Green's function formulation of Laplace's equation for electromagnetic crack detection
The authors' aim is to determine the electric potential due to a steady current in a plate having a straight crack and bounded by a regular curve. The Green's function corresponding to the infinite plate is obtained by solving a Hilbert problem and is employed to derive the boundary integral equation the solution of which yields the required potential. Intensity factor at the crack tip for the electric field and the component of magnetic field vector, induced by the current, perpendicular to the plate at a spatial point, are also evaluated as boundary integrals. Thus numerical calculations can be carried out by using the boundary element method. Hence, by measuring remotely the normal component of the magnetic field with a sufficiently sensitive device such as a superconducting quantum interference device, it becomes possible in principle to detect cracks in two-dimensional structures with a nondestructive test.
scientific article; zbMATH DE number 1358541