An Eddy Current Nondestructive Method for Crack Detection in Multilayer Riveted Structures

In the aeronautical field, economic constraints tend to increase the lifespan of appliances beyond their first cycle. In this case, for a second or third life cycle, it becomes necessary, for safety reasons, to carry out more thorough wear checks. To ensure maintenance, many non-destructive tests punctuate the aircraft's operating life in order to detect a defect before a critical threshold is reached (Figure 1).

The multilayers structures are widely used in the industries especially in the construction of the aircrafts and the space-crafts; these layers are assembled by riveted operation. The riveting is an assembly of pieces using rivets, the layers have been previously drilled each of a hole allowing the rivet rod to cross the one and the other. It is a definitive assembly, that is to say not removable without destruction of the fastener, under working of the riveted structures, are exposed various exteriors factors such as and low temperature, high pressure and noise vibration, these last product a damages and corrosions, generally these problems located around rivets [1, 2].

Rigorous damage tolerance calculations should take into account not only the size of a defect but also the location of that defect within the examined part, when predicting the lifetime of a component. This is especially true in aircraft structures, which are normally composed of multiple layers, with variable thickness, different materials, etc. For example, depending on the type, distribution and level of stress, a small surface crack might be more critical than a large hidden one [1, 2].

One of the major issues is to control the rivet lines to detect possible cracking phenomena that can be created at the foot or under the rivet propagate given the great mechanical constraints on them. Indeed, the defects present in the riveted structures are born at the bottom of the rivet and grow along the axis of the riveting line. The detection of these defects must be done early before it spreads rivet can cause the lifting of the fuselage during a flight, Figure 2.

One of the most reliable NDT technique is EC method, this method applied in conductive non-magnetic structures, EC method is based on an alternating electromagnetic reaction phenomena between the source who is generate the electromagnetic field and the tested piece who is in approximation with the source field, the electrical reaction of the plate represent in the creation of the eddy currents, the penetration the induced currents depends on skin thickness effect [3-5].

The electromagnetic reaction between the coil and the tested piece give us a state about the geometric properties and the physical properties, in our case the physical properties such as the electrical conductivity is known, otherwise, the induced currents path are closed contours which depends on the geometric state of the tested piece, which is mean that any deformation in the tested piece will effect on the paths of the induced currents although effect on the impedance variation of the eddy current sensor [5-7].

Moreover, the applied eddy current testing in multilayer structures to evaluate the cracks who they will be in the inner layer is low sensitive than the upper layer due to of the skin thickness effect, although eddy current sensor need to be more efficiency with a ferrite core, thus the electromagnetic field produce by the sensor will be more focus in small area, several studies are used magnetic field as a measurement parameter to detect the cracks such as EC-GMR (Giant Magneto-Resistance) [8-10] and EC-Hall effect sensor [11, 12] which they need a special excitation coils (complicated system) in addition rotating electromagnetic field EC-GMR which consist tow printed excitation coils to make a the electromagnetic field to be rotated [13], separated function measurement mode is used in previous works [14], this mode has two coils, one for excitation and the other for pick-up, pulsed eddy current technique used for crack detection in layered structures [15-17], these methods are used for the detection of crack in deep layers with the existing of the rivets, the rivets are electrically conductive which high possibly influence in the quality of detection, to take into account the rivets effect the sensors should be calibrate.

In this paper we are interested in the multilayer structures of riveted conductive plates controlled by an eddy current sensor with a ferrite core, in absolute mode. To highlight the effect of the defects, we propose a study with flaws that are variable from the point of view length with respect to the length of the rivet head (lower and upper) and from the point of view positioning in layers, in addition, the eddy current behavior when two rivets are close from each other. The electromagnetic problem is formulated as magnetic potential vector, finite element method is used as a method of computation for the resolution of the partial derivative equation of the magnetic potential vector to evaluate the imaginary and real part of impedance [11].

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Figure 1. Aircraft riveted multilayer structures

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Figure 2. Damaged rivet hole

Induced current are created in tested simple based on the electromagnetic field reaction between the coil and the simple, the electromagnetic phenomena is formulated using A-V formulation approach, A is the magnetic potential and V is the scalar electrical potential, the model regions are divided into five parts, the first is the solenoid coil (inductor), the air region, the three layers of the plate regions which they have the same electrical properties.

$rot\left( \frac{1}{\mu }rot(A) \right)-\left( \frac{1}{\mu }div(grad(A) \right)+j\omega \sigma A+\sigma grad(A)={{J}_{S}}$  (1)

where, A(T/m) is the magnetic potential, σ(S/m) is the electrical conductivity of the multilayer structure, ω is the frequency source (rad/s), μ magnetic permeability of air, and J (A/m²) is the source current.

After resolved the Eq. (1) using FEM, the eddy currents are computed using the following equation:

${{J}_{e}}=-\frac{\partial A}{\partial t}$  (2)   

The harmonic magnetodynamic formulation in integral form is obtained by a spatial discretization using the finite element method, which allows in addition to interpolate the unknowns on the elements of the mesh. By applying the Galerkine method and Green's theorem with homogeneous boundary conditions in Eq. (1), we obtain the integral formulation AV-A, defined on the nodes of the mesh of the domain Ω.

$\begin{align}  & \int\limits_{\Omega }{\frac{1}{\mu }}rot(A)rot({{N}_{i}})+\int\limits_{\Omega }{\frac{1}{\mu }}div(A)div({{N}_{i}})+ \\ & \int\limits_{\Omega }{j\omega \sigma {{N}_{i}}}(A+gradV)d\Omega ={{N}_{i}}{{J}_{S}}d\Omega  \\\end{align}$  (3)

with:

$\int\limits_{\Omega }{j\omega \sigma {{\alpha }_{i}}}grad(A)d\Omega +\int\limits_{\Omega }{j\omega \sigma }grad({{\alpha }_{i}})grad(V)d\Omega =0$  (4)

where, $\alpha_{\mathrm{i}}$ and $\mathrm{N}_{\mathrm{i}}$ respectively are the Scalar projection function and the vector projection function.

The impedance variation of coil is given by:

$\Delta Z=-\frac{j\omega }{{{I}_{0}}}\oint{A\Lambda dl}$  (5)

The real part and the imaginary part of impedance sensor are computed using magnetic potential vector approach such:

$real(Z)=-2\pi \omega {{N}_{turn}}imag(A)$   (6)

$real(Z)=-2\pi \omega {{N}_{turn}}imag(A)$  (7)

We define $\Delta Z$ as the difference between the sensor impedance $Z_{cal}$ when the crack is found in the multilayer plate and the sensor impedance $Z_{c l b}$ using for calibration which taken when the multilayer plate without crack:

$\Delta Z={{Z}_{cal}}-{{Z}_{clb}}$   (8)

To make several calibrations $Z_{\text {clb}}$ we calculate $Z_{\text {clb} 1}$ as sensor impedance without taking into consideration the rivet effect and $Z_{\text {clb2 }}$ as sensor impedance but taking into consideration the rivet effect on the impedance value.