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Evaluation of circumferential cracks in metal tubes based on a magnetic field response model of eddy current testing

According to the characteristics of circumferential cracks on the inner surface of metal tubes, a magnetic field response method has been proposed and a mathematical analytical model for detecting the circumferential crack has also been established. The theoretical model, based on the
 magnetic field response, could be expressed as a series sum of trigonometric and Bessel functions. The relationship between the distribution of the magnetic field in the inner region of the metal tube and the geometrical size of the cracks is also analysed. The results show that the analytical
 model can effectively explain and analyse the variation of the surrounding magnetic field caused by the crack. The characteristic parameters of the crack, Br and Bz , which are extracted from the magnetic field, have certain quantitative recognition abilities. In addition,
 an increase in the thickness of the metal tube causes a larger range of magnetic field variations and is considered to be disadvantageous for detecting a change in the magnetic induction intensity that is a result of the crack. A theoretical model and research results contribute to the development
 of eddy current testing and improve the accuracy of the non-destructive testing and evaluation of metal tubes.Publisher Note: Following the original publication of this paper, a change was made to the author affiliations on page 91. Full details can be found in the correction notice given after page 97 of the PDF for this article.