Calculation of the Field of a Flaw in Three-Dimensional Half-Space

Dyakin, V. V.; Umergalina, O. V.

doi:10.1023/b:runt.0000009086.64329.92

Cited by 14 publications

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The latter, in turn, can be proved easily by applying Parseval's equality (5) to functions f ( r ') and ε /(( r -r ') 2 + ε 2 ) 3/2 , according to which an integral of the product of two functions f ( r ) and g ( r ) is equal to the integral of their Fourier transforms ( k ) and ( k ). Substituting (3) into the left-hand side of (2), we obtain (6) where λ = ( µ -1)/(µ + 1). If the notations τ = r' -r, t = r'' -r, a = |z -d|, and b = d -z'' are introduced, the internal integral in the second term in the braces can be written as where R* = and R 0 = .…”

Section: Magnetic and Eddy Current Methodsmentioning

confidence: 99%

“…Then, the case of a spherical defect was considered where the external field was assumed to be uniform and directed normally to the surface of the semispace. Publication [6] contains typographical errors. We apologize to the readers for them and briefly iterate the main stages of the study and the most important formulas since, moreover, they are of importance for this study as well.…”

mentioning

confidence: 97%

“…In continuation of [6], we solve in this study the problem of a semispace containing a defect with finite dimensions. A technique was used in [6] that allows reduction of the problem of finding the field of a defect with finite dimensions located in a semispace to calculation of the value of the normal field component on the defect's surface alone. Then, the case of a spherical defect was considered where the external field was assumed to be uniform and directed normally to the surface of the semispace.…”

mentioning

confidence: 99%

“…A general scheme for solving the inverse problem (determination of a defect's radius and location depth) is proposed in [6]. No significant differences arise if the external field is a longitudinal.…”

mentioning

confidence: 99%

See 3 more Smart Citations

The Field of a Finite Defect in a 3D Semispace

Dyakin

Umergalina

Raevskii

2005

Russ J Nondestruct Test

Self Cite

View full text Add to dashboard Cite

The field of an arbitrary finite defect in a 3D semispace is calculated. This problem is solved by reduction to a 2D case that yields an integral equation on the surface of the defect alone. Calculation formulas for a spherical defect are presented. Results of calculations using these formulas for the case of a uniform external field normal or tangential to the surface of a magnetic semispace are presented in a graphical form.Solving the magnetostatic problem for different models of bodies containing defects remains a challenging task for practical use of magnetic testing methods. The internal defect is approximated mainly by an infinite elliptic cylinder placed either in an infinite magnetic space, in a semispace, or in a plate. (Such an approximation is used owing to its simplicity.). The symmetry of the model enables significant simplification of the problem, which can be reduced to a 2D case. Corresponding results can be found, e.g., in [5].A solution of the magnetostatic problem for a defect with finite dimensions has only been found for an infinite magnetic space containing a cavity (insert) with an ellipsoidal surface [5]. In continuation of [6], we solve in this study the problem of a semispace containing a defect with finite dimensions. A technique was used in [6] that allows reduction of the problem of finding the field of a defect with finite dimensions located in a semispace to calculation of the value of the normal field component on the defect's surface alone. Then, the case of a spherical defect was considered where the external field was assumed to be uniform and directed normally to the surface of the semispace. Publication [6] contains typographical errors. We apologize to the readers for them and briefly iterate the main stages of the study and the most important formulas since, moreover, they are of importance for this study as well.1. Let us use an integrodifferential approach to the magnetostatic problem. The equation for the strength vector of the magnetic field has the form (1) where Ω is the area occupied by a magnetic matter with magnetic permeability µ , H 0 ( r ) is the strength of the field created by external sources, and R = | r -r ' | .Using Eq. (1), let us consider the following problem: a defect characterized by a finite diameter and magnetic permeability µ d = const and confined within smooth surface S is located in the semispace z ≤ d ( d > 0) with µ = const. The frame origin is placed at the center of the defect. In this case, area Ω in (1) is a semispace containing the defect. Let us denote the area occupied by the defect as Ω d and Ω 1 = Ω / Ω d . The described situation where the defect is approximated by a sphere is illustrated by Fig. 1. It is worth stressing that, for the calculations made in the first part of this study to hold for a defect of any form, it only needs to be finite. The result of the first stage is formulated as Eq. (7) applicable to solution of the problem for a defect of any form. Moreover, Eq. (7) is preferable for practical usage since it requires the...

show abstract

Section: Magnetic and Eddy Current Methodsmentioning

confidence: 99%

mentioning

confidence: 97%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

The Field of a Finite Defect in a 3D Semispace

Dyakin

Umergalina

Raevskii

2005

Russ J Nondestruct Test

Self Cite

View full text Add to dashboard Cite

show abstract

“…So, according to the voltage and phase of the transducer, some information about surface crack can be acquired. [1,2,3,11,12,13] Eddy current sensor is based on electromagnetic field theory, so the qualitative relationship between output of eddy current sensor and surface crack can be described by Maxwell electromagnetic field theory. Many research papers have reported it.…”

Section: Analysis Of the Relationship Between Crack And Signal Inmentioning

confidence: 99%

The Reconstruction of Crack in Surface Based on Virtual Instrument

Ding

Qian

2009

2009 International Conference on Information Engineering and Computer Science

View full text Add to dashboard Cite

A way is presented for testing the surface crack with eddy current and the reconstruction of crack based on virtual instrument (VI . The reconstruction is a nondestructive technique enabled efficient crack testing based on much richer and comprehensive. Results of a relationship between surface crack and eddy current signals have been acquired by Maxwell's equations, electromagnetic field theory and experiments. Then the surface crack image is reconstructed by VI.

show abstract

One approach to solving the basic equation of magnetostatics in the case of nonhomogeneous magnets

2016

Self Cite

View full text Add to dashboard Cite

We propose a general approach for solving the basic magnetostatic equation in the case of nonhomogeneous magnetic solids when their magnetic permeability depends on the coordinates. Seeking the strength of the resulting field reduces to finding two scalar functions satisfying a system of one integral and one differential equation with certain boundary conditions. Using this approach, we obtain an analytic solution of the magnetostatic equation for a ball with a model permeability in an arbitrary external field.

show abstract

Calculation of the Field of a Flaw in Three-Dimensional Half-Space

Cited by 14 publications

References 0 publications

The Field of a Finite Defect in a 3D Semispace

The Field of a Finite Defect in a 3D Semispace

The Reconstruction of Crack in Surface Based on Virtual Instrument

One approach to solving the basic equation of magnetostatics in the case of nonhomogeneous magnets

Contact Info

Product

Resources

About