Characterization of surface-breaking cracks in metal sheets by using AC electric fields

McIver, Maureen

doi:10.1098/rspa.1989.0008

“…This uses the fact that dilation function (8), of the solution (v i−1 , q i−1 ) should be identical to the dilation function of the next solution (v i , q i ). Hence rather than using v i = 0 as prior information, we use v i = v i−1 instead for i ≥ 2.…”

Section: Multiple Transmittersmentioning

confidence: 99%

“…The operator properties considered there are relevant to the analysis of eqns (1) and (2) here. Some approaches to Electrical Impedance Tomography (EIT) [7] and crack detection [8,9] also tackle inverse boundary problems for the Laplace equation. In 2D, conditional logarithmic stability estimates for the inverse boundary problem under a regularity assumption on the unknown boundary have been given [10,11], and this theoretical result has been extended to 3D by Cheng et al [12].…”

Section: The Inverse Problemmentioning

confidence: 99%

An iterative method for electrostatic object reconstruction in a half space

Berkel¹,

Lionheart²

2006

Meas. Sci. Technol.

View full text Add to dashboard Cite

Abstract. Sensing electrodes arranged in or around a display can provide input function for interactive displays. Commercially this is interesting because the sensing electrodes and electronics can be made in the same manufacturing process as that of the display itself thus reducing cost. In engineering terms the electrodes measure capacitance changes resulting from the presence and movement of objects such as hands and fingers in front of the display. At the quasi static frequencies used (100kHz) the human body is conductive and the hands or fingers provide a screen between the capacitive electrodes. There is no need to touch the actual display and the overall system constitutes a touchless gesture input system.Determining the shape of the hand or fingers is a boundary condition reconstruction problem of finding the boundary of an earthed conductive object D from electrostatic measurements. This is the ill-posed problem of recovering the zero-surface of a solution to Laplace's equation from Cauchy data on part of the boundary of a domain. The problem has similarities with object reconstruction in EIT or inverse scattering but is complicated because only a partial Dirichelet-Neumannn map is available as experimental data.We suggest an algorithm where at each iteration we have an approximation ∂D k to ∂D on which we calculate approximate Cauchy data by solving a Tikhonov regularized linear system. This data is used to modify ∂D k by extrapolation towards the zero-surface giving the next approximation ∂D k+1 .We implemented the algorithm in two and three space dimensions using the Boundary Element Method for discretization. Numerical results using simulated data with added noise show that simply connected but not necessarily convex objects can be reconstructed with reasonable positional accuracy and approximate shape, but as might be expected the shape is more accurately determined near the plane of measurements.

show abstract

“…Once g(\jf) = Y(O,"'If) has been calculated, the shape of the crack in the physical plane is determined by evaluating X(O,'If) which is given by Mclver [3] as …”

Section: (7)mentioning

confidence: 99%

“…This formulation requires the stream function 'P along the top of the crack to be known. Using the Plemelj formulae Mciver [3] showed that this is given by…”

mentioning

confidence: 99%

Inversion of Voltage Data to Predict Crack Shape

McIver

¹

1990

Review of Progress in Quantitative Nondestructive Evaluation

View full text Add to dashboard Cite

Surface-breaking cracks in metal sheets may be detected by injecting alternating current into the sheet and observing the resulting nonuniformity in the surface electromagnetic field. The current is forced to flow in a thin skin near the surface of the metal with a skin depth, I)= ..f2tlyl, where (1) and Jl is the permability of the metal, o is the conductivity and ro is the angular frequency of the interrogating field. At a frequency of 6 kHz the skin depth of the field in mild steel is about 0.1 mm which is much less than the typical length scale associated with many of the surface-breaking flaws of interest. Using a thin skin approximation, therefore, Michael et al [1] showed that if a uniform current is incident on a crack in a ferrous metal, the electric field may be written as In ferrous metals at relatively low frequencies, Lewis et al [2] showed that it is a reasonable approximation to assume that both the normal and tangential components of the electric field are continuous at the crack edge and so the potential distribution in the plane of the crack is an analytic continuation of the potential distribution on the upper surface of the metal. Thus, the crack face may be 'unfolded' into the same plane as the metal surface resulting in a two dimensional boundary value problem for a single potential in a region with a partially unknown boundary, as illustrated in figure 1. Continuity of magnetic flux across the lower edge of the crack requires the potetnial to be zero along the line ABCDE while the uniform upstream field is modelled by

show abstract

“…(2) (3) In ferrous metals at relatively low frequencies, Lewis et al [2] showed that it is a reasonable approximation to assume that both the normal and tangential components of the electric field are continuous at the crack edge and so the potential distribution in the plane of the crack is an analytic continuation of the potential distribution on the upper surface of the metal. Thus, the crack face may be 'unfolded' into the same plane as the metal surface resulting in a two dimensional boundary value problem for a single potential in a region with a partially unknown boundary, as illustrated in figure 1.…”

mentioning

confidence: 99%

Inversion of voltage data to predict crack shape

1995

NDT & E International

0

View full text Add to dashboard Cite

Surface-breaking cracks in metal sheets may be detected by injecting alternating current into the sheet and observing the resulting nonuniformity in the surface electromagnetic field. The current is forced to flow in a thin skin near the surface of the metal with a skin depth, I)= ..f2tlyl, where (1) and Jl is the permability of the metal, o is the conductivity and ro is the angular frequency of the interrogating field. At a frequency of 6 kHz the skin depth of the field in mild steel is about 0.1 mm which is much less than the typical length scale associated with many of the surface-breaking flaws of interest. Using a thin skin approximation, therefore, Michael et al [1] showed that if a uniform current is incident on a crack in a ferrous metal, the electric field may be written as In ferrous metals at relatively low frequencies, Lewis et al [2] showed that it is a reasonable approximation to assume that both the normal and tangential components of the electric field are continuous at the crack edge and so the potential distribution in the plane of the crack is an analytic continuation of the potential distribution on the upper surface of the metal. Thus, the crack face may be 'unfolded' into the same plane as the metal surface resulting in a two dimensional boundary value problem for a single potential in a region with a partially unknown boundary, as illustrated in figure 1. Continuity of magnetic flux across the lower edge of the crack requires the potetnial to be zero along the line ABCDE while the uniform upstream field is modelled by

show abstract

Characterization of surface-breaking cracks in metal sheets by using AC electric fields

Cited by 24 publications

References 6 publications

An iterative method for electrostatic object reconstruction in a half space

An iterative method for electrostatic object reconstruction in a half space

Inversion of Voltage Data to Predict Crack Shape

Inversion of voltage data to predict crack shape

Contact Info

Product

Resources

About