Modeling of reflected ultrasonic fields in composed samples

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Abstract

Ultrasonic nondestructive testing involves the study of propagation, reflection and refraction patterns of elastic waves excited by contact or non-contact piezoelectric transducers in the inspected object. The finite element modeling usually requires high computational costs and additional postprocessing to select individual waves from the total solution. When probing joints of homogeneous materials, such as turbine blades made of heat-resistant monocrystalline alloys, the joint boundary is low-contrast, and the reflected signals are relatively weak. This causes additional difficulties for their separation from the total wave field and correct interpretation of the information they bring. To solve this problem, explicit asymptotic representations for reflected and transmitted waves in a two-layer elastic half-space with a surface source are proposed in the present work, which allow fast parametric analysis. They can be used to analyze ultrasonic probing data, for example, to estimate the state of the junction zone or to determine the mutual orientation of the crystals’ principal axes.

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About the authors

E. V. Glushkov

Kuban State University

Author for correspondence.
Email: evg@math.kubsu.ru

Institute for Mathematics, Mechanics and Informatics

Russian Federation, 350040 Krasnodar, Stavropolskaya str., 149

N. V. Glushkova

Kuban State University

Email: nvg@math.kubsu.ru

Institute for Mathematics, Mechanics and Informatics

Russian Federation, 350040 Krasnodar, Stavropolskaya str., 149

A. A. Tatarkin

Kuban State University

Email: tiamatory@gmail.com

Institute for Mathematics, Mechanics and Informatics

Russian Federation, 350040 Krasnodar, Stavropolskaya str., 149

O. A. Ermolenko

Kuban State University

Email: o.ermolenko.a@gmail.com

Institute for Mathematics, Mechanics and Informatics

Russian Federation, 350040 Krasnodar, Stavropolskaya str., 149

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Supplementary files

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2. Fig. 1. Geometry of the problem (a); polar coordinates (R, θ) for the asymptotics of the source field u0 and (R1, θ1) for the reflected field u–sc; the angle ψ determines the orientation of the principal axes of anisotropy (x^, z^) (b).

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3. Fig. 2. Reverberation of the source field in the upper layer (a); occurrence of reflected and transmitted volume waves PP, PS, SP and SS when the P and S components of the source field u0 fall on the interface between the media (b).

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4. Fig. 3. Wave field of a vertical source (θ0 = 0) in a homogeneous half-plane M1 (ψ1 = ψ2 = 0) (a) and in a two-layer M1/M2 ( ψ1 = 0, ψ2 = π/4) (b); frequency f = 1 MHz.

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5. Fig. 4. The field of an inclined source (θ0 = π/4, on the left) and the amplitude of the vertical component of the reflected field displacements |w–sc| = |w – w0| on the surface z = 0 (on the right) in the media M1/M2 (top) and M2/M1 (bottom); frequency f = 1 MHz.

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6. Fig. 5. Change in the displacement field |u| of an inclined source (θ0 = π/4 as in Fig. 4) in the half-plane M1/M2 (left) and M2/M1 (right) at frequencies f = 2, 5, and 10 MHz.

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7. Fig. 6. Dependence of the phase (a) and group (b) velocities of plane waves on the direction of propagation θ in the material M1.

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8. Fig. 7. Directivity patterns of the components of the reflected field u–1 in the IM1/IM2 and IM2/IM1 media at a distance of R1 = 20λp (the values are normalized to the maximum).

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9. Fig. 8. Directivity patterns of the components of the transmitted field u+1 in the IM1/IM2 and IM2/IM1 media at a distance of R = 20λp (the values are normalized to the maximum).

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