Fundamentals of eddy current testing

Heiko Knörzer, Sommersemester 2017

Eddy-current testing (ET) is an electromagnetic testing method used in nondestructive testing (NDT). It is used to examine electrically conductive material for defects and imperfections in near surface areas.

History

see here.

General Principle

In ET a wire coil produces an alternating magnetic field, called the primary field, around itself through an alternating current. When the coil approaches conductive material like iron, aluminium or copper, eddy currents are induced in the material. These eddy currents induce a secondary magnetic field, which is opposed to the primary field, thus weakening it. This effect can be measured and is therefore used in ET and the principle is shown in figure 1. The strength and form of the secondary field is highly dependent on the magnetic properties and shape of the tested part.^[2] Therefore the resulting magnetic field can give insights about geometrical and material imperfections and discontinuities in the tested part. In order to objectively interpret the test results, it is necessary to compare the measurements to a reference analysis where the part and all its imperfections are known.^[2]

Basic Physical Background

The alternating voltage of the eddy current $//<![CDATA[ \begin{array}{l}U(t)\end{array} //]]>$ just like the electrical current $//<![CDATA[ \begin{array}{l}I(t)\end{array} //]]>$ suffice as a time function $//<![CDATA[ \begin{array}{l}t\end{array} //]]>$ in the following formula:

$//<![CDATA[ \begin{array}{l}U(t) = U_m * sin⁡(\omega t)\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}I(t) = I_m * sin⁡(\omega t)\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}U_m\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}I_m\end{array} //]]>$ are the peak values for the voltage or the electrical current. $//<![CDATA[ \begin{array}{l}\omega\end{array} //]]>$ is the angular frequency. A magnetic field with an electrical field strength $//<![CDATA[ \begin{array}{l}H\end{array} //]]>$ is generated from the alternating current. This field strength changes according to the same correlation:

$//<![CDATA[ \begin{array}{l}H(t) = H_m * sin(\omega t)\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}H = \frac{n I}{l} [\frac{A}{m}]\end{array} //]]>$

The electrical field strength is the quotient from the product of the current, the number of coil windings and the length of the middle field lines. The other two important factors in relation to the phenomenon of electromagnetism are magnetic flux $//<![CDATA[ \begin{array}{l}\Phi\end{array} //]]>$ and magnetic flux density $//<![CDATA[ \begin{array}{l}B\end{array} //]]>$. The magnetic flux is understood as a vector representation that indicates the direction of the field lines and can be interpreted clearly by the number of field lines. The magnetic flux density $//<![CDATA[ \begin{array}{l}B\end{array} //]]>$ indicates the flux per unit area and is given in $//<![CDATA[ \begin{array}{l}\frac{V s}{m_2}\end{array} //]]>$ or also in $//<![CDATA[ \begin{array}{l}[T]\end{array} //]]>$.

$//<![CDATA[ \begin{array}{l}B = \frac{\Phi}{A} [\frac{A V s}{m_2} = T]\end{array} //]]>$

The correlation between electrical field strength and flux density is demonstrated by the following relation:

$//<![CDATA[ \begin{array}{l}B = \mu_0 * \mu_r * H\end{array} //]]>$

The magnetic field constant $//<![CDATA[ \begin{array}{l}\mu_0\end{array} //]]>$, which applies to spaces filled with certain material, together with the relative permeability $//<![CDATA[ \begin{array}{l}\mu_r\end{array} //]]>$ form the permeability $//<![CDATA[ \begin{array}{l}\mu\end{array} //]]>$. The relative permeability is one for non-ferromagnetic materials and has very high values from 6,000 (unalloyed iron) up to 300,000 (nickel) for magnetic materials. When measuring coating thickness, the inductance $//<![CDATA[ \begin{array}{l}L\end{array} //]]>$ is above all decisive and combines the essential coil properties:

$//<![CDATA[ \begin{array}{l}L = \mu_0 * \mu_r * n^2 * \frac{A}{l}\end{array} //]]>$

Inductance increases in the range of shorter distances between the test probe and the metallic substrate with an increasing distance. This can be measured. ^[1]

Impedance is the total alternating current resistance of a coil. Meaning it recognizes both ohmic resistance $//<![CDATA[ \begin{array}{l}\rho\end{array} //]]>$ and inductive resistance $//<![CDATA[ \begin{array}{l}X_{L}\end{array} //]]>$. Impedance is defined as $//<![CDATA[ \begin{array}{l}Z = \frac{U}{I}= \sqrt{R^2+X_{L}^2}\end{array} //]]>$. In eddy current testing impedance is usually depicted as a pointer in the complex plane, called impedance plane and is defined as: $//<![CDATA[ \begin{array}{l}Z = R+ i*X_{L}\end{array} //]]>$. The impedance plane is also used to depict the different locus curves and also the fault signals. ^[2]

Technical set up

Usually eddy current probes are a set of one transmitting and one receiving coil. The dimensioning of the coils (number of windings, coil core) can vary according to the use case. Generally, two types of probes can be distinguished:

• tactile probes
• continuous probes

Tactile probes are used for testing the surface of a flat part, meaning the probe axis is arranged orthogonally to the part surface. Usually the probe is moved by hand steadily to cover the tested area.

Using continuous probes, the part needs to be moved through the probe, meaning the probe axis is parallel to the part axis. This type of ET can only be used with cylindrical parts. With every geometrical deviation or change in distance of the coil to the surface of the part there would be a change in the magnetic field and consequently a defect signal visible.

In order to choose the right probe, it is important to recognize that for the best results the eddy currents should be orthogonal to the orientation of the imperfection as seen in figure 3. Otherwise the eddy currents could easily flow around the imperfection and therefore showing little effect on the resulting magnetic field. If the orientation is unknown, it is advisable to try multiple probes and testing angles.

Penetration depth

Knowing the penetration depth (skin depth) $//<![CDATA[ \begin{array}{l}\delta\end{array} //]]>$ is necessary in order to evaluate to what depth in the part defects can be detected. The penetration depth is the inverse of the product of the frequency of the current $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$, the magnetic constant $//<![CDATA[ \begin{array}{l}\mu_{0}\end{array} //]]>$, the relative permeability $//<![CDATA[ \begin{array}{l}\mu_{r}\end{array} //]]>$ and conductivity $//<![CDATA[ \begin{array}{l}\sigma\end{array} //]]>$.

$//<![CDATA[ \begin{array}{l}\delta = \frac{1}{π*µ_0*µ_r*σ*f}\end{array} //]]>$

It is possible to simplify equation 2 for quick estimates to:

$//<![CDATA[ \begin{array}{l}δ = \frac{503}{\sqrt{µ_r*σ*f}}\end{array} //]]>$

In practise the penetration depth is controlled by the test frequency^[1], which is the frequency of the alternating current $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$. The deepest penetration is achieved by using the lowest frequencies, which also increases the noise sensitivity. It is not advisable to use ET below $//<![CDATA[ \begin{array}{l}2\delta\end{array} //]]>$ because the eddy currents density is only 14% of their density on the surface. At a depth of $//<![CDATA[ \begin{array}{l}4 \delta\end{array} //]]>$ only 2% of the eddy currents density compared to the surface is left. Additionally the length of an imperfection needs to be about as big as the skin depth $//<![CDATA[ \begin{array}{l}\delta\end{array} //]]>$ to be detectable.

Locus curves

Changes of physical quantities like testing frequency $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$, electrical conductivity $//<![CDATA[ \begin{array}{l}\sigma\end{array} //]]>$, magnetic permeability $//<![CDATA[ \begin{array}{l}\mu_{r}\end{array} //]]>$ or the distance of the coil to the part $//<![CDATA[ \begin{array}{l}d\end{array} //]]>$ can be seen in the course of the measuring signal of the receiver coil. Using those locus curves, it is possible to detect defects and imperfections. For locus curves, the signal is usually depicted in the impedance plane. The imaginary and real part of the impedance are displayed as the ration between the receiving coil and empty receiving coil.

• The influence of the testing frequency on the measuring signal is depicted by the frequency locus curve (Figure 6). The curve is created by a frequency sweep while all other variables are constant.
• The conductivity locus curve (Figure 7) illustrates the dependency of the measuring signal on the conductivity of the part. It can be found by comparing the results of materials with different conductivity. Since conductivity has the same effect on eddy currents as the frequency, the conductivity locus curve is the same curve as the frequency locus curve. If there is a defect in the tested part, conductivity goes down $//<![CDATA[ \begin{array}{l}-\Delta\sigma\end{array} //]]>$. As depicted in Figure 8, the measured value transitions upwards along the locus curve.

• The influence of the distance between probe and part is depicted with the distance locus curve. With an increasing distance between coil and tested part, the secondary field gets weakened and consequently in measured signal the imaginary part increases while the real part is decreasing. For big distances $//<![CDATA[ \begin{array}{l}IM = 1\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}RE=0\end{array} //]]>$ since no eddy currents are induced in the part at all.

Figures locus curves

The influence of the distance between probe and part is depicted with the distance locus curve. With an increasing distance between coil and tested part, the secondary field gets weakened and consequently in measured signal the imaginary part increases while the real part is decreasing. For big distances IM = 1 and RE=0 since no eddy currents are induced in the part at all.

Probe circuit set ups

There is a multitude of different probe probe circuit setups.

• Using absolute measurements, the value of the receiver coil voltage is displayed. Figure 9 shows the locus curves without, with and with an imperfect part. The main disadvantage is that the defect signal is measured among noise signals. This which makes it harder to identify, compared to the other possible circuit set ups.
• For using comparison measurements, two spatially separate probes are used. The value of the receiver coil is subtracted from the value of the reference receiver coil. Only when there is an imperfection detected, a defect signal is visible (Figure 10). Compared to the absolute measurements this time the defect signal can be shown without noise, since a signal only appears when there actually is a difference between the two probes which is then identified as a defect.
• The differential method is similar to the comparison measurement, only this time the two probes are spatially combined and differentially connected (e.g. through opposed currents). The fault signal (Figure 11) now is symmetrical and only visible if the probe is moving over an imperfection. The difference between the probes themselves is always zero. The only difference to the comparison method is

• Other measuring methods
  • Multifrequency- method
  • Impulse- eddy currents testing
  • Far field - method
  • Imaging eddy current testing
  • Direction sensitive eddy current testing

Figures defect signal

Application

There is a multitude of possible applications for ET. All material properties dependent on conductivity or magnetic permeability can be displayed. In most cases imperfections are only quantified by comparison to a reference part or imperfection. For using ET purposefully, the user must have fundamental knowledge of the measuring equipment used, the physics involved, about the materials tested and measuring technology in general. Otherwise there is a great risk to misinterpret the data collected. While the method is very easy to use as an application, it requires a lot of knowledge to apply it correctly.

Here is a list of some parameters that can be quantified with ET^[2]

• Testing for material properties:
  • Structural changes
  • Changes in the alloy
  • Hardness
  • Structural robustness
  • Ferrite content determination
  • Corrosion
  • Influence of heat treatment
• Testing for material errors (discontinuities):
  • Surface cracks
  • Layer separation/ Delamination
  • Layer of corrosion
  • subsurface corrosion
• Dimensional and geometrical inspection:
  • Change in diameter ( e.g. poles, wires or pipes)
  • Change in thickness of metallic foils or sheet metal
  • Change in shape
  • Metal and non-metal layer thickness

Limitations

• ET can only be used for electrically conductive materials.
• The surface of the part needs to be accessible.
• Fundamental knowledge of the user is necessary for purposeful application.
• The surface quality can influence the test results.
• Reference measurements are necessary in order to interprete results objectively.
• ET is limited to near surface areas.
• Imperfection parallel to the eddy currents can hardly be detected.

Literature

1. Stegemann, Dieter: Der Einsatz von Wirbelströmen für die Zerstörungsfreie Werkstoffprüfung. 1. Auflage. DVS Media. Berlin 2010.
2. Stroppe, Heribert und Schiebold, Karlheinz: Wirbelstrom - Materialprüfung. 1. Auflage. Castell- Verlag GmbH. Wuppertal 2011.