A Computational Technique for Automated Recognition of Subsurface Cracks in Aeronautical Riveted Structures

The present paper concerns developing an automated system for non-destructive evaluation of riveted aluminium joints. The system features an innovative eddy-current probe providing high sensitivity at low inspection frequencies and a computational tool aimed both at computer-aided electromagnetic design of the probe and quantitative reconstruction of detected defects (inverse problem). The approach adopted for defect reconstruction exploits numerical solution of the forward problem. It is based on the edge element integral formulation of the eddy current problem and offers fast and accurate numerical modelling. The inspection cases in focus represent multi-layered aluminium structures with tiny cracks propagating from fastener holes in the subsurface layers. The experimental data exhibit favourable agreement with numerical simulations. Introduction: Fast and reliable inspection of lap-joints for minute cracks deeply buried beneath rivet heads is an important issue of the aircraft maintenance process. The objective of this work is the development of an automated system for quantitative non-destructive evaluation of riveted aluminium-to-aluminium joints by means of the eddy currents. Because of the skin effect, inspection for subsurface defects in aluminium ought to be conducted at low excitation frequencies (in the range of 1 kHz and below). Therefore the proposed eddy current probe contains as the receiving element a fluxgate sensor whose sensitivity is independent on the frequency [1]. A numerical tool was used to perform electromagnetic design of the excitation coil, as well as for defect quantitative reconstruction via the forward analysis for a thin crack of given orientation and approximate location. The inversion technique is based on the minimization of an error functional related to the root mean square difference between measurements and simulated perturbation fields of eddy currents. The paper is organized as follows. The present section (Introduction) contains description of the computational tool, the inspection instrumentation and samples. The next section (Results) presents comparison of experimental results with simulations. The evaluation of the results follows in the consequent section (Discussion) and finally Conclusions are drawn. a. Simulation technique: The numerical technique used for simulation and reconstruction of detected cracks is based on an efficient integral formulation in terms of a two-component vector potential [2] which takes advantage of the edge element representation of the field unknowns. Using superposition, the forward problem is reformulated as the determination of the modified eddy current pattern due to the presence of the defect. In particular, since density of the total current flowing through the crack region has to be zero, the variation of the eddy current density is imposed to be just the opposite of the unperturbed current in the crack region, providing the known source term of an integral equation to be solved only around crack. This fast algorithm for solving the forward problem is the key step of the inversion procedure. For generating the solution corresponding to a candidate flaw only a very small part of the whole matrix describing the model must be inverted. The actual numerical formulation [3, 4] is briefly recalled below. Its essence consists in the integral formulation in terms of a two-component electric vector potential; this approach has a number of advantages as follows. Using an integral formulation allows us to discretise only the conducting domains where the eddy currents are induced (that is neither the air nor the excitation coils need be discretised), automatically enforcing regularity conditions at infinity. The introduction of the electric vector potential T such that the current density J is J=∇×Τ, ensures that J is solenoidal [5]. Finally, the choice of the two-component gauge minimizes the number of discrete unknowns required. The equations to be solved are the standard eddy current equations in the frequency domain. We express the electric field as: E = j ω A ∇φ (1) φ is the scalar electric potential and A is the divergence-free magnetic vector potential given by: