eddy current maths

Electromagnetic Testing -Eddy Current Mathematics2014-DecemberMy ASNT Level III Pre-Exam Preparatory Self Study Notes外围学习中

Charlie Chong/ Fion Zhang

Fion Zhang at Shanghai2014/November

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

Charlie Chong/ Fion Zhang Shanghai 上海


Impedance Phasol Diagrams


Greek letter


Eddy Current Inspection Formula

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


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

V = I x R

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

Inductance of a solenoid is given by:

L=μoN2A/l https://en.wikipedia.org/wiki/Inductance


Phase Angle and Impedance

Phase angle is expressed as follows:

tan Φ = XL/R

Where:Φ = 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.


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 = MagneticFlux Density in Tesla, H = Magnetizing Force in Amps/meter.

Relative magnetic permeability is expressed as follows:

μ r = 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 non-ferrous materials.


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).


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.


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).


20,0000.003465Gold

60,00030,000

0.003820.00393

89.5100

Copper:Hard drawn· Annealed

120,0000.000013.24Constantin—0.003316.3Cobalt——55Chromium—0.003819Cadmium

70,0000.002-0.00728Brass

——

——

45-5030-45

Aluminum (alloys):· Soft-annealed· Heat-treated

30,0000.003959Aluminum (2S; pure)

TensileStrength

(lbs./sq. in.)

TemperatureCoefficient ofResistance**

RelativeConductivity*Metal

Conductivity & Resistivity

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


120,0000.00612-16Nickel150,0000.00041.45Nichrome160,0000.0024Monel

—0.00433.2Molybdenum00.000891.66Mercury

150,0000.000013.7Manganin33,0000.004—Magnesium3,0000.00397Lead

———

0.005——

17.72-1211.4

Iron:· Pure· Cast· Wrought



10,0000.003728.2Zinc500,0000.004528.9Tungsten130,000—5Titanium, 6A14V50,000—5Titanium4,0000.004213Tin

42,000-230,0000.004-0.0053-15Steel42,0000.0038106Silver

55,0000.00315Platinum

25,0000.001836Phosphor bronze150,0000.000145.3Nickel silver (18%)



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

Legendk = √(ωμσ) = electromagnetic wave propagation constant forconducting materialr = 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)


Legendk = √(ωμσ) = electromagnetic wave propagation constant forconducting materialr = 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


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.


Magnetic permeability of free space:

μ0 = 4 π × 10–7 H·m–1


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

We show magnetic flux with the Greek letter; Ф. We find it with following formula;Ф =B∙A ∙ cos ϴWhere Ф is the magnetic flux and unit of Ф is Weber (Wb)B is the magnetic field and unit of B is TeslaA is the area of the surface and unit of A is m2

Following pictures show the two different angle situation of magnetic flux.

ϴ

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) (b)



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 µ. Magnetic permeability is the distinguishing property of the matter, every matter has specific µ. Picture given below shows the behavior of magnetic field lines in vacuum and in two different matters having different µ.



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



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.



Magnetic Permeability



Standard Depth


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.


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


Current Density Change with Depth

The change in current density with depth is expressed as follows:

Jx = Jo e–x/δ

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 δ = standard depth of penetration in meters.


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.


Depth of Penetration & Current Density

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


Standard Depth Calculation

Where: μ = μ0 x μr


The applet below illustrates how eddy current density changes in a semi-infinite 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 = 3.14f = Test Frequency (Hz)μ = Magnetic Permeability (H/mm)σ = Electrical Conductivity (% IACS)


Defect Detection / Electrical conductivity measurement

1/e or 37% of surface density at target

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

Defect Detection 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.

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

(1/e)

(1/e)2

(1/e)3


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.


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.


Standard Depth of Penetration Versus Frequency Chart

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


Magnetic Field & Size of CoilTypically, 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

D

β0

0.1β0

0.1D


Flaw Detection DepthTo 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.


Phase Lag


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.


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


Frequency?????

Frequency is expressed as follows:

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

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


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.)


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.


Phase Lag

Where:β = phase lagX = distance below surfaceδ = standard depth of penetration

Eq. (4.2).


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

(1/e)

(1/e)2

(1/e)3

2δ

1δ

3δ


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.

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

Charlie Chong/ Fion Zhang 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 lagX = distance below surface in mm.δ = standard depth of penetration in mm.

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


Phase lag β = x/ δ radian

δ = (π fσμ) -½

β = x(π fσμ) -½


Impedance


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.

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


Reactance Voltage = Current x Inductive ReactanceE1 = I∙XL

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


The Inductive & Capacitive Reactance

XL = ωL = 2 πfLXC = 1/(ωC) = 1/ (2πfC)


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.


3.1.1 Induction and Reception FunctionThere are two methods of sensing changes in the eddy current characteristics:(a) The impedance method(b) The send receive method

Impedance methodIn 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


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.



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



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

, ω = 2πf


Eddy Impedance plane responses


Magnetism


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 longstraight 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

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


Phase Shifts


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.


Capacitor circuit:Current lead voltage by 90o

Inductor circuit:Current lagging voltage by 90o


Resonance Frequency


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.


Eddy current inspection

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


Balance Bridge Circuit


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.


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.


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.

FIG. 3.17. Common Testing Arrangement


At balance:

IAZ1 = IB Z3 , IA Z2 = IB Z4

IAZ1/ IA Z2 = IB Z3 / IB 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.

FIG. 3.17. Common Testing Arrangement

IA IB

IA


At balance:

V1=V1IAZ1 = IB Z3 , IAZ2 = IBZ4IAZ/ IA Z2 = IBZ3 / IBZ4



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


Subject on Balance Circuit- more reading


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.

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


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

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

C2R2

R3R1 L3

R4

Charlie Chong/ Fion Zhang http://www.allaboutcircuits.com/vol_1/chpt_8/10.html


Circuits Wheatstone Bridge Part 1

■ https://www.youtube.com/watch?v=Kf5XkK0465A


Conductivity Measurement


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 increasedelectrical conductivity. The influence of temperature on the resistivity of a metal can be determined from the following equation.

whereRt = resistivity of the metal at the test temperature,R0 = resistivity of the metal at standard temperatureα = resistivity temperature coefficientT = difference between the standard and test temperature (°C).

(4.3)


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/ρWhere:IACS = international annealed copper standardρ = resistivity (unit?)ρIACS = 1.724110-8 Ωm

(4.4)

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


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.

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.


Fill Factors


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 (4.6)

whereη = fill factorD1 = part diameterD2 = coil diameter


Thus the fill factor must be less than 1 since if η = 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%).


Frequency Selections


Probe and frequency selectionThe 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 57°. 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 28.5°.

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


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 istermed 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), andσ = the conductivity of the test material (% IACS).


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.


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.


Probes Frequency


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 titaniumalloys, the penetration would be excessive at these frequencies, and higher frequencies are required. Typically 2 MHz to 6 MHz should be used.

Al: .2MHz ~ .5MHzSS, Ni, Ti & Alloys: 2MHz ~ 6MHzFerromagnetic Mtls: ?


Eddy Impedance plane responses


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


FIG. 5.19. Impedance diagrams and the conductivity curve at three differentfrequencies, 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 100KHz 1000KHz


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).


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 lift-off curves for this and various other thicknesses are also shown.

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


Phase lag β = x/δ radian

δ = (πfσμ) -½


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 19° rotated to their approximate orientation on an eddy current instrument display.


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 ° 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 non-ferromagnetic support tested at f90.

Impedance Phasol Diagrams1. conductivity measurement2. permeability measurement3. metal thickness measurement4. coating thickness measurements5. flaw detection

Conductivity

constant frequency

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5Normalized Resistance

Nor

mal

ized

Rea

ctan

ce

StainlessSteel, 304

CopperAluminum, 7075-T6

Titanium, 6Al-4V

Magnesium, A280

Lead

Copper 70%,Nickel 30%

Inconel

Nickel

Conductivity versus Probe Impedance

IACS = International Annealed Copper Standard σIACS = 5.8107 Ω-1m-1 at 20 °C

ρIACS = 1.724110-8 Ωm

20

30

40

50

60

Con

duct

ivity

[% IA

CS]

T3 T4T6

T0

2014

T4

T6T0

6061

T6

T73T76

T0

70752024

T3 T4

T6

T72T8

T0

Various Aluminum Alloys

Conductivity versus Alloying & Temper

• high accuracy ( 0.1 %)

• controlled penetration depth

specimen

eddy currents

probe coil

magnetic field

0

0.2

0.4

0.6

0.8

1.0

0.10 0.2 0.3 0.4 0.5

lift-offcurves

conductivity

curve(frequency)

Normalized Resistance

Nor

mal

ized

Rea

ctan

ce

= 0

= s

1

23

4


Nor

mal

ized

Rea

ctan

ce

Apparent Eddy Current Conductivity

inductive(low frequency)

capacitive(high frequency)

“Horizontal” Component“V

ertic

al”

Com

pone

nt

lift-off

.

conductivity

σ2

σ1

σ

ℓ = s ℓ = 0

“Horizontal” Component

“Ver

tical

”C

ompo

nent

.

conductivity

lift-off

σ2

σ1

σ

ℓ = s ℓ = 0

Lift-Off Curvature

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.1 1 10 100Frequency [MHz]

Rel

ativ

e ΔA

ECC

[%] .

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0


Rel

ativ

e ΔA

ECC

[%] .

63.5 μm50.8 μm38.1 μm25.4 μm19.1 μm12.7 μm6.4 μm0.0 μm

-100

1020304050607080


AEC

L [μ

m]

.

-100

1020304050607080


AEC

L [μ

m]

. .

63.5 μm50.8 μm38.1 μm25.4 μm19.1 μm12.7 μm6.4 μm0.0 μm

4 mm diameter 8 mm diameter

1.5 %IACS 1.5 %IACS

Inductive Lift Off Effects

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0


AEC

C C

hang

e [%

] .

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

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

conductivity spectra comparison on IN718 specimens of different peening intensities.

Instrument Calibration

Permeability Phasol Diagram

0

0.2

0.4

0.6

0.8

1.0

0.10 0.2 0.3 0.4 0.5

lift-off

frequency(conductivity)

Normalized ResistanceN

orm

aliz

ed R

eact

ance

permeability


Nor

mal

ized

Rea

ctan

ce

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1 1.2

2

3

1

µr = 4permeability

moderately high susceptibility low susceptibility

paramagnetic materials with small ferromagnetic phase content

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

frequency(conductivity)

Magnetic Susceptibility

10-4

10-3

10-2

10-1

100

101

0 10 20 30 40 50 60Cold Work [%]

Mag

netic

Sus

cept

ibili

ty

SS304L

IN276

IN718

SS305

SS304SS302

IN625

cold work (plastic deformation at room temperature) causesmartensitic (ferromagnetic) phase transformation

in austenitic stainless steels

Magnetic Susceptibility versus Cold Works

Metal Thickness Phasol Diagram

thickness loss due to corrosion, erosion, etc.

probe coil

scanning

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6

thickplate


Nor

mal

ized

Rea

ctan

ce

thinplate

lift-off

thinning

-0.2

0

0.2

0.4

0.6

0.8

1

0 1 2 3Depth [mm]

Re

{ F

}

f = 0.05 MHzf = 0.2 MHzf = 1 MHz

aluminum (σ = 46 %IACS)

/ /( ) x i xF x e e

Thickness versus Normalized Impedance

1.0

1.1

1.2

1.3

1.4

0.1 1 10Frequency [MHz]

Con

duct

ivity

[%IA

CS]

1.0 mm1.5 mm2.0 mm2.5 mm3.0 mm3.5 mm4.0 mm5.0 mm6.0 mm

thickness

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

Thickness Correction

Coating Thickness Phasol Diagrams

non-conductingcoating

probe coil, ao

t

d

ℓ

conducting substrate

ao > t, d > δ, AECL = ℓ + t

-100

1020304050607080


AEC

L [μ

m]

-100

1020304050607080


AEC

L [μ

m]

63.5 μm50.8 μm

38.1 μm25.4 μm

19.1 μm12.7 μm

6.4 μm

0 μm

ao = 4 mm, simulatedlift-off:

ao = 4 mm, experimental

Non-Conductive Coating

conductingcoating

probe coil, ao

t

d

ℓ

conducting substrate (µs,σs)

approximate: large transducer, weak perturbation

equivalent depth:

e1AECC( )

2 s sf

f

21( ) AECC

4 s sz

z

se 2

analytical: Fourier decomposition (Dodd and Deeds)

numerical: finite element, finite difference, volume integral, etc.(Vic-3D, Opera 3D, etc.)

zJe

z = δe

Conductive Coating

AEC

C C

hang

e [%

]

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.001 0.1 10 1000

Frequency [MHz]

AEC

C C

hang

e [%

]

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.001 0.1 10 1000

Frequency [MHz]

Depth [mm]

Con

duct

ivity

Cha

nge

[%]

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

input profile

inverted from AECC

uniform

Depth [mm]

Con

duct

ivity

Cha

nge

[%]

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

input profile

inverted fromAECC

Gaussian

0.254-mm-thick surface layer of 1% excess conductivity

Simplistic Inversion of AECC Spectra

Flaw Detection Phasol Diagrams


0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

conductivity(frequency)

crackdepth

flawlessmaterial

ω1

lift-off

Nor

mal

ized

Rea

ctan

ce

ω2

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

Impedance Diagram

probe coil

crack

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5Flaw Length [mm]

Nor

mal

ized

AEC

C

semi-circular crack

-10% threshold

detectionthreshold

ao = 1 mm, ai = 0.75 mm, h = 1.5 mmaustenitic stainless steel, σ = 2.5 %IACS, μr = 1

Vic-3D simulation

f = 5 MHz, δ 0.19 mm

Crack Contrast & Resolution

Al2024, 0.025-mil crack Ti-6Al-4V, 0.026-mil-crack

0.5” 0.5”, 2 MHz, 0.060”-diameter coil

probe coil

crack

Eddy Current of Small Fatigue Crack

J E

1 1 1

2 2 2

3 3 3

0 00 00 0

J EJ EJ E

generally anisotropic hexagonal (transversely isotropic)

1 1 1

2 2 2

3 2 3

0 00 00 0

J EJ EJ E

cubic (isotropic)

1 1 1

2 1 2

3 1 3

0 00 00 0

J EJ EJ E

σ1 conductivity normal to the basal plane

σ2 conductivity in the basal plane

θ polar angle from the normal of the basal plane

σm minimum conductivity in the surface plane

σM maximum conductivity in the surface plane

σa average conductivity in the surface plane2 2

a 1 2( ) 絒 sin (1 cos )]

2 2n 1 2( ) cos sin

M 2

1 2

2 2m 1 2( ) sin cos

x1

x3

x2basal plane

θ

surface plane

σnσm

σM

Crystallographic Texture

1.00

1.01

1.02

1.03

1.04

1.05

0 30 60 90 120 150 180Azimuthal Angle [deg]

Con

duct

ivity

[%IA

CS]

highly textured Ti-6Al-4V plate equiaxed GTD-111

1.30

1.32

1.34

1.36

1.38

1.40

0 30 60 90 120 150 180Azimuthal Angle [deg]

Con

duct

ivity

[%IA

CS]

500 kHz, racetrack coil

Electric “Birefringence” Due to Texture

as-received billet material solution treated and annealed heat-treated, coarse

heat-treated, very coarse heat-treated, large colonies equiaxed beta annealed

1” 1”, 2 MHz, 0.060”-diameter coil

Grain Noise in Ti-6Al-4V

5 MHz eddy current 40 MHz acoustic

1” 1”, coarse grained Ti-6Al-4V sample

Eddy Current versus Acoustic Microscopy

AECC Images of Waspaloy and IN100 Specimens

homogeneous IN100

2.2” 1.1”, 6 MHz

conductivity range 1.33-1.34 %IACS

±0.4 % relative variation

inhomogeneous Waspaloy

4.2” 2.1”, 6 MHz

conductivity range 1.38-1.47 %IACS

±3 % relative variation

Inhomogeneity

1.30

1.32

1.34

1.36

1.38

1.40

1.42

1.44

1.46

1.48

1.50

0.1 1 10Frequency [MHz]

AEC

C [%

IAC

S]

Spot 1 (1.441 %IACS)



Spot 4 (1.382% IACS)

as-forged Waspaloy

no (average) frequency dependence

Conductive Material Noise

1” 1”, stainless steel 304

f = 0.1 MHz, ΔAECC 6.4 %

f = 5 MHz, ΔAECC 0.8 %

intact

f = 0.1 MHz, ΔAECC 8.6 %

f = 5 MHz, ΔAECC 1.2 %

0.51×0.26×0.03 mm3 edm notch

Magnetic Susceptibility Material Noise


Impedance Phase Responses


Phasor Diagram

Al

Steel


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.


Impedance Plane Respond - Non magnetic materials


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)

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).


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.


DiscussionTopic: 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


Magnetic Materials


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.


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.


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).


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. 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.



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.

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


Exercise: Explains the impedance plane responds for Aluminum andSteel

Al:1. Eddy current reduces coil current show-up as ↑R,↓XL

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

3. Increase in conductivity increase eddy current, increasing the effects on R & XL

Steel:1. Eddy current reduces coil current show-up as ↑R,↓XL. However net ↑XL increase, as magnetic permeability of the steel concentrates the coil's magnetic field

1

23

1


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.


Impedance Plane Respond – Fe, Cu, Al

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

Fe

Al

Cu

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


ExperimentGenerate 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

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


Hurray


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) liftoff and edge effects, (2) cracks, (3) material separation and spacing, (4) permeability, (5) specimen thinning, (6) conductivity and (7) 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.


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

LegendCa = crack in aluminumCs = crack in steelPa = plating (aluminum on copper)Pc = plating (copper on aluminum)Pn = plating (nonmagnetic)S = spacing between Al layersT = thinning in aluminumμ = permeabilityσm = conductivity for magnetic materialsσn = conductivity for nonmagnetic materials


Electric & Magnetic Factors


A. Length of the test sampleB. Thickness of the test sampleC. Cross sectional area of the test sample

A. Heat treatment give the metalB. Cold working performed on the metalC. Aging process used on the metalD. Hardness

Crack & discontinuities

Magnetic(Permeability & Dimensions)

Conductivity


Characteristic Frequency fg


31. The abscissa values on the impedance plane shown in Figure 2 are given in terms of:A. Absolute conductivityB. Normalized resistanceC. Absolute inductanceD. Normalized inductance


32. In Figure 2 (an impedance diagram for solid nonmagnetic rod), the fg or characteristic frequency is calculated by the formula:A. fg= σμ/d²B. fg= δμ/dC. fg= 5060/σμd²D. 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 coilB. A change in only the phase of the voltage across the coilC. A change in both the phase and magnitude of the voltage across the

coilD. No change in the phase or magnitude of the voltage across the coil


34. In Figure 3, the solid curves are plots for different values of:A. Heat treatmentB. ConductivityC. Fill factorD. Permeability


3.1.2 Limiting Frequency fg of Encircling Coils

Encircling coils are used more frequently than surface-mounted coils. Withencircling coils, the degree of filling has a similar effect to clearance withsurface-mounted coils. The degree of filling is the ratio of the test materialcross-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. Fortubes, the limiting frequency (point where ohmic losses of the materialare the greatest) can be calculated precisely from Eq. (3.2):

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

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


Figure 4

Charlie C

hong/ Fion Zhang

Figure 5


51. Which of the following is not a factor that affects the inductance of an eddy current test coilA. Diameter of coilsB. Test frequency L=μoN2A/lC. Overall shape of the coilsD. 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 coilB. Can exist only in the secondary winding of an eddy current coilC. Can exist in both the primary and secondary windings of an eddy current coilD. Exists only in the test specimen


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.

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


DiscussionTopic: What is Pulse Eddy Current


Good Luck!

eddy current maths

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