Issue 28

B. Ye et alii, Frattura ed Integrità Strutturale, 28 (2014) 32-41; DOI: 10.3221/IGF-ESIS.28.04 34 The energy functional of magnetic vector potential (stepA) For simplifying analysis, we assume the existing current of coil uniformly distributes at its window, not considering the harmonic component. The conductivity andpermeability can vary from layer to layer, but are constant in eachone. Aftermagnetic vector potential A ( B =  × A ) is introduced, theMaxwell equation is  2 A + k 2 A =− μJ s (1) where A represents magnetic vector potential, k 2 =− jωμ ( σ + jωε ), j is an imaginary unit, ω is the angular frequency of excitation current (rad), ω =2π f , f is the frequency of excitation current (Hz), J s is the density of excitation current (Amp/m 2 ), σ is the electrical conductivity (S/m), μ is the magnetic permeability of the media involved (H/m), and ε is dielectric constant (F/m). To simplify the eddy current scanning detective problem into a two-dimension axisymmetric problem, and using cylindrical coordinatesO ( ρ , θ , z ) shown inFig. 2, theLaplace expression  2 A of the vector function A is Figure 2 : The cylindrical coordinates and triangle unit subdivision. 2 2 2 2 2 2 2 2 2 2 2 A A A A A A 1 A A A A 1 z z                                                (2) omitting the suffix θ of A θ , Eq. (2) canbe predigested to 2 2 2 2 2 A 1 A A A A s J j z                  (3) According toEq. (3) the energy functional is 2 2 2 1 A A A A A A 2 2 ( ) d d s R j F J z z                                 (4) where, R is the solution region. The solution region (step B) The solution region is shown in Fig. 3. This is a two-layered aluminium alloy structure (region 2 and 4). There is a rectangle defect 3 in the two-layered aluminium alloy structures. Its boundary is EFGH supposing the air in it. The probe is placed on the surface of the aluminium alloy structures in the EC detection and scans from left to right. In order to compute accurately inFEM, region 5 is assumed air andmust be taken into account.