Larissa Fradkin

The high-frequency asymptotic description of pulses radiated by a circular normal transducer into an elastic half-space

A new method for simulating the propagation of pulses radiated by a circular normal ultrasonic transducer which is directly coupled to a homogeneous and isotropic elastic half-space is proposed. Both nonuniform and uniform high-frequency asymptotics inside geometrical regions as well as boundary layers (penumbra, an axial region, and a vicinity of the critical rays) have been used to describe the transient field by means of harmonic synthesis. The nonuniform asymptotic formulas involving elementary or well-known special functions elucidate the physics of the problem and give explicit dependence of the radiated waves upon the model parameters. The formulas are applicable in the radiating near field which is the near-field with the evanescent wave zone excluded. The code based on the uniform asymptotics has been tested in all regions against an exact numerical solution. It is orders of magnitude faster, but in many realistic cases the accuracy does not suffer. The limits of applicability of the model have b...

A new method for assessing the mean grain size of polycrystalline materials using ultrasonic NDE

We re-analyze published data on ultrasonic inspection of a number of pure metals and alloys involving a range of mean grain sizes (from 0.0125 mm to 0.3 mm). We show that they may be described by one master curve graph consisting mainly of two distinct but parallel linear segments. This means that our presentation clusters the data under study into two distinct groups, each chracterized by its own generalized material constant. The slope of the segments suggests the predominance of scattering other than Rayleighs, since it is consistent with the second power law rather than the fourth. We argue that the attenuation is likely to be due to multiple scattering, particularly since our generalized material constants seem to be similar to the published stochastic scattering factors. The master curve graph suggests a new fast and simple method for assessing the mean grain size which may be carried out without recourse to standard specimens or measurements other than those routinely carried out during ultrasonic inspection. As the range of materials and grain sizes are in extensive use in industry the simple schedule proposed should prove of substantial use in practical material evaluation and production process control.

A system model for ultrasonic NDT based on the Physical Theory of Diffraction (PTD)

Simulation of ultrasonic Non Destructive Testing (NDT) is helpful for evaluating performances of inspection techniques and requires the modelling of waves scattered by defects. Two classical flaw scattering models have been previously usually employed and evaluated to deal with inspection of planar defects, the Kirchhoff approximation (KA) for simulating reflection and the Geometrical Theory of Diffraction (GTD) for simulating diffraction. Combining them so as to retain advantages of both, the Physical Theory of Diffraction (PTD) initially developed in electromagnetism has been recently extended to elastodynamics. In this paper a PTD-based system model is proposed for simulating the ultrasonic response of crack-like defects. It is also extended to provide good description of regions surrounding critical rays where the shear diffracted waves and head waves interfere. Both numerical and experimental validation of the PTD model is carried out in various practical NDT configurations, such as pulse echo and Time of Flight Diffraction (TOFD), involving both crack tip and corner echoes. Numerical validation involves comparison of this model with KA and GTD as well as the Finite-Element Method (FEM).

SIMULATION OF DISORIENTED FLAWS IN A TOFD TECHNIQUE CONFIGURATION USING GTD APPROACH

The TOFD (Time of Flight Diffraction) Technique is commonly used to detect and to characterize embedded disoriented flaws using their edge diffraction echoes. We present a TOFD simulation module which includes GTD coefficients allowing to predict diffraction echoes from embedded planar flaws. Other dedicated development have been added in the CIVA software platform to simulate lateral surface waves, backwall echoes and shadowing effects from flaws. Experimental validations have been performed on various specimen containing rectangular and CAD contour planar flaws with different possible disorientations (tilt, vertical misorientation, skew) and show an overall good agreement between simulation and measure.

The Uniform geometrical Theory of Diffraction for elastodynamics: Plane wave scattering from a half-plane.

Diffraction phenomena studied in electromagnetism, acoustics, and elastodynamics are often modeled using integrals, such as the well-known Sommerfeld integral. The far field asymptotic evaluation of such integrals obtained using the method of steepest descent leads to the classical Geometrical Theory of Diffraction (GTD). It is well known that the method of steepest descent is inapplicable when the integrands stationary phase point coalesces with its pole, explaining why GTD fails in zones where edge diffracted waves interfere with incident or reflected waves. To overcome this drawback, the Uniform geometrical Theory of Diffraction (UTD) has been developed previously in electromagnetism, based on a ray theory, which is particularly easy to implement. In this paper, UTD is developed for the canonical elastodynamic problem of the scattering of a plane wave by a half-plane. UTD is then compared to another uniform extension of GTD, the Uniform Asymptotic Theory (UAT) of diffraction, based on a more cumbersome ray theory. A good agreement between the two methods is obtained in the far field.

Elastic wave diffraction by infinite wedges

We compare two recently developed semi-analytical approaches to the classical problem of diffraction by an elastic two dimensional wedge, one based on the reciprocity principle and Fourier Transform and another, on the representations of the elastodynamic potentials in the form of Sommerfeld Integrals. At present, in their common region of validity, the approaches are complementary, one working better than the other at some isolated angles of incidence.

The complete far–field asymptotic description of a point source acting on a transversely isotropic half–space

The elastic wavefield generated by a point source of tractions acting on the surface of a transversely isotropic half–space is studied. The symmetry axis of the solid is oriented arbitrarily with respect to the surface of the half–space. First, the integral representation of the time–harmonic Greens tensor is given. Then the complete far–field asymptotic approximation of a quasi–longitudinal (qP) and two quasi–shear (qSH and qSV) waves is derived. The qP wave is described by the leading term of the ray series, since there is only one arrival of this wave. The qSH wave is treated similarly everywhere apart from the so–called kissing–point boundary layer, where the qSH and qSV wavefronts are tangentially close to each other. A special asymptotic formula is obtained for this case. The qSV sheet of the wave surface is allowed to have conical points and cuspidal edges. Thus, the far–field approximation of the qSV wave involves ray–asymptotic expressions while inside the geometrical regions (where either one or three qSV arrivals exist), or else boundary–layer asymptotics inside conical–point, cuspidal–edge and kissing–point boundary layers. At the end of the paper we present numerical results of the simulation of pulse propagation. A good agreement between the asymptotic and direct numerical codes is achieved but the former is orders of magnitude faster.

Mathematical modelling of ultrasonic non-destructive evaluation

High-frequency asymptotics have been used at our Centre to develop codes for modelling pulse propagation and scattering in the near-field of the ultrasonic transducers used in NDE (Non-Destructive Evaluation), particularly of walls of nuclear reactors. The codes are hundreds of times faster than the direct numerical codes but no less accurate.

Scatter of toroidal elastic waves from a plane

Experiments indicate that the radiating near zone of a compressional circular transducer directly coupled to a homogeneous and isotropic solid has the following structures: there are geometrical zones where one can distinguish a plane compressional wave and toroidal waves, both compressional and shear, radiated by the transducer rim. As we have shown previously, the modern diffraction theory allows to describe these explicitly. It also gives explicit asymptotic description of waves present in the transition zones. A lot of work has been done by other authors in calculating the fields obtained as the result of a plane wave incident on a plane crack. Here, we present calculations which have been carried out in the framework of Geometrical Elastodynamics and pertain to scattering of toroidal waves by an infinite plane crack. We demonstrate that when the incident wave is toroidal shear there are gaps in the portion of the crack which at a given moment in time contribute to the scattered compressional waves. U...

Simulation of the UT inspection of planar defects using a generic GTD-Kirchhoff approach

The modeling of ultrasonic Non Destructive Evaluation often plays an important part in the assessment of detection capabilities or as a help to interpret experiments. The ultrasonic modeling tool of the CIVA platform uses semi-analytical approximations for fast computations. Kirchhoff and GTD are two classical approximations for the modeling of echoes from plane-like defects such as cracks, and they aim at taking into account two different types of physical phenomena. The Kirchhoff approximation is mainly suitable to predict specular reflections from the flaw surface, whereas GTD is dedicated to the modeling of edge diffraction. As a consequence, these two approximations have distinct and complementary validity domains. Choosing between them requires expertise and is problematic in some inspection configurations. The Physical Theory of Diffraction (PTD) was developed based on both Kirchhoff and GTD in order to combine their advantages and overcome their limitations. The theoretical basis for PTD and its integration in the CIVA modeling approach are discussed in this communication. Several results that validate this newly developed model and illustrate its advantages are presented.