Characterization of Surface Wave Scattering by Surface Breaking Cracks

Various analytical methods based on the real reciprocity relation are applied to the problem of Rayleigh wave scattering by a surface crack. In one formulation, the reflection coefficient observed at the transducer terminals is expressed in terms of an integral over the crack surface of the product of the perturbed and unperturbed fields. This integral is then converted to a volume integral and the Born Approximation is applied. In the other formulation a Kirchoff type approach is used such that the effect of the crack is expressed as an equivalent body force distribution. That force distribution is then approximated and normal mode techniques are used to find the scattered field amplitude. The two methods are compared with each other and with the results obtained from geometrical diffraction theory. An experimental procedure is also proposed for the inverse problem

Resonances and Crack Roughness Effects in Surface Breaking Cracks

This study deals with two different aspects of scattering from the cracks. The first one is the measurement of crack resonances by local probes and the second is the effect of the roughness of the crack forces on the scattering data. Unlike the scattering measurement reported elsewhere, these measurements of crack resonances are to be performed by local probes. Two different types of probes are described and their problems are discussed. The effect of crack roughness on the scattering data is investigated via the reciprocity relation. The crack roughness is analyzed using perturbation theory and the equivalent boundary condition concept developed by Brekhovskikh is used to express the fields in the presence of the roughness. The effect of roughness on the scattering data is then discussed in qualitative terms

On the Resonances of Surface Breaking Cracks

The resonance phenomenon observed in Rayleigh wave scattering from surface-breaking cracks has been investigated using Freund\u27s results on reflection of Rayleigh waves from an infinite crack edge. To model the crack as a section of acoustic waveguide, resonances are treated as standing waves in the length and depth directions. The model takes both faces of the crack into consideration, and this makes it possible to explain the observations of all order resonances in the length direction for excitation by a Rayleigh wave beam at normal incidence. Calculations are made for rectangular and half-penny shaped cracks and differences between the two cases are discussed

Eddy Current Signal Calculations for Surface Breaking Cracks

This paper contains a brief status report on analytical modeling of the probe-flaw interactions for surface breaking cracks and some data on comparisons of theory and experiment for EDM notches and true fatigue cracks. The goal of the work reported here and in companion papers by Rummel and Rathke (1984), Auld, et al. (1984), and Martinez and Bahr (1984) is to improve the quantitative character of eddy current testing. In this joint effort, the role of probe-flaw interaction modeling is to provide engineering tools not previously available for: (1) setting design guidelines to optimize sensitivity and spatial resolution, (2) permitting analytic extrapolation of measured flaw response data, (3) defining a test basis for monitoring probe calibration, and (4) establishing a rational inversion procedure based on multifrequency measurements and the shape signature of a scanned flaw signal as a function of position

Characterization of Surface Wave Scattering by Surface Breaking Cracks

Various analytical methods based on the real reciprocity relation are applied to the problem of Rayleigh wave scattering by a surface crack. In one formulation, the reflection coefficient observed at the transducer terminals is expressed in terms of an integral over the crack surface of the product of the perturbed and unperturbed fields. This integral is then converted to a volume integral and the Born Approximation is applied. In the other formulation a "Kirchoff" type approach is used such that the effect of the crack is expressed as an equivalent body force distribution. That force distribution is then approximated and normal mode techniques are used to find the scattered field amplitude. The two methods are compared with each other and with the results obtained from geometrical diffraction theory. An experimental procedure is also proposed for the inverse problem.</p

Characterization of Surface Wave Scattering by Surface Breaking Cracks

Various analytical methods based on the real reciprocity relation are applied to the problem of Rayleigh wave scattering by a surface crack. In one formulation, the reflection coefficient observed at the transducer terminals is expressed in terms of an integral over the crack surface of the product of the perturbed and unperturbed fields. This integral is then converted to a volume integral and the Born Approximation is applied. In the other formulation a "Kirchoff" type approach is used such that the effect of the crack is expressed as an equivalent body force distribution. That force distribution is then approximated and normal mode techniques are used to find the scattered field amplitude. The two methods are compared with each other and with the results obtained from geometrical diffraction theory. An experimental procedure is also proposed for the inverse problem.</p

On the Resonances of Surface Breaking Cracks

The resonance phenomenon observed in Rayleigh wave scattering from surface-breaking cracks has been investigated using Freund's results on reflection of Rayleigh waves from an infinite crack edge. To model the crack as a section of acoustic waveguide, resonances are treated as standing waves in the length and depth directions. The model takes both faces of the crack into consideration, and this makes it possible to explain the observations of all order resonances in the length direction for excitation by a Rayleigh wave beam at normal incidence. Calculations are made for rectangular and half-penny shaped cracks and differences between the two cases are discussed.</p

On the Resonances of Surface Breaking Cracks

The resonance phenomenon observed in Rayleigh wave scattering from surface-breaking cracks has been investigated using Freund's results on reflection of Rayleigh waves from an infinite crack edge. To model the crack as a section of acoustic waveguide, resonances are treated as standing waves in the length and depth directions. The model takes both faces of the crack into consideration, and this makes it possible to explain the observations of all order resonances in the length direction for excitation by a Rayleigh wave beam at normal incidence. Calculations are made for rectangular and half-penny shaped cracks and differences between the two cases are discussed.</p

Resonances and Crack Roughness Effects in Surface Breaking Cracks

This study deals with two different aspects of scattering from the cracks. The first one is the measurement of crack resonances by local probes and the second is the effect of the roughness of the crack forces on the scattering data. Unlike the scattering measurement reported elsewhere, these measurements of crack resonances are to be performed by local probes. Two different types of probes are described and their problems are discussed. The effect of crack roughness on the scattering data is investigated via the reciprocity relation. The crack roughness is analyzed using perturbation theory and the equivalent boundary condition concept developed by Brekhovskikh is used to express the fields in the presence of the roughness. The effect of roughness on the scattering data is then discussed in qualitative terms.</p