We present a topical review which summarizes the main contributions to ‘multiple scattering of acoustic and elastic waves’ including the most recent advances. The review is divided into five main parts. In the first part, the effects of multiple scattering on ultrasonic propagation are illustrated on the basis of three experimental examples. In the second and third parts, we present the two possible descriptions for the propagation of an acoustic wave in a random medium. The first one is based on the study of the coherent wave, i.e. the wave amplitude averaged over disorder, whereas the second one deals with the propagation of the incoherent intensity, i.e. the intensity averaged over disorder. We especially insist on the microscopic basis for the phenomenological radiative transfer equation and show how it can be solved in the diffusion approximation. The theory is illustrated with experimental results obtained on a two-dimensional multiple-scattering prototype made of thousands of steel rods ra...

Multiple scattering of sound

A radiative transfer equation is used to model the diffuse multiple scattering of ultrasound in a medium containing discrete random scatterers. An assumption of uncorrelated phases allows one to write an equation of energy balance for the diffuse intensity. This ultrasonic radiative transfer equation contains single‐scattering and propagation parameters that are calculated using the elastic wave equation. Polarization effects are included through the introduction of an elastodynamic Stokes vector which contains a longitudinal Stokes parameter and four shear Stokes parameters similar to the four Stokes parameters used in optical radiative transfer theory. The theory is applied to a statistically homogeneous, isotropic elastic half‐space containing randomly distributed spherical voids illuminated by a harmonic plane wave. Results on the angular dependence of backscattered intensity are presented. It is anticipated that this approach may be applicable to materials characterization through the study of the ti...

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Radiative transfer of ultrasound

A model is presented which relates the absolute backscattered noise level observed in an ultrasonic immersion inspection to details of the measurement system and properties of the metal specimen under study. The model assumes that the backscattered noise signal observed for a given transducer position is an incoherent superposition of echoes from many grains. The model applies to normal-incidence, pulse-echo inspections of weakly-scattering materials using toneburst pulses from either a planar or focused transducer. The model can be used in two distinct ways. Measured noise echoes can be analyzed to deduce a “Figure-of-Merit” (FOM) which is a property of the specimen alone, and which parameterizes the contribution of the microstructure to the observed noise. If the FOM is known, the model can be used to predict the absolute noise levels that would be observed under various inspection scenarios. Tests of the model are reported, using both synthetic noise echoes, and measured noise echoes from metal specimens having simple and complicated microstructures.

Backscattered microstructural noise in ultrasonic toneburst inspections

A set of ultrasonic experimental methods was developed to characterize a multiple scattering medium in terms of l(s), l*, l(a), respectively, the elastic, transport, and absorption mean free paths and D the diffusion constant. Actually, these quantities are the key parameters for a wave propagating in a disordered medium. Although they are widely used in optics, they are less common in acoustics. The underlying model is based on the expansion of the average solution for the heterogeneous Green's function equation. To validate this theoretical approach, a sample made of randomly located steel rods was used as a prototype. Through time-resolved measurements of the transmitted amplitude, the difference between the ballistic and the coherent wave is highlighted. In varying the sample thickness, l(s) is determined, the coherent and diffusive regime are distinguished, and the transition from one to the other is followed. Furthermore, as a limit to a description of the average intensity based on the diffusion approximation, the existence of a coherent backscattering effect is shown. This latter gives a method to estimate D and l*. These quantities being determined, it becomes possible to infer l(a) using average time-resolved intensity measurements. Finally, some applications to coarse-grain stainless steels are discussed.

Transport parameters for an ultrasonic pulsed wave propagating in a multiple scattering medium

As a solid-state welding process, Friction Stir Welding (FSW) offers a variety of advantages over traditional welding processes. Problems that are typically occurring due to the cooling of the liquid phase, such as solidification cracking and formation of porosity, generally do not occur in FSW. Nevertheless, as a result of suboptimal settings of the welding process parameters and certain uncontrollable conditions, FSWs are still associated with a number of specific flaws, e.g. root flaws and wormholes. Ultrasonic non-destructive testing and evaluation techniques (NDT&E) can be used for quality assessment of friction stir welded joints. In this paper, a novel approach for the detection of root flaws is proposed using an immersion ultrasonic testing method in oblique incidence and backscatter mode. The backscattered energy C-scan images obtained after an empirical positioning and proper time gating can be straightforwardly interpreted by direct comparison with typical ‘flaw’ patterns, allowing for identification and localization of the root flaws in the weld. The method is illustrated for FSW butt joints of the AlZnMgCu (7XXX series) alloy.

Non-destructive ultrasonic examination of root defects in friction stir welded butt-joints

Grain noise power spectrum estimation for weak scattering polycrystalline materials using experimentally estimated backscatter coefficients: oblique incidence

M.D. Russell

Papers

Grain noise power spectrum estimation for weak scattering polycrystalline materials using experimentally estimated backscatter coefficients: oblique incidence