Scattering of Plane Waves by a Partially Closed Crack

Punjani, M.; Bond, Leonard J.

doi:10.1007/978-1-4615-7763-8_6

Cited by 9 publications

(5 citation statements)

References 4 publications

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“…In contrast, the wd-SDD method is not limited to high frequencies and takes into account the interactions between different locations on the fracture. Although numerical methods such as the boundary element method 16 and the finite difference method 17,18 can also be used to examine the scattering of elastic waves at full range of frequencies, applications of these methods to threedimensional problems results in high computational costs, particularly large computer memory. Further, the analytical nature of the introduced method can provide clearer insights into the mechanism of wave scattering by a heterogeneous fracture.…”

Section: Introductionmentioning

confidence: 99%

Plane wave solution for elastic wave scattering by a heterogeneous fracture

Nakagawa

Nihei

Myer

2004

The Journal of the Acoustical Society of America

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A plane-wave method for computing the three-dimensional scattering of propagating elastic waves by a planar fracture with heterogeneous fracture compliance distribution is presented. This method is based upon the spatial Fourier transform of the seismic displacement-discontinuity ͑SDD͒ boundary conditions ͑also called linear slip interface conditions͒, and therefore, called the wave-number-domain SDD method ͑wd-SDD method͒. The resulting boundary conditions explicitly show the coupling between plane waves with an incident wave number component ͑specular component͒ and scattered waves which do not follow Snell's law ͑nonspecular components͒ if the fracture is viewed as a planar boundary. For a spatially periodic fracture compliance distribution, these boundary conditions can be cast into a linear system of equations that can be solved for the amplitudes of individual wave modes and wave numbers. We demonstrate the developed technique for a simulated fracture with a stochastic ͑correlated͒ surface compliance distribution. Low-and high-frequency solutions of the method are also compared to the predictions by low-order Born series in the weak and strong scattering limit.

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Section: Introductionmentioning

confidence: 99%

Plane wave solution for elastic wave scattering by a heterogeneous fracture

Nakagawa

Nihei

Myer

2004

The Journal of the Acoustical Society of America

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“…Crack surfaces can be in contact and have significant roughness. Papers examining inspection models with real crack interface conditions include Thompson and Fiedler (1984), Punjani and Bond (1986), Thompson et al (1986), Rehbein et al (1986Rehbein et al ( , 1988Rehbein et al ( , 1990, Buck et al (1988), Hirose and Kitahara (1991), Ogilvy and Culverwell (1991), Bostrom (1993), Bostrom et al, (1994), Eriksson et al, (1995), Solodov (1998).…”

Section: Discussionmentioning

confidence: 99%

Overview of Mathematical Modeling in Nondestructive Evaluation (NDE)

Aldrin¹

2002

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“…Further work needs to be done to incorporate effects neglected in these calculations, including the effect of asperities in the crack [6,7], and to extend the calculations to three dimensions. The potential use of these calculations is illustrated in Figure 6 where signals from a real acoustic emission event from a growing crack in an aluminum specimen are displayed.…”

Section: Discussionmentioning

confidence: 99%

Acoustic Emissions at an Open Crack

Johnson

1988

Review of Progress in Quantitative Nondestructive Evaluation

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Both finite difference and finite element techniques have been shown to be capable of modeling the propagation of acoustic emissions (AE) [1,2]. However, those calculations could also be done using the simpler Green's function methods [3]. In this work the finite element method is used to model a problem that includes complexities that cannot be handled using the Green's function methods.In particular, the effect of the presence of a macrocrack on the received signal is investigated. We assume that the macrocrack interacts only as a geometric structure from which sound may reflect and mode convert, thereby complicating the signal at the receiving transducer. Numerical calculations of the AE field due to an open crack are compared to the Green's function results in a solid with no flaw. FINITE ELEMENT CALCULATIONSThe computer program DYNA2D[4] was used to calculate the acoustic field due to a dipole force near the tip of a simulated crack. The calculation assumed a two-dimensional, plane-strain geometry. The surface-breaking crack was about halfway through the thickness of a 6.35-mm (0.25-in.) steel plate. This geometry is similar to that used in fracture tests of surface-crack specimens monitored with acoustic emission signals [5]. A dipole stress, perpendicular to the plane of the crack, was applied to the region near the crack tip, simulating the dynamic stress that would be present when the crack grows.The grid is chosen to be made of quadrilateral elements about 0.2 mm on a side. The elements are square except in the region around the crack. The part is 32 elements thick; there are 73 elements to the right of the crack and 136 elements to the left. These last two distances were chosen so that a longitudinal wave from the crack would not reflect off the boundaries and return to a receiver 12.7 mm to the left of the crack.The forcing function is chosen to have a Gaussian shape in time with a rise time of about 0.16 ~s and a bandwidth of 3 MHz (20 dB). The minimum wavelength is then the shear wavelength, 1.07 mm, and the element size is less than one-fifth of this wavelength. The stress is also spread over three elements at the crack tip to prevent numerical noise.1503

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Scattering of Plane Waves by a Partially Closed Crack

Cited by 9 publications

References 4 publications

Plane wave solution for elastic wave scattering by a heterogeneous fracture

Plane wave solution for elastic wave scattering by a heterogeneous fracture

Overview of Mathematical Modeling in Nondestructive Evaluation (NDE)

Acoustic Emissions at an Open Crack

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