Long Wavelength Rayleigh Wave Scattering from Microscopic Surface Fatigue Cracks

Resch, M. T.; Shyne, J. C.; Kino, G. S.; Nelson, D. V.

doi:10.1007/978-1-4684-4262-5_73

Cited by 10 publications

(5 citation statements)

References 3 publications

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“…The results showed that the scattering amplitude appears to increase quadratically, which is in agreement with the theoretical expectation from a quasistatic approximation for long wavelength (low frequency) scattering [ 32 ]. In a previous edge crack problem [ 3 ], a linear trend was observed for 0.07 < a/λ < 0.22.…”

Section: Discussionsupporting

confidence: 86%

Experimental and Computational Studies on the Scattering of an Edge-Guided Wave by a Hidden Crack on a Racecourse Shaped Hole

2017

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Reliable and quantitative non-destructive evaluation for small fatigue cracks, in particular those in hard-to-inspect locations, is a challenging problem. Guided waves are advantageous for structural health monitoring due to their slow geometrical decay of amplitude with propagating distance, which is ideal for rapid wide-area inspection. This paper presents a 3D laser vibrometry experimental and finite element analysis of the interaction between an edge-guided wave and a small through-thickness hidden edge crack on a racecourse shaped hole that occurs, in practice, as a fuel vent hole. A piezoelectric transducer is bonded on the straight edge of the hole to generate the incident wave. The excitation signal consists of a 5.5 cycle Hann-windowed tone burst of centre frequency 220 kHz, which is below the cut-off frequency for the first order Lamb wave modes (SH1). Two-dimensional fast Fourier transformation (2D FFT) is applied to the incident and scattered wave field along radial lines emanating from the crack mouth, so as to identify the wave modes and determine their angular variation and amplitude. It is shown experimentally and computationally that mid-plane symmetric edge waves can travel around the hole’s edge to detect a hidden crack. Furthermore, the scattered wave field due to a small crack length, a, (compared to the wavelength λ of the incident wave) is shown to be equivalent to a point source consisting of a particular combination of body-force doublets. It is found that the amplitude of the scattered field increases quadratically as a function of a/λ, whereas the scattered wave pattern is independent of crack length for small cracks a << λ. This study of the forward scattering problem from a known crack size provides a useful guide for the inverse problem of hidden crack detection and sizing.

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Section: Discussionsupporting

confidence: 86%

Experimental and Computational Studies on the Scattering of an Edge-Guided Wave by a Hidden Crack on a Racecourse Shaped Hole

2017

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“…A case of particular interest is a Mode I (tensile) crack element, with the crack surface R lying in the yz-plane, i.e., n ¼ ð1; 0; 0Þ in Fig. 3, which can be specified as follows Du x ¼ UdðyÞdðz À lÞ on x ¼ 0; Du y ¼ Du z ¼ 0; (28) where the source strength U represents the crack volume, i.e., the integral of the crack opening Du x over the area R, which can be estimated by a quasi-static approximation for small cracks (relative to the wavelength), 31 and the location ð0; 0; lÞ can be regarded as the centroid for this volume. On substituting Eq.…”

Section: Solution For Buried Cracksmentioning

confidence: 99%

“…[20][21][22][23][24][25] In general, this induced source density can only be determined computationally, [26][27][28][29][30] but it is often sufficient to estimate the source density by using, for example, a quasi-static approximation that is appropriate in the short crack (or long wavelength) limit. 31 Indeed, in that limit, the radiated or scattered field from a crack can be approximated by a point source consisting of a particular combination of force doublets (or dipoles), which represents the field due to an infinitesimal crack element. [20][21][22][23] The present work will only consider in detail the field for a buried force or crack element in a half-plane or half-space, but it will be clear that the approach is also advantageous for any configuration for which there is a convenient analytical solution for the field due to an incident plane wave.…”

mentioning

confidence: 99%

Using reciprocity to derive the far field displacements due to buried sources and scatterers

Rose

Chiu

Nadarajah

et al. 2017

The Journal of the Acoustical Society of America

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It is shown that elastodynamic reciprocity provides a simpler approach for deriving the far-field displacements due to buried (sub-surface) sources in a half-space, compared with integral transform techniques. The auxiliary fields employed in this approach are the fields associated with the reflection of plane waves of the three possible polarisations, and the required far field can be expressed in terms of these well-known auxiliary fields. The crucial step in this approach is to evaluate a surface integral involving cross-work terms between an outgoing spherical wavefront and the auxiliary fields consisting of incident and reflected plane waves. This integral can be evaluated by the stationary phase approximation for the two-dimensional case, or by a generalisation of this approximation for the three-dimensional case. Although this evaluation involves several distinct contributions, the final result is shown to be very simple, and it can be interpreted as a generalisation of a known result for the one-dimensional case, whereby the net contribution arises only from counter-propagating waves of the same mode. The results derived for a buried force are extended to the case of buried cracks by exploiting the body force equivalents for displacement discontinuities across a surface.

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“…Resch et al [3][4][5] have shown that the maximum crack depth, a, of a surface crack can be evaluated by acoustically measuring the SAW reflection coefficient from a crack and optically measuring the length, 2c, of the intersection of the crack with the free surface.…”

Section: Verification And· Practical Limitations Of the Scattering Thmentioning

confidence: 99%

Saw NDE Techniques for Monitoring the Growth Behavior of Small Surface Fatigue Cracks

Resch

London

Ramusat

et al. 1984

Review of Progress in Quantitative Nondestructive Evaluation

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Long Wavelength Rayleigh Wave Scattering from Microscopic Surface Fatigue Cracks

Cited by 10 publications

References 3 publications

Experimental and Computational Studies on the Scattering of an Edge-Guided Wave by a Hidden Crack on a Racecourse Shaped Hole

Experimental and Computational Studies on the Scattering of an Edge-Guided Wave by a Hidden Crack on a Racecourse Shaped Hole

Using reciprocity to derive the far field displacements due to buried sources and scatterers

Saw NDE Techniques for Monitoring the Growth Behavior of Small Surface Fatigue Cracks

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