Finite element and boundary element analysis of electromagnetic NDE phenomena

Abstract

The endeavor to produce quality products coupled with a drive to minimize fail­ ure in major industries such as aerospace, power and transportation is the driving force behind studies of electromagnetic nondestructive evaluation (NDE) methods. Popular domain and integral methods used for the purpose of modeling electromag­ netic NDE phenomena include the finite element and boundary element methods. However no single numerical modeling technique has emerged as the optimal choice for all electromagnetic NDE processes. In a computer aided design environment, where the choice of an optimum modeling technique is critical, an evaluation of the various aspects of different numerical approaches is extremely helpful. In this dissertation, a comparison is made of the relative advantages and disad­ vantages of the finite element (FE) and boundary element (BE) methods as applied to the DC and AC Potential drop (DCPD and ACPD) methods for characterizing fatigue cracks. The comparison covers aspects of robustness, computer resource re­ quirements and ease of numerically implementing the methods. Two dimensional FE and BE models are used to model an infinitely thin fatigue crack using the ACPD method, and a two and three dimensional FE and BE model is used to study the com­ pact tension and single edge notch specimen using the DCPD method. Calibration curves and field plots in the specimen are compared to experimental and analytical data. The FE and BE methods are complementary numerical techniques and are combined to exploit their individual merits in the latter part of this dissertation. A three dimensional hybrid formulation to model eddy current NDE is then developed which discretizes the interior with finite elements and the exterior with boundary, elements. The three dimensional model is applied to an absolute eddy current coil over a finite block. A feasibility study to confirm the validity of the formulation is undertaken by comparing the numerical results for probe lift-off and coil impedance measurements with published data. This comparative study outlined above indicates that when the solution is re­ quired at discrete points, as in the potential drop methods, or the model needs to handle infinite boundaries, as in eddy current NDE, the boundary element model is more suitable. Since it is based on the Green's function, the BE method is lim­ ited to linear problems. Finite element analysis gives full field solutions, making it ideal for studying energy/defect interactions. The hybrid FE/BE formulation han­ dles non-linearity and infinite boundaries naturally, thus utilizing the best of both worlds.