Simulation of Ultrasonic Examinations Using Surface Acoustic Waves

The UT simulation tools developed at the French Atomic Energy Commission (CEA) in the CIVA software platform were up to now limited to methods based on bulk ultrasonic waves. This study aims at extending the capabilities of the models to deal with testing configurations using surface acoustic waves (SAW). In such configurations, specific transducer arrangement is made to generate and receive surface waves. Very often, the field is generated by refracting a bulk longitudinal beam at the surface under test at a specific angle (e.g. Rayleigh angle). In the present work, a model has been derived to predict the SAW wavefield in the part under test by an arbitrary transducer as well as the leaky surface acoustic wave associated to the SAW propagation radiated in the coupling medium. First, asymptotic expressions for SAW and leaky surface waves are derived in the case of a point source radiating from a fluid medium over an elastic half-space. A geometrical interpretation is proposed allowing to derive a more general model based on the pencil method. Fields radiated by an arbitrary transducer are obtained and expressed as impulse responses to be convolved with an excitation pulse to quantitatively predict useful quantities (particle displacement, stress etc...). Examples of surface wavefields computed by the proposed model are given and compared with exact results (planar interface) showing its accuracy. The method should allow one to predict surface wavefields not only at planar surfaces but also propagating along curved surfaces described by CAD or analytically. Introduction: NDT simulation plays an increasingly important role at various stages in the design-processingmanufacturing-service chain of events [1]. It makes easier the design of new NDT methods, helps to demonstrate the performances of already existing or newly developed ones (performance demonstration, qualification), to interpret experiments (through simple comparison of measured data with predicted ones or more sophisticated model-based inversion algorithms). This is principally true for quantitative NDT methods such as ultrasonic testing (UT). For more than a decade, the French Atomic Energy Commission has been developing a platform software called CIVA that includes various quantitative UT simulation tools, together with tools for eddy-current methods [2]. Currently, CIVA simulation tools can handle very complex UT configurations: parts may be of complex geometry defined by 3D-CAD and composed of heterogeneous and anisotropic materials. Arbitrary transducers can be also considered (used in immersion or contact configuration, monolithic or phased-arrays), used in pulse-echo or in pitch-catch configurations. Similarly, various geometries of defects within the elastic medium can be accounted for and different scattering theories are used depending on defect geometry and position in the part. Only semi-analytic modeling can permit to handle such a complexity while keeping computation time compatible with intensive use of the software. Until now and as far as UT is concerned, most of the efforts in developing modeling tools and associated software were dedicated to methods relying on bulk wave propagation into parts. The present paper is dedicated to the development of new capabilities to deal with UT methods involving surface wave propagation. Previous to the development presented hereafter, our experience in modeling testing configurations involving surface waves was based on two developments which are briefly described. The first modeling work was carried out for the development of an original method of characterization of elastic properties of materials using Rayleigh wavespeed measurement similar to what is done in acoustic microscopy, that is, based on inversion of the so-called V(z,θ) curves. The originality in this work is that these curves are measured using a specific phased-array transducer that avoids transducer motion relatively to the part under test but rather uses computerized delay-laws to simulate z translation and θ rotation [3]. A model has been developed to, first, properly optimize the transducer design and further to simulate the effects of the various parameters of this configuration on measurement accuracy. The method being based on leaky Rayleigh wave measurements, the model deals with the decomposition of the incident field radiated at the interface between the water coupling and the part into a spectrum of plane waves which makes reflection easy to compute. Once the various reflection coefficients are computed, an inverse transform of the reflected plane waves allows the prediction of both specular and non-specular reflection phenomena, these including leaky Rayleigh wave generation. The second modeling work involving Rayleigh waves was carried out when considering the generation of Rayleigh waves by diffraction of an incident bulk wave at a crack edge, their propagation onto the crack surface and their scattering by crack edges as both bulk and surface waves. In this study, the various phenomena are modeled by means of a theoretical transient formulation of the Geometrical Theory of Diffraction for elastic waves, that is, an approximate formulation based on high frequency asymptotics. In this theory, the various phenomena can be interpreted geometrically [4]. The solution presented here to simulate UT using surface waves benefits from these two previous experiences. From the former, exact results can be obtained and used as reference results very helpful to check the accuracy of an approximate solution. From the latter, the possibility of developing asymptotic solutions is demonstrated, this allowing easy-to-understand geometrical interpretation of surface wave propagation and scattering. Of primary interest is the development of a tool for predicting the wavefield radiated by a transducer. A detailed description of how the energy is radiated depending on transducer diffraction effects is a very useful information in itself and in practice, the choice of a transducer is greatly helped by such a result. Moreover, this constitutes an input for the simulation of an experiment involving the interaction of an incident wavefield with a defect. Such a tool may be therefore seen as the kernel of any model involving surface wave propagation. The tool is expected to deal with parts not necessarily planar and with arbitrary transducers to be included in CIVA that deals with these cases when bulk waves are concerned. Moreover, our experience in the development of the model and software for predicting fields of bulk waves leads us to seek a solution for the surface waves compatible with the existing solution for the bulk waves, based on the pencil method [5]. To deal with arbitrary ultrasonic sources, the source surface is discretized as a set of source points of infinitesimal surface. Predicting transducer diffraction effects at a given field point requires the solution for the field radiated at this field point by a source point to be integrated over the discrete surface of the transducer. These effects are predicted in exactly the same way for bulk waves. What differs from one case to the other is the elementary solution used. However, surface waves are generally generated by refracting an incident beam of bulk waves at the critical angle corresponding to the surface wave speed. The radiation of the beam of bulk waves involved in the surface wave generation may simply be computed using the existing code. The way of accounting for non-planar interfaces is presented in the paragraph dedicated to discussions. The contributions of a source point P in the fluid (see Figs. 1 and 2) at a field point in the fluid after scattering by the planar interface with the solid can be written as exact integral formulations [6,7]. For the reflected waves in the fluid, the Fourier transform of the scalar potential response ( ) / refl M P φ at a point M from writes: ( ) ( ) ( ) 0 cos (1) 0 0 0 0 / sin M P jk z z refl sin M P jk R H k r e θ d φ φ θ θ θ +