Eddy current maths

Electromagnetic Testing Eddy Current Mathematics

2014-December My ASNT Level III Pre-Exam Preparatory Self Study Notes 外围学习中

Charlie Chong/ Fion Zhang

Charlie Chong/ Fion Zhang

Fion Zhang at Shanghai 2014/November

http://meilishouxihu.blog.163.com/

Shanghai 上海 Charlie Chong/ Fion Zhang

Impedance Phasol Diagrams

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Impedance Phasol Diagrams

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Greek letter

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Eddy Current Inspection Formula

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https://www.nde-ed.org/GeneralResources/Formula/ECFormula/ECFormula.htm

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https://www.nde-ed.org/GeneralResources/Formula/ECFormula/ECFormula.htm

Charlie Chong/ Fion Zhang

https://www.nde-ed.org/GeneralResources/Formula/ECFormula/ECFormula.htm

Charlie Chong/ Fion Zhang

https://www.nde-ed.org/GeneralResources/Formula/ECFormula/ECFormula.htm

Charlie Chong/ Fion Zhang

https://www.nde-ed.org/GeneralResources/Formula/ECFormula/ECFormula.htm

Units

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Ohms Law: According to Ohms Law, the voltage is the product of current and resistance.

V=IxR Where V = Voltage in volts, I = Current in Amps and R = Resistance in Ohms

Inductance of a solenoid is given by: L=ÎźoN2A/l

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https://en.wikipedia.org/wiki/Inductance

Phase Angle and Impedance Phase angle is expressed as follows: tan ÎŚ = XL/R Where: ÎŚ = Phase Angle in degrees, XL = Inductive Reactance in ohms and R = Resistance in ohms.

Impedance is defined as follows:

Where Z = Impedance in ohms, R = Resistance in ohms and XL = Reactance in ohms.

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Magnetic Permeability and Relative Magnetic Permeability Magnetic permeability is the ratio between magnetic flux density and magnetizing force. μ =B/H Where μ = Magnetic Permeability in Henries per meter (mu), B = Magnetic Flux Density in Tesla, H = Magnetizing Force in Amps/meter.

Relative magnetic permeability is expressed as follows: μr = μ / μ o Where μ r = Relative magnetic permeability (mu) and μ o = Magnetic permeability of free space (Henries per meter = 1.257 * 10-6). μ r = 1 for nonferrous materials.

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Conductivity and Resistivity Conductivity and resistivity is related as follows: σ =1/ ρ Where σ = Conductivity (sigma) and ρ =Resistivity (rho). Conductivity can be quantified in Siemens per m (S/m) or in Aerospace NDT in % lACS (International Annealed Copper Standard). One Siemen is the inverse of an ohm. Another common unit used for conductivity measurement is Siemen per cm (S/cm).

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Electrical Conductivity and Resistivity Resistance can be defined as follows: R = l /(Aσ) or R = ρl/A Where: R = the resistance of a uniform cross section conductor in ohms (Ω), l = the length of the conductor in the same linear units as the conductivity or resistivity is quantified, A=Cross Sectional area, σ = conductivity in S/m and ρ = Resistivity in Ω m.

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In eddy current testing, instead of describing conductivity in absolute terms, an arbitrary unit has been widely adopted. Because the relative conductivities of metals and alloys vary over a wide range, a conductivity benchmark has been widely used. In 1913, the International Electrochemical Commission established that a specified grade of high purity copper, fully annealed measuring 1 m long, having a uniform section of 1 mm2 and having a resistance of 17.241 mΩ at 20°C (1.7241x10-8 ohm-meter at 20°C) - would be arbitrarily considered 100 percent conductive. The symbol for conductivity is σ and the unit is Siemens per meter. Conductivity is also often expressed as a percentage of the International Annealed Copper Standard (IACS).

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Conductivity & Resistivity Relative Conductivity*

Temperature Coefficient of Resistance**

Tensile Strength (lbs./sq. in.)

59

0.0039

30,000

45-50 30-45

— —

— —

Brass

28

0.002-0.007

70,000

Cadmium

19

0.0038

—

Chromium

55

—

—

Cobalt

16.3

0.0033

—

Constantin

3.24

0.00001

120,000

Copper: Hard drawn · Annealed

89.5 100

0.00382 0.00393

60,000 30,000

65

0.0034

20,000

Metal Aluminum (2S; pure) Aluminum (alloys): · Soft-annealed · Heat-treated

Gold Charlie Chong/ Fion Zhang

http://www.wisetool.com/designation/cond.htm

Conductivity & Resistivity Iron: · Pure · Cast · Wrought

17.7 2-12 11.4

0.005 — —

— — —

Lead

7

0.0039

3,000

Magnesium

—

0.004

33,000

Manganin

3.7

0.00001

150,000

Mercury

1.66

0.00089

0

Molybdenum

33.2

0.004

—

4

0.002

160,000

1.45

0.0004

150,000

12-16

0.006

120,000

Monel Nichrome Nickel

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Conductivity & Resistivity Nickel silver (18%)

5.3

0.00014

150,000

Phosphor bronze

36

0.0018

25,000

Platinum

15

0.003

55,000

Silver

106

0.0038

42,000

Steel

3-15

0.004-0.005

42,000-230,000

Tin

13

0.0042

4,000

Titanium

5

—

50,000

Titanium, 6A14V

5

—

130,000

Tungsten

28.9

0.0045

500,000

Zinc

28.2

0.0037

10,000

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FIGURE 13. Normalized impedance diagram for long coil encircling solid cylindrical non-ferromagnetic bar and for thin wall tube. Coil fill factor = 1.0.

Legend k = √(ωμσ) = electromagnetic wave propagation constant for conducting material r = radius of conducting cylinder (m) μ = magnetic permeability of bar (4 πx10–7 H·m-1 if bar is nonmagnetic) σ= electrical conductivity of bar (S·m-1) ω = angular frequency = 2πf where f = frequency (Hz) √(ω L0G) = equivalent of √(ωμσ) for simplified electrical circuits, where G = conductance (S) and L0 = inductance in air (H)

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Legend k = √(ωμσ) = electromagnetic wave propagation constant for conducting material r = radius of conducting cylinder (m) μ = magnetic permeability of bar (4 π x10–7 H·m-1 if bar is nonmagnetic) σ = electrical conductivity of bar (S·m-1) ω = angular frequency = 2 π f where f = frequency (Hz) √(ω L0G) = equivalent of √(ωμσ) for simplified electrical circuits, where G = conductance (S) and L0 = inductance in air (H) Keywords: ? δ = √(2/ωμσ) = 1/√(ωμσ) = 1/k = 1/(π f μσ)½ For √(ω L0G) = √(ωμσ) , L0G = μσ

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The magnetic permeability μ is the ratio of flux density B to magnetic field intensity H: μ = B∙H-1 where B = magnetic flux density (tesla) and H = magnetizing force or magnetic field intensity (A·m–1). In free space, magnetic permeability μ0 = 4 π × 10–7 H·m–1.

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Magnetic permeability of free space: μ0 = 4 π × 10–7 H·m–1

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Magnetic Permeability Magnetic Flux: Magnetic flux is the number of magnetic field lines passing through a surface placed in a magnetic field.

ϴ

We show magnetic flux with the Greek letter; Ф. We find it with following formula; Ф =B∙A ∙ cos ϴ Where Ф is the magnetic flux and unit of Ф is Weber (Wb) B is the magnetic field and unit of B is Tesla A is the area of the surface and unit of A is m2 Following pictures show the two different angle situation of magnetic flux.

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http://www.physicstutorials.org/home/magnetism/magnetic-flux-and-magnetic-permeability

In (a), magnetic field lines are perpendicular to the surface, thus, since angle between normal of the surface and magnetic field lines 0° and cos 0° =1 equation of magnetic flux becomes; Ф =B ∙ A In (b), since the angle between the normal of the system and magnetic field lines is 90° and cos 90° = 0 equation of magnetic flux become; Ф =B ∙ A ∙ cos 90° = B ∙ A ∙ 0 = 0

(a)

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(b)

http://www.physicstutorials.org/home/magnetism/magnetic-flux-and-magnetic-permeability

Magnetic Permeability - In previous units we have talked about heat conductivity and electric conductivity of matters. In this unit we learn magnetic permeability that is the quantity of ability to conduct magnetic flux. We show it with Âľ. Magnetic permeability is the distinguishing property of the matter, every matter has specific Âľ. Picture given below shows the behavior of magnetic field lines in vacuum and in two different matters having different Âľ.

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http://www.physicstutorials.org/home/magnetism/magnetic-flux-and-magnetic-permeability

Magnetic permeability of the vacuum is denoted by; µo and has value; µo = 4 π.10-7 Wb/Amps.m We find the permeability of the matter by following formula; µ= B / H Where; H is the magnetic field strength and B is the flux density Relative permeability is the ratio of a specific medium permeability to the permeability of vacuum. µr=µ/µo

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http://www.physicstutorials.org/home/magnetism/magnetic-flux-and-magnetic-permeability

Diamagnetic matters: If the relative permeability f the matter is a little bit lower than 1 then we say these matters are diamagnetic.

Paramagnetic matters: If the relative permeability of the matter is a little bit higher than 1 then we say these matters are paramagnetic.

Ferromagnetic matters: If the relative permeability of the matter is higher than 1 with respect to paramagnetic matters then we say these matters are ferromagnetic matters.

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http://www.physicstutorials.org/home/magnetism/magnetic-flux-and-magnetic-permeability

Magnetic Permeability

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http://www.physicstutorials.org/home/magnetism/magnetic-flux-and-magnetic-permeability

Standard Depth

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Standard Depth of Penetration Standard depth of penetration is given as follows:

Where δ = standard depth of penetration in m; f = frequency (Hz); μ = Magnetic Permeability (Henries per meter); and σ = conductivity in S/m.

The influence of frequency and conductivity on standard depth of penetration is illustrated in Figure 1.

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Figure 1. Influence of frequency and conductivity on standard depth of penetration.

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Current Density Change with Depth The change in current density with depth is expressed as follows:

Jx = Jo e窶度/ﾎｴ Where Jx = Current Density at distance x below the surface (amps/m2); J0 = Current Density at the surface (amps/m2); e = the base of the natural logarithm (Euler's number) = 2.71828; x = Distance below the surface; and ﾎｴ = standard depth of penetration in meters.

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Depth of Penetration and Probe Size Smith et al have introduced the idea of spatial frequency.

Where D = the effective diameter of the probe field in meters, limiting the depth of penetration to D/4. The probe effective diameter is considered to be infinite in the usual equation.

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Depth of Penetration & Current Density

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http://www.suragus.com/en/company/eddy-current-testing-technology

Standard Depth Calculation

Where: μ = μ0 x μr

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The applet below illustrates how eddy current density changes in a semiinfinite conductor. The applet can be used to calculate the standard depth of penetration. The equation for this calculation is:

Where: δ = Standard Depth of Penetration (mm) π = 3.14 f = Test Frequency (Hz) μ = Magnetic Permeability (H/mm) σ = Electrical Conductivity (% IACS)

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Defect Detection / Electrical conductivity measurement

1/e or 37% of surface density at target

Defect Detection

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(1/e)3 or 5% of surface density at material interface

Electrical conductivity measurement

The skin depth equation is strictly true only for infinitely thick material and planar magnetic fields. Using the standard depth δ , calculated from the above equation makes it a material/test parameter rather than a true measure of penetration.

(1/e)

(1/e)2

(1/e)3

FIG. 4.1. Eddy current distribution with depth in a thick plate and resultant phase lag.

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Sensitivity to defects depends on eddy current density at defect location.

Although eddy currents penetrate deeper than one standard depth (δ) of penetration they decrease rapidly with depth. At two standard depths of penetration (2δ ), eddy current density has decreased to (1/ e)2 or 13.5% of the surface density. At three depths (3δ), the eddy current density is down to only (1/ e)3 or 5% of the surface density.

However, one should keep in mind these values only apply to thick sample (thickness, t > 5r ) and planar magnetic excitation fields. Planar field conditions require large diameter probes (diameter > 10t) in plate testing or long coils (length > 5t) in tube testing. Real test coils will rarely meet these requirements since they would possess low defect sensitivity. For thin plate or tube samples, current density drops off less than calculated from Eq. (4.1).

For solid cylinders the overriding factor is a decrease to zero at the centre resulting from geometry effects.

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One should also note that the magnetic flux is attenuated across the sample, but not completely. Although the currents are restricted to flow within specimen boundaries, the magnetic field extends into the air space beyond.

This allows the inspection of multi-layer components separated by an air space. The sensitivity to a subsurface defect depends on the eddy current density at that depth, it is therefore important to know the effective depth of penetration. The effective depth of penetration is arbitrarily defined as the depth at which eddy current density decreases to 5% of the surface density.

For large probes and thick samples, this depth is about three standard depths of penetration. Unfortunately, for most components and practical probe sizes, this depth will be less than 3δ , the eddy currents being attenuated more than predicted by the skin depth equation.

Keywords: For large probes and thick samples, this depth is about three standard depths of penetration. Unfortunately, for most components and practical probe sizes, this depth will be less than 3δ.

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Standard Depth of Penetration Versus Frequency Chart

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https://www.nde-ed.org/GeneralResources/Formula/ECFormula/DepthFreqChart/ECDepth.html

Magnetic Field & Size of Coil Typically, the magnetic field β in the axial direction is relatively strong only for a distance of approximately one tenth of the coil diameter, and drops rapidly to only approximately one tenth of the field strength near the coil at a distance of one coil diameter.

D=Coil diameter 0.1D

β0

D

0.1β0

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Flaw Detection Depth To penetrate deeply, therefore, large coil diameters are required. However as the coil diameter increases, the sensitivity to small flaws, whether surface or subsurface, decreases. For this reason, eddy current flaw detection is generally limited to depths most commonly of up to approximately 5 mm only, occasionally up to 10 mm.

For materials or components with greater cross-sections, eddy current testing is usually used only for the detection of surface flaws and assessing material properties, and radiography or ultrasonic testing is used to detect flaws which lie below the surface, although eddy current testing can be used to detect flaws near the surface. However, a very common application of eddy current testing is for the detection of flaws in thin material and, for multilayer structures, of flaws in a subsurface layer.

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Phase Lag

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Phase change with Depth Phase change with depth is expressed as follows: θº = 57.3 x / δ Where, θº = Phase lag (degrees); 57.3 = 1 radian expressed in degrees; x = Distance below the surface; and δ = standard depth of penetration.

The change in phase and current density with depth of penetration is depicted in Figure 2.

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Figure 2. Phase and current density change with depth of penetration.

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Frequency?????

Frequency is expressed as follows:

Where f = frequency (Hz); x= material thickness in meters; Îź = Magnetic Permeability (Henries per meter); and Ďƒ = conductivity in S/m.

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http://www.azom.com/article.aspx?ArticleID=10953#4

Impedance Phasol Diagrams

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Phase Lag Phase lag is a parameter of the eddy current signal that makes it possible to obtain information about the depth of a defect within a material. Phase lag is the shift in time between the eddy current response from a disruption on the surface and a disruption at some distance below the surface. The generation of eddy currents can be thought of as a time dependent process, meaning that the eddy currents below the surface take a little longer to form than those at the surface. Disruptions in the eddy currents away from the surface will produce more phase lag than disruptions near the surface. Both the signal voltage and current will have this phase shift or lag with depth, which is different from the phase angle discussed earlier. (With the phase angle, the current shifted with respect to the voltage.)

Keywords: Both the signal voltage and current will have this phase shift or lag with depth, which is different from the phase angle discussed earlier. (With the phase angle, the current shifted with respect to the voltage.)

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Phase lag is an important parameter in eddy current testing because it makes it possible to estimate the depth of a defect, and with proper reference specimens, determine the rough size of a defect. The signal produced by a flaw depends on both the amplitude and phase of the eddy currents being disrupted. A small surface defect and large internal defect can have a similar effect on the magnitude of impedance in a test coil. However, because of the increasing phase lag with depth, there will be a characteristic difference in the test coil impedance vector.

Phase lag can be calculated with the following equation. The phase lag angle calculated with this equation is useful for estimating the subsurface depth of a discontinuity that is concentrated at a specific depth. Discontinuities, such as a crack that spans many depths, must be divided into sections along its length and a weighted average determined for phase and amplitude at each position below the surface.

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Phase Lag

Eq. (4.2).

Where: β = phase lag X = distance below surface δ = standard depth of penetration

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(1/e)

(1/e)2

(1/e)3

1δ

2δ

3δ

FIG. 4.1. Eddy current distribution with depth in a thick plate and resultant phase lag.

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More on Phase lag Phase lag is a parameter of the eddy current signal that makes it possible to obtain information about the depth of a defect within a material. Phase lag is the shift in time between the eddy current response from a disruption on the surface and a disruption at some distance below the surface. Phase lag can be calculated using the equations to the right. The second equation simply converts radians to degrees by multiplying by 180/p or 57.3.

The phase lag calculated with these equations should be about 1/2 the phase rotation seen between the liftoff signal and a defect signal on an impedance plane instrument. Therefore, choosing a frequency that results in a standard depth of penetration of 1.25 times the expected depth of the defect will produce a phase lag of 45o and this should appear as a 90o separation between the liftoff and defect signals.

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https://www.nde-ed.org/GeneralResources/Formula/ECFormula/PhaseLag1/PhaseLag.htm

The phase lag angle is useful for estimating the distance below the surface of discontinuities that concentrated at a specific depth. Discontinuities such as a crack must be divided into sections along its length and a weighted average determined for phase and amplitude at each position below the surface. For more information see the page explaining phase lag.

Where: β = phase lag X = distance below surface in mm. δ = standard depth of penetration in mm.

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https://www.nde-ed.org/GeneralResources/Formula/ECFormula/PhaseLag1/PhaseLag.htm

FIG. 5.32. Impedance diagram showing the signals from a shallow inside surface flaw and a shallow outside surface flaw at three different frequencies.

The increase in the phase separation and the decrease in the amplitude of the outside surface flaw relative to that of the inside surface flaw with increasing frequency 2f90 can be seen.

Phase separation

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Phase lag β = x/ δ radian δ = (π fσμ) -½ β = x(π fσμ) -½

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Impedance

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Inductive reactance (XL) in terms of frequency and inductance is given by: XL = ω∙L = 2πf∙L Similarly the Capacitance Reactance: XC = 1/(ω∙C) = 1/ (2πf ∙C) Inductive reactance is directly proportional to frequency, and its graph, plotted against frequency (ƒ) is a straight line. Capacitive reactance is inversely proportional to frequency, and its graph, plotted against ƒ is a curve.

These two quantities are shown, together with R, plotted against ƒ in Fig 9.2.1 It can be seen from this diagram that where XC and XL intersect, they are equal and so a graph of (XL − XC ) must be zero at this point on the frequency axis.

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http://www.learnabout-electronics.org/ac_theory/lcr_series_92.php

Reactance Voltage = Current x Inductive Reactance E1 = I∙XL

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http://www.learnabout-electronics.org/ac_theory/lcr_series_92.php

The Inductive & Capacitive Reactance XL = ωL = 2 πfL XC = 1/(ωC) = 1/ (2πfC)

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The relationship between impedance and its individual components (resistance and inductive reactance) can be represented using a vector as shown below. The amplitude of the resistance component is shown by a vector along the x-axis and the amplitude of the inductive reactance is shown by a vector along the y-axis.

The amplitude of the impedance is shown by a vector that stretches from zero to a point that represents both the resistance value in the x-direction and the inductive reactance in the y-direction.

Eddy current instruments with impedance plane displays present information in this format.

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3.1.1 Induction and Reception Function There are two methods of sensing changes in the eddy current characteristics: (a) The impedance method (b) The send receive method Impedance method In the impedance method, the driving coil is monitored. As the changes in coil voltage or a coil current are due to impedance changes in the coil, it is possible to use the method for sensing any material parameters that result in impedance changes. The resultant impedance is a sum of the coil impedance (in air) plus the impedance generated by the eddy currents in the test material.

The impedance method of eddy current testing consists of monitoring the voltage drop across a test coil. The impedance has resistive and inductive components. The impedance magnitude is calculated from the equation:

|Z| = [ R2+ (XL)2 ] ½ (Xc was assume nil) Where: Z = impedance, R = resistance, XL = inductive reactance

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and the impedance phase is calculated as:

θ = tan-1 (XL/ R) Where: θ = phase angle, R = resistance, XL = inductive reactance The voltage across the test coil is V= IZ, where I is the current through coil and Z is the impedance.

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Impedance Phasol Diagrams

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http://hyperphysics.phy-astr.gsu.edu/hbase/electric/impcom.html

Impedance Phasol Diagrams

, ω = 2πf

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http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html

Eddy Impedance plane responses

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Magnetism

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The magnetic field B surrounds the current carrying conductor. For a long straight conductor carrying a unidirectional current, the lines of magnetic flux are closed circular paths concentric with the axis of the conductor. Biot and Savart deduced, from the experimental study of the field around a long straight conductor, that the magnetic flux density B associated with the infinitely long current carrying conductor at a point P which is at a radial distance r, as illustrated in FIG. below, is

B

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http://electrical4u.com/magnetic-flux-density-definition-calculation-formula/

Phase Shifts

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Current Phase Shift – Inductance a vector sum of resistance & reactance If more resistance than inductive reactance is present in the circuit, the impedance line will move toward the resistance line and the phase shift will decrease. If more inductive reactance is present in the circuit, the impedance line will shift toward the inductive reactance line and the phase shift will increase.

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Capacitor circuit: Current lead voltage by 90o

Inductor circuit: Current lagging voltage by 90o

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Resonance Frequency

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3.2 Resonant Circuits Eddy current probes typically have a frequency or a range of frequencies that they are designed to operated. When the probe is operated outside of this range, problems with the data can occur. When a probe is operated at too high of a frequency, resonance can occurs in the circuit. In a parallel circuit with resistance (R), inductance (XL) and capacitance (XC), as the frequency increases XL decreases and XC increase. Resonance occurs when XL and XC are equal but opposite in strength. At the resonant frequency, the total impedance of the circuit appears to come only from resistance since XL and XC cancel out.

Every circuit containing capacitance and inductance has a resonant frequency that is inversely proportional to the square root of the product of the capacitance and inductance.

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Eddy current inspection

At resonant frequency Xc and XL cancelled out each other. Thus the phase angle is zero, only the resistance component exist. The current is at it maximum.

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Balance Bridge Circuit

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Coil impedance is normally balanced using an AC bridge circuit. A common bridge circuit is shown in general form of FIG. 3.16. The arms of the bridge are being indicated as impedance of unspecified sorts. The detector is represented by a voltmeter. Balance is secured by adjustments of one or more of the bridge arms. Balance is indicated by zero response of the detector which means that points B and C are at the same potential (have the same instantaneous voltage). Current will flow through the detector (voltmeter) if points B and C on the bridge arms are at different voltage levels. Current may flow in either direction depending on whether B or C is at higher potential.

FIG. 3.16. Common bridge circuit.

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If the bridge is made of four impedance arms, having inductive and resistive components, the voltage from A-B-D must equal the voltage from A-C-D in both amplitude and phase for the bridge to be balanced.

FIG. 3.16. Common bridge circuit.

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At balance: I1Z1 = I2 Z2 and I1 Z3 = I2 Z4 From above equations we have: (3.4)

The equation (3.4) states that ratio of impedance of pair of adjacent arms must equal the ratio of impedance of the other pair of adjacent arms for bridge balance. In a typical bridge circuit in eddy current instruments as shown in FIG. 3.17., the probe coils are placed in parallel to the variable resistors. The balancing is achieved by varying these resistors until null or balance condition is achieved.

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FIG. 3.17. Common Testing Arrangement

At balance: IAZ1 = IB Z3 , IA Z2 = IB Z4

IA IB

IAZ1/ IA Z2 = IB Z3 / IB Z4 From above equations we have:

IA

(3.4)

The equation (3.4) states that ratio of impedance of pair of adjacent arms must equal the ratio of impedance of the other pair of adjacent arms for bridge balance. In a typical bridge circuit in eddy current instruments as shown in FIG. 3.17., the probe coils are placed in parallel to the variable resistors. The balancing is achieved by varying these resistors until null or balance condition is achieved.

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FIG. 3.17. Common Testing Arrangement

At balance: V1=V1 IAZ1 = IB Z3 , IAZ2 = IBZ4 IAZ/ IA Z2 = IBZ3 / IBZ4

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Impedance Phasol Diagrams

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https://www.youtube.com/watch?v=2XuRGrGZ_9M

Subject on Balance Circuit- more reading

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A Maxwell bridge (in long form, a Maxwell-Wien bridge) is a type of Wheatstone bridge used to measure an unknown inductance (usually of low Q value) in terms of calibrated resistance and capacitance. It is a real product bridge.

It uses the principle that the positive phase angle of an inductive impedance can be compensated by the negative phase angle of a capacitive impedance when put in the opposite arm and the circuit is at resonance; i.e., no potential difference across the detector and hence no current flowing through it. The unknown inductance then becomes known in terms of this capacitance.

With reference to the picture, in a typical application R1 and R4 are known fixed entities, and R2 and C2 are known variable entities. R2 and C2 are adjusted until the bridge is balanced.

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http://en.wikipedia.org/wiki/Maxwell_bridge

R3 and L3 can then be calculated based on the values of the other components:

R4

C2 R2

R1

L3 R3

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http://en.wikipedia.org/wiki/Maxwell_bridge

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http://www.allaboutcircuits.com/vol_1/chpt_8/10.html

Circuits Wheatstone Bridge Part 1

â– https://www.youtube.com/watch?v=Kf5XkK0465A Charlie Chong/ Fion Zhang

Conductivity Measurement

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Influence of temperature on the resistivity Higher temperature increases the thermal activity of the atoms in a metal lattice. The thermal activity causes the atoms to vibrate around their normal positions. The thermal vibration of the atoms increases the resistance to electron flow, thereby lowering the conductivity of the metal. Lower temperature reduces thermal oscillation of the atoms resulting in increased electrical conductivity. The influence of temperature on the resistivity of a metal can be determined from the following equation.

(4.3) where Rt = resistivity of the metal at the test temperature, R0 = resistivity of the metal at standard temperature ι = resistivity temperature coefficient T = difference between the standard and test temperature (°C).

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From Eq. (4.3) it can be seen that if the temperature is increased, resistivity increases and conductivity decreases from their ambient temperature levels.

Conversely, if temperature is decreased the resistivity decreases and conductivity increases. To convert resistivity values, such as those obtained from Eq. (4.3) to conductivity in terms of% IACS, the conversion formula is,

%IACS = 172.41/ρ

(4.4)

Where: IACS = international annealed copper standard ρ = resistivity (unit?) ρIACS = 1.724110-8 Ωm

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http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

3.3.2

Electrical Conductivity and Resistivity

In eddy current testing, instead of describing conductivity in absolute terms, an arbitrary unit has been widely adopted. Because the relative conductivities of metals and alloys vary over a wide range, a conductivity benchmark has been widely used. In 1913, the International Electrochemical Commission established that a specified grade of high purity copper, fully annealed measuring 1 m long, having a uniform section of 1 mm2 and having a resistance of 1.7241x10-8 ohm-meter at 20°C (100% IACS = 1.7241x10-8 ohm-meter at 20°C) - would be arbitrarily considered 100 percent conductive.

The symbol for conductivity is σ and the unit is Siemens per meter.

Conductivity is also often expressed as a percentage of the International Annealed Copper Standard (IACS).

Note: 100% IACS = 1.7241x10-8 ohm-meter at 20°C

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Example: The eddy current conductivity should be corrected by using Equations (4.3) and (4.4). In aluminium alloy, for example, a change of approximately 12% IACS for a 55°C change in temperature, using handbook resistivity values of 2.828 micro-ohm centimeters and a temperature coefficient of 0.0039 at 20°C. If the conductivity of commercially pure aluminium is 62% IACS at 20°C, then one would expect a conductivity of 55% IACS at 48°C and a conductivity of 69% IACS at –10 °C.

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http://www.centurionndt.com/Technical%20Papers/condarticle.htm

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http://www.centurionndt.com/Technical%20Papers/condarticle.htm

Charlie Chong/ Fion Zhang

http://www.centurionndt.com/Technical%20Papers/condarticle.htm

Charlie Chong/ Fion Zhang

http://www.centurionndt.com/Technical%20Papers/condarticle.htm

Conductivity and its measurement The SI unit of conductivity is the Siemens/metre (S/m), but because it is a very small unit, its multiple, the megaSiemens/metre (MS/m) is more commonly used.

Eddy current conductivity meters usually give readouts in the practical unit of conductivity,% IACS (% International Annealed Copper Standard), which give the conductivity relative to annealed commercially pure copper. To convert % IACS to MS/m, multiply by 0.58, and to convert MS/m to % IACS, multiply by 1.724.

For instance, the conductivity of Type 304 stainless steel is 2.5% IACS or 1.45MS/m. Resistivity is the inverse of conductivity, and some publications on eddy current testing refer to resistivity values rather than conductivity values.

However, conductivity in % IACS is universally used in the aluminium and aerospace industries.

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Fill Factors

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Centering, fill factor η (Eta) In an encircling coil, or an internal coil, fill factor “η Eta” is a measure of how well the conductor (test specimen) fits the coil. It is necessary to maintain a constant relationship between the diameter of the coil and the diameter of the conductor. Again, small changes in the diameter of the conductor can cause changes in the impedance of the coil. This can be useful in detecting changes in the diameter of the conductor but it can also mask other indications.

For an external coil: Fill Factor η = (D1/D2)2

(4.5)

For an internal coil: Fill Factor η = (D2/D1)2 where η = fill factor D1 = part diameter D2 = coil diameter Charlie Chong/ Fion Zhang

(4.6)

Thus the fill factor must be less than 1 since if Ρ = 1 the coil is exactly the same size as the material. However, the closer the fill factor is to 1 the more precise the test. The fill factor can also be expressed as a %. For maximum sensitivity, the fill factor should be as high as possible compatible with easy movement of the probe in the tube. Note that the fill factor can never exceed 1 (100%).

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Frequency Selections

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Probe and frequency selection The essential requirements for the detection of subsurface flaws are, sufficient penetration for sensitivity to the subsurface flaws sought, and sufficient phase separation of the signals for the location or depth of the flaws to be identified. As standard depth of penetration increases, the phase difference between discontinuities of different depth decreases. Therefore, making interpretation of location or depth of the flaws difficult. Example: If the frequency is set to obtain a standard depth of penetration of 2 mm, the separation between discontinuities at 1 mm and 2 mm would be 57째. If the frequency is set to obtain a standard depth of penetration of 4 mm, the separation between discontinuities at 1 mm and 2 mm would be 28.5째.

Keywords: As standard depth of penetration increases, the phase difference between discontinuities of different depth decreases.

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An acceptable compromise which gives both adequate sensitivity to subsurface flaws and adequate phase separation between near side and far side flaw signals is to use a frequency for which the thickness (t) = 0.8 δ. At this frequency, the signal from a shallow far side flaw is close to 90° clockwise from the signal from a shallow near side flaw, so this frequency is termed f90. By substituting t = 0.8 δ into the standard depth of penetration formula, and changing Hz to kHz, the following formula is obtained:

f90 = 280/ (t2σ)

(5.1)

Where: f90 = the operating frequency (kHz), t = the thickness or depth of material to be tested (mm), and σ = the conductivity of the test material (% IACS).

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FIG. 5.15. Eddy current signals from a thin plate with a shallow near side flaw, a shallow far side flaw, and a through hole, at three different frequencies.

1. At 25 kHz (a), the sensitivity to far side flaws is high, but the phase difference between near side and far side signals is relatively small.

2. At 200 kHz (c), the phase separation between near side and jar side signals is large. but the sensitivity to far side flaws is poor.

3. For this test part, a test frequency of100 kHz (b) shows both good sensitivity to far side flaws and good phase separation between near side and far side signals.

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To obtain adequate depth of penetration, not only must the frequency be lower than for the detection of surface flaws, but also the coil diameter must be larger. On flat surfaces, a spot probe, either absolute or reflection, should be used in order to obtain stable signals (see FIG. 5.16). On curved surfaces, a spot probe with a concave face or a pencil probe should be used. Spring loaded spot probes can be used to minimize lift-off, and shielded spot probes are available for scanning close to edges, fasteners, and sharp changes in configuration.

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Probes Frequency

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Typically, for aluminium alloys, frequencies in the range approximately 200 kHz to 500 kHz are appropriate, with approximately 200 kHz being preferred.

For low conductivity materials like stainless steel, nickel alloys, and titanium alloys, the penetration would be excessive at these frequencies, and higher frequencies are required. Typically 2 MHz to 6 MHz should be used.

Al: .2MHz ~ .5MHz SS, Ni, Ti & Alloys: 2MHz ~ 6MHz Ferromagnetic Mtls: ?

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Impedance Phasol Diagrams

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Eddy Impedance plane responses

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FIGURE 11. Measured conductivity locus, with conductivity expressed in siemens per meter (percentages of International Annealed Copper Standard)

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FIG. 5.19. Impedance diagrams and the conductivity curve at three different frequencies, showing that, as frequency increases, the operating point moves down the conductivity curve. It can also be seen that the angle θ between the conductivity and lift-off curve is quite small for operating points near the top of the conductivity curve, but greater in the middle and lower parts of the curve. The increased sensitivity to variations in conductivity towards the centre of the conductivity curve can also be seen.

20KHz

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100KHz

1000KHz

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FIG. 5.24. Impedance diagram showing the conductivity curve and the locus of the operating points for thin red brass (conductivity approximately 40% IACS) at 120 kHz (the thickness curve). The thickness curve meets the conductivity curve when the thickness equals the Effective Depth of Penetration (EDP).

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FIG. 5.25. Impedance diagram showing the conductivity curve, and the thickness curve for brass at a frequency of 120 kHz, the f90 frequency for a thickness of 0.165 mm. The operating point for this thickness is shown, and liftoff curves for this and various other thicknesses are also shown.

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FIG. 5.32. Impedance diagram showing the signals from a shallow inside surface flaw and a shallow outside surface flaw at three different frequencies.

The increase in the phase separation and the decrease in the amplitude of the outside surface flaw relative to that of the inside surface flaw with increasing frequency 2f90 can be seen.

Phase separation

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Phase lag β = x/δ radian δ = (πfσμ) -½

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FIG. 5.35. Impedance diagram showing flaw signals and a signal from an inside surface ferromagnetic condition at three different frequencies. The insert shows the signals at 19째 rotated to their approximate orientation on an eddy current instrument display.

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FIG. 5.36 shows the signal from a ferromagnetic condition at the outside surface. It could be confused with a signal from a dent, but the two can readily be distinguished if required by retesting at a different test frequency. The signal from a ferromagnetic condition at the outside surface will show phase rotation with respect to the signal from an inside surface flaw, as stated above, whereas a dent signal will remain approximately 180 째 from the inside surface flaw signal.

FIG. 5.36. The signals from a typical absolute probe from flaws. an outside surface ferromagnetic condition, a dent, a ferromagnetic baffle plate and a nonferromagnetic support tested at f90.

Charlie Chong/ Fion Zhang

Impedance Phasol Diagrams 1.

2.

3.

4.

5.

conductivity measurement permeability measurement metal thickness measurement coating thickness measurements flaw detection

Conductivity

Conductivity versus Probe Impedance constant frequency

1 Titanium, 6Al-4V

Normalized Reactance

0.8

Inconel Stainless Steel, 304

0.6

Copper 70%, Nickel 30%

0.4 Lead

0.2 Copper

Magnesium, A280 Nickel Aluminum, 7075-T6

0 0

0.1

0.2 0.3 Normalized Resistance

0.4

0.5

Conductivity versus Alloying & Temper

IACS = International Annealed Copper Standard σIACS = 5.8107 Ω-1m-1 at 20 °C ρIACS = 1.724110-8 Ωm 60 Conductivity [% IACS]

2014

2024

6061

7075

50 T0

T0

40

T6

T72 T6

30

T6

T8

T0

T0

T73 T76

T4

T3 T4 T3 T4

20 Various Aluminum Alloys

T6

Apparent Eddy Current Conductivity

magnetic field probe coil specimen

Normalized Reactance

1.0 0.8 lift-off curves

0.6 0.4

conductivity (frequency) curve

0.2 0

eddy currents

0

0.1 0.2 0.3 0.4 Normalized Resistance

• high accuracy ( 0.1 %) • controlled penetration depth

Normalized Reactance

 4

 3 =0

=s

 

2

1

Normalized Resistance

0.5

Lift-Off Curvature

inductive (low frequency) lift-off

ℓ =0

ℓ =s

lift-off

ℓ =0 σ2

σ2 conductivity σ σ1

“Vertical” Component.

“Vertical” Component.

ℓ =s

capacitive (high frequency)

conductivity

σ

σ1

“Horizontal” Component

“Horizontal” Component

Inductive Lift Off Effects 4 mm diameter

8 mm diameter

2.0

2.0

1.5 %IACS

-1.0

63.5 μm 50.8 μm 38.1 μm 25.4 μm 19.1 μm 12.7 μm 6.4 μm

-1.5

-1.5

0.0 μm

-2.0

-2.0

1.0 0.5 0.0 -0.5 -1.0

0.1

1 10 Frequency [MHz]

1.0 0.5 0.0 -0.5

100

0.1

1 10 Frequency [MHz]

100

80

80

70

70

63.5 μm

60

60

50.8 μm

50

50

38.1 μm 25.4 μm

AECL [μm] . .

AECL [μm] .

1.5 %IACS

1.5 Relative ΔAECC [%].

Relative ΔAECC [%] .

1.5

40 30 20

40 30 20

10

10

0

0

-10

-10

0.1

1 10 Frequency [MHz]

100

19.1 μm 12.7 μm 6.4 μm 0.0 μm 0.1

1 10 Frequency [MHz]

100

Instrument Calibration conductivity spectra comparison on IN718 specimens of different peening intensities.

3.0

12A Nortec 8A Nortec 4A Nortec 12A Agilent 8A Agilent 4A Agilent 12A UniWest 8A UniWest 4A UniWest 12A Stanford 8A Stanford 4A Stanford

2.5

AECC Change [%] .

2.0 1.5 1.0 0.5 0.0 -0.5 0.1

1

10

100

Frequency [MHz]

Nortec 2000S, Agilent 4294A, Stanford Research SR844, and UniWest US-450

Permeability Phasol Diagram

Magnetic Susceptibility paramagnetic materials with small ferromagnetic phase content moderately high susceptibility

low susceptibility 1.0

4 Âľr = 4

3

permeability

3

2

2 1

frequency (conductivity)

1 0

Normalized Reactance

Normalized Reactance

permeability

0.8 lift-off

0.6

frequency (conductivity)

0.4 0.2 0

0

0.2

0.4 0.6 0.8 1 Normalized Resistance

1.2

0

0.1 0.2 0.3 0.4 Normalized Resistance

increasing magnetic susceptibility decreases the apparent eddy current conductivity (AECC)

0.5

Magnetic Susceptibility versus Cold Works

cold work (plastic deformation at room temperature) causes martensitic (ferromagnetic) phase transformation in austenitic stainless steels

Magnetic Susceptibility

101

SS304L SS302 SS304

100 10-1 10-2

SS305

10-3

IN718 IN625 IN276

10-4 0

10

20

30 Cold Work [%]

40

50

60

Metal Thickness Phasol Diagram

Thickness versus Normalized Impedance scanning probe coil

thickness loss due to corrosion, erosion, etc.

1 0.8

1

thinning

0.6 0.4

thick plate

0.2

f = 0.05 MHz f = 0.2 MHz f = 1 MHz

0.8

lift-off Re { F }

Normalized Reactance

aluminum (σ = 46 %IACS)

0.6 0.4

F ( x )  e  x /  e i x / 

0.2

thin plate

0 -0.2

0

0

0

0.1 0.2 0.3 0.4 0.5 Normalized Resistance

0.6

1

2 Depth [mm]

3

Thickness Correction

Vic-3D simulation, Inconel plates (Ďƒ = 1.33 %IACS) ao = 4.5 mm, ai = 2.25 mm, h = 2.25 mm

Conductivity [%IACS]

1.4

1.3

thickness 1.0 mm 1.5 mm 2.0 mm 2.5 mm 3.0 mm 3.5 mm 4.0 mm 5.0 mm 6.0 mm

1.2

1.1

1.0 0.1

1 Frequency [MHz]

10

Coating Thickness Phasol Diagrams

Non-Conductive Coating probe coil, ao

non-conducting coating

ℓ t d

conducting substrate ao > t, d > δ, AECL = ℓ + t

80 70 60 50 40 30 20 10 0 -10 0.1

ao = 4 mm, experimental lift-off: 63.5 μm 50.8 μm 38.1 μm 25.4 μm 19.1 μm 12.7 μm 6.4 μm 0 μm

1 10 100 Frequency [MHz]

AECL [μm]

AECL [μm]

ao = 4 mm, simulated

80 70 60 50 40 30 20 10 0 -10 0.1

1 10 100 Frequency [MHz]

Conductive Coating probe coil, ao

conducting coating

z = δe z

ℓ t

Je

d

conducting substrate (µs,σs) approximate:

large transducer, weak perturbation equivalent depth: e 

s 2

 1 AECC( f )     e     2  f   s s 

 1  ( z )  AECC   4  z2   s s 

  

   

analytical:

Fourier decomposition (Dodd and Deeds)

numerical:

finite element, finite difference, volume integral, etc.

(Vic-3D, Opera 3D, etc.)

Simplistic Inversion of AECC Spectra 0.254-mm-thick surface layer of 1% excess conductivity 1.2 uniform

1

input profile

AECC Change [%]

Conductivity Change [%]

1.2 0.8 0.6 inverted from AECC

0.4 0.2 0 0.2

0.4

0.6

0.8

0.8 0.6 0.4 0.2 0 -0.2 0.001

-0.2 0

1

1

Depth [mm]

10

1000

Frequency [MHz] 1.2

1.2 Gaussian

1

input profile

AECC Change [%]

Conductivity Change [%]

0.1

0.8 0.6 inverted from AECC

0.4 0.2 0 -0.2 0

0.2

0.4

0.6

Depth [mm]

0.8

1

1 0.8 0.6 0.4 0.2 0 -0.2 0.001

0.1

10

1000

Frequency [MHz]

Flaw Detection Phasol Diagrams

Impedance Diagram 1

Normalized Reactance

0.8

conductivity (frequency)

lift-off 0.6 crack depth

0.4

ω1

flawless material

ω2 0.2

0

0

0.1

0.2 0.3 Normalized Resistance

0.4

apparent eddy current conductivity (AECC) decreases apparent eddy current lift-off (AECL) increases

0.5

Crack Contrast & Resolution Vic-3D simulation ao = 1 mm, ai = 0.75 mm, h = 1.5 mm austenitic stainless steel, σ = 2.5 %IACS, μr = 1

probe coil

f = 5 MHz, δ  0.19 mm

crack

Normalized AECC

1 -10% threshold

0.8 0.6 0.4 0.2 detection threshold

0 0 semi-circular crack

1

2 3 Flaw Length [mm]

4

5

Eddy Current of Small Fatigue Crack

probe coil crack

0.5”  0.5”, 2 MHz, 0.060”-diameter coil Al2024, 0.025-mil crack

Ti-6Al-4V, 0.026-mil-crack

Crystallographic Texture J  E

generally anisotropic  J1   1 J    0  2   J 3   0

0 2 0

0 0   3 

hexagonal (transversely isotropic)  J1   1 J    0  2   J 3   0

 E1  E   2  E3 

0 2 0

0  0    2 

cubic (isotropic)  J1   1 J    0  2   J 3   0

 E1  E   2  E3 

0 1 0

0 0  1 

 E1  E   2  E3 

x1 θ σn

σM

x3 σm

basal plane

x2

surface plane

1   2

σ1

conductivity normal to the basal plane

 n ()  1 cos 2    2 sin 2 

σ2

conductivity in the basal plane

θ

polar angle from the normal of the basal plane

 m ( )  1 sin 2    2 cos 2 

M  2  a ( )  絒 1 sin 2    2 (1  cos 2 )]

σm minimum conductivity in the surface plane σM maximum conductivity in the surface plane σa

average conductivity in the surface plane

Electric “Birefringence” Due to Texture 500 kHz, racetrack coil equiaxed GTD-111

1.05

1.40

1.04

1.38

Conductivity [%IACS]

Conductivity [%IACS]

highly textured Ti-6Al-4V plate

1.03 1.02 1.01 1.00

1.36 1.34 1.32 1.30

0

30 60 90 120 150 180 Azimuthal Angle [deg]

0

30 60 90 120 150 180 Azimuthal Angle [deg]

Grain Noise in Ti-6Al-4V 1”  1”, 2 MHz, 0.060”-diameter coil as-received billet material

solution treated and annealed

heat-treated, coarse

heat-treated, very coarse

heat-treated, large colonies

equiaxed beta annealed

Eddy Current versus Acoustic Microscopy

1”  1”, coarse grained Ti-6Al-4V sample 5 MHz eddy current

40 MHz acoustic

Inhomogeneity

AECC Images of Waspaloy and IN100 Specimens inhomogeneous Waspaloy

homogeneous IN100

4.2”  2.1”, 6 MHz

2.2”  1.1”, 6 MHz

conductivity range 1.38-1.47 %IACS

conductivity range 1.33-1.34 %IACS

±3 % relative variation

±0.4 % relative variation

Conductive Material Noise as-forged Waspaloy 1.50 1.48 1.46 AECC [%IACS]

1.44 1.42 1.40 1.38 1.36

Spot 1 (1.441 %IACS)

1.34

Spot 2 (1.428 %IACS) Spot 3 (1.395 %IACS)

1.32

Spot 4 (1.382% IACS)

1.30 0.1

1 Frequency [MHz] no (average) frequency dependence

10

Magnetic Susceptibility Material Noise 1”  1”, stainless steel 304 intact

0.51×0.26×0.03 mm3 edm notch

f = 0.1 MHz, ΔAECC  6.4 %

f = 0.1 MHz, ΔAECC  8.6 %

f = 5 MHz, ΔAECC  0.8 %

f = 5 MHz, ΔAECC  1.2 %

Impedance Phase Responses

Charlie Chong/ Fion Zhang

Eddy current inspection

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Phasor Diagram Steel

Al

Charlie Chong/ Fion Zhang

If the eddy current circuit is balanced in air and then placed on a piece of aluminum, the resistance component will increase (eddy currents are being generated in the aluminum and this takes energy away from the coil, which shows up as resistance) and the inductive reactance of the coil decreases (the magnetic field created by the eddy currents opposes the coil's magnetic field and the net effect is a weaker magnetic field to produce inductance). If a crack is present in the material, fewer eddy currents will be able to form and the resistance will go back down and the inductive reactance will go back up. Changes in conductivity will cause the eddy current signal to change in a different way.

Charlie Chong/ Fion Zhang

Impedance Plane Respond - Non magnetic materials

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Eddy current inspection

Charlie Chong/ Fion Zhang

ď Ž The resistance component R will increase (eddy currents are being generated in the aluminum and this takes energy away from the coil, which shows up as resistance) ď Ž The inductive reactance XL of the coil decreases (the magnetic field created by the eddy currents opposes the coil's magnetic field and the net effect is a weaker magnetic field to produce inductance).

Charlie Chong/ Fion Zhang

If a crack is present in the material, fewer eddy currents will be able to form and the resistance will go back down and the inductive reactance will go back up.

Charlie Chong/ Fion Zhang

Changes in conductivity will cause the eddy current signal to change in a different way.

Charlie Chong/ Fion Zhang

Discussion Topic: Discuss on “Changes in conductivity will cause the eddy current signal to change in a different way.”

Answer: Increase in conductivity will increase the intensity of eddy current on the surface of material, the strong eddy current generated will reduce the current of the coil, show-up as ↑ R &↓XL

Charlie Chong/ Fion Zhang

Magnetic Materials

Charlie Chong/ Fion Zhang

When a probe is placed on a magnetic material such as steel, something different happens. Just like with aluminum (conductive but not magnetic), eddy currents form, taking energy away from the coil, which shows up as an increase in the coils resistance. And, just like with the aluminum, the eddy currents generate their own magnetic field that opposes the coils magnetic field. However, you will note for the diagram that the reactance increases.

This is because the magnetic permeability of the steel concentrates the coil's magnetic field. This increase in the magnetic field strength completely overshadows the magnetic field of the eddy currents. The presence of a crack or a change in the conductivity will produce a change in the eddy current signal similar to that seen with aluminum.

Charlie Chong/ Fion Zhang

 The eddy currents form, taking energy away from the coil, which shows up as an increase in the coils resistance.  The reactance increases. This is because the magnetic permeability of the steel concentrates the coil's magnetic field.  This increase in the magnetic field strength completely overshadows the effects magnetic field of the eddy currents on decreasing the inductive reactance.

Charlie Chong/ Fion Zhang

This increase in the magnetic field strength completely overshadows the magnetic field of the eddy currents.

The inductive reactance XL of the coil decreases (the magnetic field created by the eddy currents opposes the coil's magnetic field and the net effect is a weaker magnetic field to produce inductance).

Charlie Chong/ Fion Zhang

The presence of a crack or a change in the conductivity will produce a change in the eddy current signal similar to that seen with aluminum. ď Ž If a crack is present in the material, fewer eddy currents will be able to form and the resistance will go back down and the inductive reactance will go back up ď Ž Changes in conductivity will cause the eddy current signal to change in a different way.

Charlie Chong/ Fion Zhang

Eddy current inspection The increase of Inductive Reactance: this is due to concentration of magnetic field by the effects magnetic permeability of steel

The increase in Resistance R: this was due to the decrease in current due to generation of eddy current, shown-up as increase in resistance R.

Charlie Chong/ Fion Zhang

Exercise: Explains the impedance plane responds for Aluminum and Steel Al: 1. Eddy current reduces coil current showup as ↑R,↓XL

1

2. Crack reduce eddy current, reduce the effects on R & XL 2 3 1

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3. Increase in conductivity increase eddy current, increasing the effects on R & XL Steel: 1. Eddy current reduces coil current showup as ↑R,↓XL. However net ↑XL increase, as magnetic permeability of the steel concentrates the coil's magnetic field

In the applet below, liftoff curves can be generated for several nonconductive materials with various electrical conductivities. With the probe held away from the metal surface, zero and clear the graph. Then slowly move the probe to the surface of the material. Lift the probe back up, select a different material and touch it back to the sample surface.

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Impedance Plane Respond – Fe, Cu, Al

Fe

Al Cu

Question: Why impedance plane respond of steel (Fe) in the same quadrant as the non-magnetic Cu and Al

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https://www.nde-ed.org/EducationResources/CommunityCollege/EddyCurrents/Instrumentation/Popups/applet3/applet3.htm

Experiment Generate a family of liftoff curves for the different materials available in the applet using a frequency of 10kHz. Note the relative position of each of the curves. Repeat at 500kHz and 2MHz. (Note: it might be helpful to capture an image of the complete set of curves for each frequency for comparison.)

1) Which frequency would be best if you needed to distinguish between two high conductivity materials?

2) Which frequency would be best if you needed to distinguish between two low conductivity materials?

The impedance calculations in the above applet are based on codes by Jack Blitz from "Electrical and Magnetic Methods of Nondestructive Testing," 2nd ed., Chapman and Hill

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http://en.wikipedia.org/wiki/Electrical_reactance

Hurray

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With phase analysis eddy current instruments, an operator can produce impedance plane loci plots or curves automatically on a flying dot oscilloscope or integral cathode ray tube. Such impedance plane plots can be presented for the following material conditions (as shown in Fig. 8): (1) (2) (3) (4) (5) (6) (7)

liftoff and edge effects, cracks, material separation and spacing, permeability, specimen thinning, conductivity and plating thickness.

Evaluation of these plots shows that ferromagnetic material conditions produce higher values of inductive reactance than values obtained from nonmagnetic material conditions. Hence the magnetic domain is at the upper quadrant of the impedance plane whereas nonmagnetic materials are in the lower quadrant. The separation of the two domains occurs at the inductive reactance values obtained with the coil removed from the conductor (sample); this is proportional to the value of the coil’s self-inductance L. Charlie Chong/ Fion Zhang

FIGURE 8. Impedance changes in relation to one another on impedance plane.

Legend Ca = crack in aluminum Cs = crack in steel Pa = plating (aluminum on copper) Pc = plating (copper on aluminum) Pn = plating (nonmagnetic) S = spacing between Al layers T = thinning in aluminum Îź = permeability Ďƒm = conductivity for magnetic materials Ďƒn = conductivity for nonmagnetic materials

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Electric & Magnetic Factors

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Conductivity

Magnetic (Permeability & Dimensions)

A. Heat treatment give the metal

A. Length of the test sample

B. Cold working performed on the metal

B. Thickness of the test sample

C. Aging process used on the metal

C. Cross sectional area of the test sample

D. Hardness Crack & discontinuities

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Characteristic Frequency fg

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31. The abscissa values on the impedance plane shown in Figure 2 are given in terms of: A. Absolute conductivity B. Normalized resistance C. Absolute inductance D. Normalized inductance

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32. In Figure 2 (an impedance diagram for solid nonmagnetic rod), the fg or characteristic frequency is calculated by the formula: A. fg= σμ/d² B. fg= δμ/d C. fg= 5060/σμd² D. fg= R/L 33. In Figure 2, a change in the f/fg ratio will result in: A. A change in only the magnitude of the voltage across the coil B. A change in only the phase of the voltage across the coil C. A change in both the phase and magnitude of the voltage across the coil D. No change in the phase or magnitude of the voltage across the coil

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34. In Figure 3, the solid curves are plots for different values of: A. Heat treatment B. Conductivity C. Fill factor D. Permeability

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3.1.2 Limiting Frequency fg of Encircling Coils Encircling coils are used more frequently than surface-mounted coils. With encircling coils, the degree of filling has a similar effect to clearance with surface-mounted coils. The degree of filling is the ratio of the test material cross-sectional area to the coil cross-sectional area. Figure 3.7 shows the effect of degree of filling on the impedance plane of the encircling coil. For tubes, the limiting frequency (point where ohmic losses of the material are the greatest) can be calculated precisely from Eq. (3.2):

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Introduction to Nondestructive Testing: A Training Guide, Second Edition, by Paul E. Mix

fg = 5056/(σ∙ di ∙ w∙ μr)

(3.2)

Where: fg = limiting frequency σ = conductivity di = inner diameter w = wall thickness μr (rel) = relative permeability For Solid Rod: fg = 5060/(σμrd 2)

(3.2)

Where: d= solid rod diameter

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Introduction to Nondestructive Testing: A Training Guide, Second Edition, by Paul E. Mix

Figure 4

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Figure 5

51. Which of the following is not a factor that affects the inductance of an eddy current test coil A. Diameter of coils L=ÎźoN2A/l B. Test frequency C. Overall shape of the coils D. Distance from other coils 52. The formula used to calculate the impedance of an eddy current test coil is: D

53. An out of phase condition between current and voltage: A. Can exist only in the primary winding of an eddy current coil B. Can exist only in the secondary winding of an eddy current coil C. Can exist in both the primary and secondary windings of an eddy current coil D. Exists only in the test specimen

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Inductance The increasing magnetic flux due to the changing current creates an opposing emf in the circuit.

The inductor resists the change in the current in the circuit. If the current changes quickly the inductor responds harshly.

If the current changes slowly the inductor barely notices. Once the current stops changing the inductor seems to disappear.

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http://sdsu-physics.org/physics180/physics196/Topics/inductance.html

Discussion Topic: What is Pulse Eddy Current

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Good Luck!

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Good Luck!

Charlie Chong/ Fion Zhang