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

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Charlie Chong/ Fion Zhang

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Fion Zhang at Shanghai
2014/November
http://meilishouxihu.blog.163.com/
Charlie Chong/ Fion Zhang
Shanghai 上海

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Charlie Chong/ Fion Zhang
Impedance Phasol Diagrams

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Impedance Phasol Diagrams

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Charlie Chong/ Fion Zhang

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Charlie Chong/ Fion Zhang

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Charlie Chong/ Fion Zhang

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Greek letter

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

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Charlie Chong/ Fion Zhang https://www.nde-ed.org/GeneralResources/Formula/ECFormula/ECFormula.htm

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Charlie Chong/ Fion Zhang https://www.nde-ed.org/GeneralResources/Formula/ECFormula/ECFormula.htm

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Charlie Chong/ Fion Zhang https://www.nde-ed.org/GeneralResources/Formula/ECFormula/ECFormula.htm

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Charlie Chong/ Fion Zhang https://www.nde-ed.org/GeneralResources/Formula/ECFormula/ECFormula.htm

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Units

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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 μ
o
N
2
A/l https://en.wikipedia.org/wiki/Inductance

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Phase Angle and Impedance
Phase angle is expressed as follows:
tan Φ X
L
/R
Where:
Φ Phase Angle in degrees X
L
Inductive Reactance in ohms and R
Resistance in ohms.
Impedance is defined as follows:
Where Z Impedance in ohms R Resistance in ohms and X
L
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:
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.

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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 /A σor 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
ACross 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 mm
2
and having a
resistance of 17.241 m Ω 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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20000 0.0034 65 Gold
60000
30000
0.00382
0.00393
89.5
100
Copper:
Hard drawn
· Annealed
120000 0.00001 3.24 Constantin
— 0.0033 16.3 Cobalt
— — 55 Chromium
— 0.0038 19 Cadmium
70000 0.002-0.007 28 Brass
—
—
—
—
45-50
30-45
Aluminum alloys:
· Soft-annealed
· Heat-treated
30000 0.0039 59
Aluminum 2S
pure
Tensile
Strength
lbs./sq. in.
Temperature
Coefficient of
Resistance
Relative
Conductivity
Metal
Conductivity Resistivity
http://www.wisetool.com/designation/cond.htm

Charlie Chong/ Fion Zhang
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 2 πf where f
frequency Hz
√ ω L
0
G equivalent of √ ωμσ for
simplified electrical circuits
where G conductance S and L
0
inductance in air H

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Charlie Chong/ Fion Zhang
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 L
0
G equivalent of √ ωμσ for simplified electrical circuits
where G conductance S and L
0
inductance in air H
Keywords:
δ √2/ωμσ 1/ √ωμσ 1/k 1/ π f μσ
½
For √ ω L
0
G √ ωμσ L
0
G 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
μ
0
4 π× 10
–7
H·m
–1
.

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Magnetic permeability of free space:
μ
0
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.
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 m
2
Following pictures show the two different angle situation of magnetic flux.
ϴ
http://www.physicstutorials.org/home/magnetism/magnetic-flux-and-magnetic-permeability

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

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

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Magnetic permeability of the vacuum is denoted by µ
o
and has value
µ
o
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.
µ
r
µ/µ
o
http://www.physicstutorials.org/home/magnetism/magnetic-flux-and-magnetic-permeability

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

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

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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:
J
x
J
o
e
–x/ δ
Where J
x
Current Density at distance x below the surface amps/m
2
J0
Current Density at the surface amps/m
2
e the base of the natural
logarithm Eulers number 2.71828 x Distance below the surface and
δ 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
http://www.suragus.com/en/company/eddy-current-testing-technology

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Standard Depth Calculation
Where: μ μ
0
x μ
r

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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 3.14
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
1/e
3
or 5 of
surface density at
material interface
Defect Detection Electrical conductivity measurement

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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

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Sensitivity to defects depends on eddy current density at defect location.
Although eddy currents penetrate deeper than one standard depth δof
penetration they decrease rapidly with depth. At two standard depths of
penetration 2 δ eddy current density has decreased to 1/ e
2
or 13.5 of
the surface density. At three depths 3 δ 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 3 δ 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 3 δ.

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Standard Depth of Penetration Versus Frequency Chart
https://www.nde-ed.org/GeneralResources/Formula/ECFormula/DepthFreqChart/ECDepth.html

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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.
DCoil diameter
D
β
0
0.1 β
0
0.1D

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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 μ Magnetic
Permeability Henries per meter and σ conductivity in S/m.
http://www.azom.com/article.aspxArticleID109534

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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
Where:
β phase lag
X distance below surface
δ standard depth of penetration
Eq. 4.2.

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FIG. 4.1. Eddy current distribution with depth in a thick plate and resultant phase lag.
1/e
1/e
2
1/e
3
2 δ
1 δ
3 δ

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

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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 lag
X distance below surface in mm.
δ standard depth of penetration in mm.

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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 2f
90
can be seen.
Charlie Chong/ Fion Zhang
Phase separation

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Phase lag β x/ δ radian
δ π f σμ
-½
β x π f σμ -½

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Impedance

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Inductive reactance XL in terms of frequency and inductance is given
by:
X
L
ω∙L 2 πf ∙L
Similarly the Capacitance Reactance:
X
C
1/ ω∙C 1/ 2 πf ∙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

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Reactance Voltage Current x Inductive Reactance
E
1
I ∙X
L
http://www.learnabout-electronics.org/ac_theory/lcr_series_92.php

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The Inductive Capacitive Reactance
X
L
ωL 2 πfL
X
C
1/ ωC 1/ 2 πfC

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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| R
2
+ X
L
2
½
X
c
was assume nil
Where: Z impedance R resistance X
L
inductive reactance

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and the impedance phase is calculated as:
θ tan
-1
X
L
/ R
Where: θ phase angle R resistance X
L
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
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/impcom.html

Charlie Chong/ Fion Zhang
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
http://electrical4u.com/magnetic-flux-density-definition-calculation-formula/

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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 90
o
Inductor circuit:
Current lagging
voltage by 90
o

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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 X
c
and X
L
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:
I
1
Z
1
I
2
Z
2
and I
1
Z
3
I
2
Z
4
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

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At balance:
I
A
Z
1
I
B
Z
3
I
A
Z
2
I
B
Z
4
I
A
Z
1
/ I
A
Z
2
I
B
Z
3
/ I
B
Z
4
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
I
A
I
B
I
A

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Charlie Chong/ Fion Zhang
At balance:
V
1
V
1
I
A
Z
1
I
B
Z
3
I
A
Z
2
I
B
Z
4
I
A
Z/ I
A
Z
2
I
B
Z
3
/ I
B
Z
4

slide 88:

Charlie Chong/ Fion Zhang
Impedance Phasol Diagrams
https://www.youtube.com/watchv2XuRGrGZ_9M

slide 89:

Charlie Chong/ Fion Zhang
Subject on Balance Circuit- more reading

slide 90:

Charlie Chong/ Fion Zhang
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

slide 91:

Charlie Chong/ Fion Zhang
R3 and L3 can then be calculated based on the values of the other
components:
http://en.wikipedia.org/wiki/Maxwell_bridge
C2
R2
R3
R1 L3
R4

slide 92:

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

slide 93:

Charlie Chong/ Fion Zhang
Circuits Wheatstone Bridge Part 1
■ https://www.youtube.com/watchvKf5XkK0465A

slide 94:

Charlie Chong/ Fion Zhang
Conductivity
Measurement

slide 95:

Charlie Chong/ Fion Zhang
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.
where
R
t
resistivity of the metal at the test temperature
R
0
resistivity of the metal at standard temperature
α resistivity temperature coefficient
T difference between the standard and test temperature °C.
4.3

slide 96:

Charlie Chong/ Fion Zhang
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
Where:
IACS international annealed copper standard
ρ resistivity unit
ρ
IACS
1.7241 10
-8
Ωm
4.4
http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

slide 97:

Charlie Chong/ Fion Zhang
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 mm
2
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

slide 98:

Charlie Chong/ Fion Zhang
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.

slide 99:

Charlie Chong/ Fion Zhang http://www.centurionndt.com/Technical20Papers/condarticle.htm

slide 100:

Charlie Chong/ Fion Zhang http://www.centurionndt.com/Technical20Papers/condarticle.htm

slide 101:

Charlie Chong/ Fion Zhang http://www.centurionndt.com/Technical20Papers/condarticle.htm

slide 102:

Charlie Chong/ Fion Zhang http://www.centurionndt.com/Technical20Papers/condarticle.htm

slide 103:

Charlie Chong/ Fion Zhang
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.

slide 104:

Charlie Chong/ Fion Zhang
Fill Factors

slide 105:

Charlie Chong/ Fion Zhang
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 D
1
/D
2
2
4.5
For an internal coil:
Fill Factor η D
2
/D
1
2
4.6
where
η fill factor
D
1
part diameter
D
2
coil diameter

slide 106:

Charlie Chong/ Fion Zhang
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.

slide 107:

Charlie Chong/ Fion Zhang
Frequency Selections

slide 108:

Charlie Chong/ Fion Zhang
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 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.

slide 109:

Charlie Chong/ Fion Zhang
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 f
90
. By substituting t 0.8 δ into the standard depth of penetration
formula and changing Hz to kHz the following formula is obtained:
f
90
280/ t
2
σ 5.1
Where:
f
90
the operating frequency kHz
t the thickness or depth of material to be tested mm and
σ the conductivity of the test material IACS.

slide 110:

Charlie Chong/ Fion Zhang
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.

slide 111:

Charlie Chong/ Fion Zhang
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.

slide 112:

Charlie Chong/ Fion Zhang
Probes Frequency

slide 113:

Charlie Chong/ Fion Zhang
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:

slide 114:

Charlie Chong/ Fion Zhang
Impedance Phasol
Diagrams

slide 115:

Charlie Chong/ Fion Zhang
Eddy Impedance plane responses

slide 116:

Charlie Chong/ Fion Zhang

slide 117:

Charlie Chong/ Fion Zhang
FIGURE 11. Measured conductivity locus with conductivity expressed in
siemens per meter percentages of International Annealed Copper Standard

slide 118:

Charlie Chong/ Fion Zhang
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 100KHz 1000KHz

slide 119:

Charlie Chong/ Fion Zhang

slide 120:

Charlie Chong/ Fion Zhang

slide 121:

Charlie Chong/ Fion Zhang

slide 122:

Charlie Chong/ Fion Zhang
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.

slide 123:

Charlie Chong/ Fion Zhang
FIG. 5.25. Impedance diagram showing the conductivity curve and the
thickness curve for brass at a frequency of 120 kHz the f
90
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.

slide 124:

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 2f
90
can be seen.
Charlie Chong/ Fion Zhang
Phase separation

slide 125:

Charlie Chong/ Fion Zhang
Phase lag β x/ δ radian
δ πfσμ
-½

slide 126:

Charlie Chong/ Fion Zhang
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.

slide 127:

Charlie Chong/ Fion Zhang
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 f
90
.

0
0.2
0.4
0.6
0.8
1.0
0.1 0 0.2 0.3 0.4 0.5
lift-off
frequency
conductivity
Normalized Resistance
Normalized Reactance
permeability
Normalized Resistance
Normalized Reactance
0
1
2
3
4
0 0.2 0.4 0.6 0.8 1 1.2
2
3
1
µ
r
4
permeability
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

slide 138:

10
-4
10
-3
10
-2
10
-1
10
0
10
1
010 20 30 40 50 60
Cold Work
Magnetic Susceptibility
SS304L
IN276
IN718
SS305
SS304
SS302
IN625
cold work plastic deformation at room temperature causes
martensitic ferromagnetic phase transformation
in austenitic stainless steels
Magnetic Susceptibility versus Cold Works

slide 139:

Metal Thickness Phasol Diagram

slide 140:

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
thick
plate
Normalized Resistance
Normalized Reactance
thin
plate
lift-off
thinning
-0.2
0
0.2
0.4
0.6
0.8
1
01 2 3
Depth mm
Re F
f 0.05 MHz
f 0.2 MHz
f 1 MHz
aluminum σ 46 IACS
//
x ix
Fx e e
Thickness versus Normalized Impedance

slide 141:

1.0
1.1
1.2
1.3
1.4
0.1 1 10
Frequency MHz
Conductivity IACS
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
thickness
Vic-3D simulation Inconel plates σ 1.33 IACS
a
o
4.5 mm a
i
2.25 mm h 2.25 mm
Thickness Correction

slide 142:

Coating Thickness Phasol Diagrams

slide 143:

non-conducting
coating
probe coil a
o
t
d
ℓ
conducting substrate
a
o
t d δ AECL ℓ + t
-10
0
10
20
30
40
50
60
70
80
0.1 1 10 100
Frequency MHz
AECL μm
-10
0
10
20
30
40
50
60
70
80
0.1 1 10 100
Frequency MHz
AECL μm
63.5 μm
50.8 μm
38.1 μm
25.4 μm
19.1 μm
12.7 μm
6.4 μm
0 μm
a
o
4 mm simulated
lift-off:
a
o
4 mm experimental
Non-Conductive Coating

slide 144:

conducting
coating
probe coil a
o
t
d
ℓ
conducting substrate µ
s
σ
s
approximate: large transducer weak perturbation
equivalent depth:
e
1
AECC
2
s s
f
f
2
1
AECC
4
s s
z
z
s
e
2
analytical: Fourier decomposition Dodd and Deeds
numerical: finite element finite difference volume integral etc.
Vic-3D Opera 3D etc.
z
J
e
z δ
e
Conductive Coating

probe coil
crack
0
0.2
0.4
0.6
0.8
1
01 2 3 4 5
Flaw Length mm
Normalized AECC
semi-circular crack
-10 threshold
detection
threshold
a
o
1 mm a
i
0.75 mm h 1.5 mm
austenitic stainless steel σ 2.5 IACS μ
r
1
Vic-3D simulation
f 5 MHz δ 0.19 mm
Crack Contrast Resolution

slide 149:

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

slide 150:

JE
11 1
22 2
333
00
00
00
JE
JE
JE
generally anisotropic hexagonal transversely isotropic
11 1
22 2
323
00
00
00
JE
JE
JE
cubic isotropic
11 1
21 2
313
00
00
00
JE
JE
JE
σ
1
conductivity normal to the basal plane
σ
2
conductivity in the basal plane
θ polar angle from the normal of the basal plane
σ
m
minimum conductivity in the surface plane
σ
M
maximum conductivity in the surface plane
σ
a
average conductivity in the surface plane
22
a1 2
絒 sin 1 cos
22
n1 2
cos sin
M2
12
22
m1 2
sin cos
x
1
x
3
x
2
basal plane
θ
surface plane
σ
n
σ
m
σ
M
Crystallographic 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

slide 153:

5 MHz eddy current 40 MHz acoustic
1” 1” coarse grained Ti-6Al-4V sample
Eddy Current versus Acoustic Microscopy

slide 154:

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

slide 155:

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 10
Frequency MHz
AECC IACS
Spot 1 1.441 IACS
Spot 2 1.428 IACS
Spot 3 1.395 IACS
Spot 4 1.382 IACS
as-forged Waspaloy
no average frequency dependence
Conductive Material Noise

slide 156:

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 mm
3
edm notch
Magnetic Susceptibility Material Noise

slide 157:

Charlie Chong/ Fion Zhang
Impedance Phase
Responses

slide 158:

Charlie Chong/ Fion Zhang
Eddy current inspection

slide 159:

Charlie Chong/ Fion Zhang
Phasor Diagram
Al
Steel

slide 160:

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
coils 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.

slide 161:

Charlie Chong/ Fion Zhang
Impedance Plane Respond - Non magnetic materials

slide 162:

Charlie Chong/ Fion Zhang
Eddy current inspection

slide 163:

Charlie Chong/ Fion Zhang
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 X
L
of the coil decreases
the magnetic field created by the eddy currents opposes the coils
magnetic field and the net effect is a weaker magnetic field to
produce inductance.

slide 164:

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.

slide 165:

Charlie Chong/ Fion Zhang
Changes in conductivity will cause the eddy current signal to
change in a different way.

slide 166:

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 ↓X
L

slide 167:

Charlie Chong/ Fion Zhang
Magnetic Materials

slide 168:

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 coils
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.

slide 169:

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 coils magnetic field.
This increase in the magnetic field strength completely overshadows
the effects magnetic field of the eddy currents on decreasing the
inductive reactance.

slide 170:

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 coils magnetic
field and the net effect is a weaker magnetic field to produce inductance.

slide 171:

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.
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.

slide 172:

Charlie Chong/ Fion Zhang
Eddy current inspection
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

slide 173:

Charlie Chong/ Fion Zhang
Exercise: Explains the impedance plane responds for Aluminum and
Steel
Al:
1. Eddy current reduces coil current show-
up as ↑R ↓X
L
2. Crack reduce eddy current reduce the
effects on R X
L
3. Increase in conductivity increase eddy
current increasing the effects on R X
L
Steel:
1. Eddy current reduces coil current show-
up as ↑R ↓X
L
. However net ↑X
L
increase
as magnetic permeability of the steel
concentrates the coils magnetic field
1
2
3
1

slide 174:

Charlie Chong/ Fion Zhang
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.

slide 175:

Charlie Chong/ Fion Zhang
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

slide 176:

Charlie Chong/ Fion Zhang
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
http://en.wikipedia.org/wiki/Electrical_reactance

slide 177:

Charlie Chong/ Fion Zhang
Hurray

slide 178:

Charlie Chong/ Fion Zhang
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.

slide 179:

Charlie Chong/ Fion Zhang
FIGURE 8. Impedance changes in relation to one another on impedance
plane.
Legend
C
a
crack in aluminum
C
s
crack in steel
P
a
plating aluminum on copper
P
c
plating copper on aluminum
P
n
plating nonmagnetic
S spacing between Al layers
T thinning in aluminum
μ permeability
σ
m
conductivity for magnetic materials
σ
n
conductivity for nonmagnetic materials

slide 180:

Charlie Chong/ Fion Zhang
Electric Magnetic
Factors

slide 181:

Charlie Chong/ Fion Zhang
A. Length of the test sample
B. Thickness of the test sample
C. Cross sectional area of the test sample
A. Heat treatment give the metal
B. Cold working performed on the metal
C. Aging process used on the metal
D. Hardness
Crack discontinuities
Magnetic
Permeability Dimensions
Conductivity

slide 182:

Charlie Chong/ Fion Zhang
Characteristic Frequency
fg

slide 183:

Charlie Chong/ Fion Zhang
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

slide 184:

Charlie Chong/ Fion Zhang
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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Charlie Chong/ Fion Zhang
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 f
g
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:
Introduction to Nondestructive Testing: A Training Guide Second Edition by Paul E. Mix

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f
g
5056/ σ∙ d
i
∙ w∙μ
r
3.2
Where:
f
g
limiting frequency
σ conductivity
d
i
inner diameter
w wall thickness
μ
r
rel relative permeability
For Solid Rod:
fg 5060/ σμ
r
d
2
3.2
Where:
d solid rod diameter
Introduction to Nondestructive Testing: A Training Guide Second Edition by Paul E. Mix

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Figure 4

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Figure 5

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51. Which of the following is not a factor that affects the inductance of an eddy current
test coil
A. Diameter of coils
B. Test frequency L μ
o
N
2
A/l
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.
http://sdsu-physics.org/physics180/physics196/Topics/inductance.html

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Discussion
Topic: What is Pulse Eddy Current

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Good Luck

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Charlie Chong/ Fion Zhang
Good Luck

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