection for structural waves in rods. Hence, it helps in explaining the fundamental discrepancy between the reflection characteristics at a solid/liquid interface between low frequency structural waves and high frequency bulk waves, and confirms that the detected echo within a burning metallic rod clearly represents a reflection from the solid/liquid interface.     

Impact of localized inhomogeneity on the surface-wave velocity and bulk-wave reflection in solids

The effect of a weak surface, near-surface and interfacial inhomogeneity on the frequency dependence of the surface wave velocity and of the SH (shear horizontal) wave reflectivity in isotropic elastic media is studied analytically and numerically. The inhomogeneity is modeled as an infinite planar layer with continuously varying properties. Weak inhomogeneity may markedly affect the dispersion of the Rayleigh velocity and especially of the reflectivity. It is demonstrated how this effect, particularly pronounced at high frequency, depends on the extent of inhomogeneity. The material data for damaged and ideal concrete and several simple examples of inhomogeneity profiles are utilized for the numerical calculations based on the Peano expansion. The use of explicit low- and high-frequency approximations is also exemplified. Among these, simple WKB asymptotics are shown to be particularly helpful for the Rayleigh velocity in the case of a prominent inhomogeneity attached to the surface and for the reflection on weak interfaces.     

Mode-switching: A new technique for electronically varying the agglomeration position in an acoustic particle manipulator

Acoustic radiation forces offer a means of manipulating particles within a fluid. Much interest in recent years has focussed on the use of radiation forces in microfluidic (or “lab on a chip”) devices. Such devices are well matched to the use of ultrasonic standing waves in which the resonant dimensions of the chamber are smaller than the ultrasonic wavelength in use. However, such devices have typically been limited to moving particles to one or two predetermined planes, whose positions are determined by acoustic pressure nodes/anti-nodes set up in the ultrasonic standing wave. In most cases devices have been designed to move particles to either the centre or (more recently) the side of a flow channel using ultrasonic frequencies that produce a half or quarter wavelength over the channel, respectively.It is demonstrated here that by rapidly switching back and forth between half and quarter wavelength frequencies - mode-switching - a new agglomeration position is established that permits beads to be brought to any arbitrary point between the half and quarter-wave nodes. This new agglomeration position is effectively a position of stable equilibrium. This has many potential applications, particularly in cell sorting and manipulation. It should also enable precise control of agglomeration position to be maintained regardless of manufacturing tolerances, temperature variations, fluid medium characteristics and particle concentration.     

Estimation of critical and viscous frequencies for Biot theory in cancellous bone

The use of Biot theory for modelling ultrasonic wave propagation in porous media involves the definition of a "critical frequency" above which both fast and slow compressional waves will, in principle, propagate. Critical frequencies have been evaluated for healthy and osteoporotic cancellous bone filled with water or marrow, using data from the literature. The range of pore sizes in bone gives rise to a critical frequency band rather than a single critical frequency, the mean of which is lower for osteoporotic bone than normal bone. However, the critical frequency is a theoretical concept and previous researchers considered a more realistic "viscous frequency" above which both fast and slow waves may be experimentally observed. Viscous frequencies in bone are found to be several orders of magnitude greater than calculated critical frequencies. Whereas two waves may well be observed at all ultrasonic frequencies for water-filled cancellous bone at 20 degrees C, it is probable megahertz frequencies would be needed for observation of two waves in vivo.     

Analysis of laser-generated ultrasonic force source at specimen surface and display of bulk wave in transversely isotropic plate by numerical method

Taking into account the effects of thermal diffusion and optical penetration, as well as the finite width and duration of the laser source, the laser-generated ultrasonic force source at surface vicinity is presented. The full acoustic fields of laser-generated ultrasonic bulk wave are obtained and displayed in transversely isotropic plate. The features of laser-generated ultrasound bulk waves are analyzed. The features of laser-generated ultrasonic bulk wave are in good agreement with the theoretical results (the phase velocity surfaces), demonstrating the validity of this simulation. The numerical results indicate that the features of laser-generated ultrasound waveforms in anisotropic specimen, different from the case in isotropic materials, have a close relation with the propagating plane and propagation direction. This method can provide insight to the generation and propagation of laser-generated ultrasonic bulk wave in transversely isotropic material.     

Analytical methods for modeling of ultrasonic nondestructive testing of anisotropic media

Many modern structural materials exhibit anisotropic elastic behavior leading to complicated wave propagation phenomena. To ensure the reliability of ultrasonic nondestructive testing techniques, these material properties as well as the influence of microstructural inhomogeneities and the effects of interfaces on ultrasonic wave propagation have to be taken into account. In this respect, mathematical modeling provides an efficient method of assisting analysis. Two computationally efficient analytical approaches--a Gaussian beam and a point source superposition technique--are presented, which are well-suited for performing ultrasonic wave propagation and scattering simulations for anisotropic media. Results for homogeneous as well as inhomogeneous anisotropic media like composites and weld material are presented.