Quantitative Estimation of Rectangular Surface Crack Based on the 2-D Modeling of Surface Magnetic Field With Long Straight Rectangular Wire

A 2-D analytical model for surface magnetic field generated by a long straight rectangular wire is proposed. Based on Maxwell’s equations, the magnetic vector potential equations are obtained. Then, the equations are solved by applying the method of separation of variables and the boundary conditions at the interface. The truncated region eigenfunction expansion method is also used to replace the infinite solution region with finite region, so the analytical solution of surface magnetic field with rectangular crack is finally deduced. According to the magnetic field distribution obtained by the model calculation, the influences of the crack depth and width on the horizontal and vertical magnetic induction intensity and phase are studied. The quantitative characteristics of depth and width are extracted. The analytical model is used to make up the theory of electromagnetic nondestructive testing, and provides a reference for the detection and quantification of crack defects in practice.