##### STP722

### A Boundary Integral Equation Method for Calculating the Eddy-Current Distribution in a Long Cylindrical Bar with a Crack

**Abstract**

We report calculations of the impedance of a long solenoid which surrounds a cylinder of conducting material containing a crack. The calculation is approached by expressing the eddy-current problem as an integral equation for the normal derivative of the magnetic field on the boundary of the conductor. This method is generally applicable to any cylindrical problem, regardless of the cross-sectional shape of the conductor. The boundary integral equation is solved in the case of the crack problem by discretizing and converting to a system of linear algebraic equations for the normal derivative of the field. The complex impedance is thereby obtained for a wide range of values of the ratio of crack depth to radius to skin depth. The results are displayed in graphical form, which gives the fractional changes of the real and imaginary parts of the impedance caused by the presence of the crack.

**Keywords:**

crack detection, eddy currents, nondestructive evaluation

**Author Information:**

Kahn, AH

*Physicist, National Bureau of Standards, Washington, D.C.,*

Spal, R

*Physicist, National Bureau of Standards, Washington, D.C.,*

**Committee/Subcommittee:** E07.07

**DOI:** 10.1520/STP27594S

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