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ANDE Course Electric, Magnetic and Electromagnetic Techniques

Part 1

October 15, 2009 C.V.Krishnamurthy

Electromagnetic Spectrum

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Statics, Dynamics and Waves

Quasistatics

Frequency, f Lightdc

Dynamics

Statics

Statics: f = 0; dc (time derivatives vanish)Dynamics: No restriction; complete Maxwells equations;

Electromagnetic wavesQuasistatics: Low-frequency extension of statics, or

low-frequency approximation of dynamics; Non-radiative

Overview

Electric fields Capacitive

Conductive

Magnetic fields MFL

Barkhausen Noise

Electromagnetic fields Eddy current (low frequencies)

Radiative (high frequencies)

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Faradays Law

E dl d

dtC B dSS dS

SC

B

Voltage around C, also known as electromotive

force (emf) around C (but not really a force),

2 2Wb m m , or Wb.Magnetic flux crossing S,

Time rate of decrease of magnetic flux crossing S,

Right-hand screw Rule The magnetic flux crossing the surface S is to be evaluated toward that side of S a right-hand screw advances as it is turned in the sense of C.

C

A loop of wire coinciding along the imaginary contour C will result in a current flowing in the wire.

Lenzs Law States that the sense of the induced emf is such that any current it produces, if the closed path were a loop of wire, tends to oppose the change in the magnetic flux that produces it. Thus the magnetic flux produced by the induced current and that is bounded by C must be such that it opposes the change in the magnetic flux producing the induced emf.

B

Et

BvF qLorentz force on a current carrying wire is :

The emf is known as motional emf.

Amperes Law

H dl C J dS

d

dtS D dSS

dS

SC

J, D

Magnetomotive force (only by analogy with electromotive force),

A m m, or A.

Current due to flow of charges crossing S,

2 2A m m , or A.

Displacement flux, or electric flux, crossing S,

2 2C m m , or C.

Time rate of increase of displacement flux crossing S, or, displacement current crossing S,

C s, or A.

Right-hand screw rule applies.

DH J

t

J dS=S1 I but J dS =S2

0

D dS =S1 0 but D dS S2

0

d

dtD dS must be I

S2

so that H dlC is unique.

C

S1

S2

I(t)

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Gausss Law and

B dS = 0SD dS S dvV

Magnetic flux emanating from a closed surface S = 0.

B 0Solenoidal property of magnetic field lines.

aaa

J t 0

J dS +d

dt dv 0

VSCurrent due to flow of charges emanating from a closed surface S = Time rate of decrease of charge enclosed by S.

ContinuityEquation

LAW OF CONSERVATION OF CHARGE

D

Displacement flux emanating from a closed surface S = charge contained in the volume bounded by S = charge enclosed by S.

Maxwells Equations

B

Et

DH J

t

aaa

J t 0

0 B

D

Faradays Law

Amperes Circuital Law

Gauss Law for the Electric Field

Continuity Equation

Gauss Law for the Magnetic Field

E dl = C

d

dtB dSS

H dl =C J dS+

d

dtS D dSS

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Radiative and Non-RadiativeElectromagnetic Fields

Non-radiative case:Electric field lines are perpendicular to the Electrodes. Electric and Magnetic

fields are independent

Radiative case: Electric and Magnetic fields are inter-dependent and

mutually perpendicular to the propagation direction

E

H

k

Transmitter Receiver

Direction of propagation

E

H

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t

EE

t

DJH

t

H

t

BE

2

22

t

E

t

EE

t

EE

2

)]([)(~

;0~~ 22 tEEEkE

f

2

Propagation constant

e.g., for an Al alloy, 7 mm at f 9 kHz

EM Wave in a ConductorMaxwells Equations

EEE 2)(

Use

To get the wave equation

Eddy current testing is typically performed at frequencies lower than 10 MHz, with probe coil and defect dimensions less than 1 cm. In the air medium outside the metal testpiece, the characteristic length is the wavelength . At usual eddy current test frequencies, is in the range of kilometers, so the quasistatic approximation is always applicable in the air medium.

i

i

2

We get the diffusion equation !

In a highly conducting testpiece, the time derivative terms in the wave equation reduce to

in the frequency range for eddy current testing andconvert the wave equation into the diffusion equation,where the characteristic length is the skin depth

For time harmonic fields, Fourier transform leads to

Low Frequency Effects

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Inductive ReactanceThe reduction of current flow in a circuit due to induction is called inductive reactance.

The direction of the magnetic field can be determined by taking your right hand and pointing your thumb in the direction of the current. Your fingers will then point in the direction of the magnetic field.

It can be seen that the magnetic field from one loop of the wire will cut across the other loops in the coil and this will induce current flow (shown in green) in the circuit.

The induced current working against the primary current results in a reduction of current flow in the circuit.

It should be noted that the inductive reactance will increase if the number of winds in the coil is increased since the magnetic field from one coil will have more coils to interact with.

According to Lenz's law, the induced current must flow in the opposite direction of the primary current.

Induction Effects

Current carrying wire produces primary

magnetic field

Primary magnetic field induces currents in a

nearby conductor

Eddy currents generate secondary magnetic field which will oppose the

primary magnetic field

Eddy Current Generation

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Secondary magnetic field opposing the primary magnetic field alters

the current flow in the wire leading to inductive reactance

Near a flaw, eddy current flow is disturbed, changing the secondary

magnetic field, which in turn modifies the inductive reactance

Eddy Current Changes

The impedance of an eddy current probe may be affected by the following factors:

variations in operating frequency

variations in electrical conductivity and the magnetic permeability of a object or structure, caused by structural changes such as grain structure, work hardening, heat treatment, etc.

changes in liftoff or fill factor resulting from probe wobble, uneven surfaces, and eccentricity of tubes caused by faulty manufacture or damage

the presence of surface defects such as cracks, and subsurface defects such as voids and nonmetallic inclusions

dimensional changes, for example, thinning of tube walls due to corrosion, deposition of metal deposits or sludge, and the effects of denting

the presence of supports, walls, and brackets

the presence of discontinuities such as edges

ECT measures Impedance changes

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mmHz H/mm % IACS

Skin Depth

If the eddy current circuit is balanced in air and then placed on a piece of aluminum, the resistance component will increase and the inductive reactance of the coil decreases.

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.

When a probe is placed on a magnetic material such as steel, 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.

Impedance Plane Diagram

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Flaw Detection Using ECT

Response at 50 kHz Response at 300 kHz

A B C

Rea

ctan

ce

Rea

ctan

ce

Resistance Resistance

ECT probe movement

Flaw Detection using ECT in Tubes

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Electrical conductivity of a metal depends on several factors, such as its chemical composition and the stress state of its crystalline structure.

It can be used for sorting metals, checking for proper heat treatment, and inspecting for heat damage.

The technique can be used to easily sort magnetic materials from nonmagnetic materials but it is difficult to separate the conductivity effects from the magnetic permeability effects, so conductivity measurements are limited to nonmagnetic materials.

The technique usually involves nulling an absolute probe in air and placing the probe in contact with the sample surface. The thickness of the specimen should generally be greater than three standard depths of penetration.

Generally large pancake type, surface probes are used to get a value for a relatively large sample area.

To sort materials using an impedance plane device, the signal from the unknown sample must be compared to a signal from a variety of reference standards such as the IACS (International Annealed Copper Standard).

Electrical Conductivity Measurements

Ait

AEJ

Induced eddy currents

On the impedance plane, thickness variations exhibit the same type of eddy current signal response as a subsurface defect, except that the signal represents a void of infinite size and depth. The phase rotation pattern is the same, but the signal amplitude is greater.

The depth of penetration of the eddy currents must cover the entire range of thicknesses being measured. Typically, a frequency is selected that produces about one standard depth of penetration at the maximum thickness.

But at lower frequencies the probe impedance is more sensitive to changes in electrical conductivity. Any variations of conductivity over the region of interest have to be at a sufficiently low level for reliable measurements..

Metal thickness measurements

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The thickness of nonmetallic coatings on metal substrates can be determined simply from the effect of liftoff on impedance. The coating serves as a spacer between the probe and the conductive surface. Thicknesses between 0.5 and 25 m can be measured to an accuracy between 10% for lower values and 4% for higher values.

Contributions to impedance changes due to conductivity variations should be phased out, unless it is known that conductivity variations are negligible, as normally found at higher frequencies.

Thickness of Nonmetallic Coatings on Metal Substrates

Schematic representations of defect profile curves. (a) Small probe diameter. (b) Large probe diameter.

Imaging with ECT

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Recent developments

Typical MWM sensor and MWM-Arrays: (a) MWM sensor, (b) scanning five-element MWM-Array, (c) eight-element MWM-Array for detection on fatigue initiation, (d) four-element MWM-Rosette for detection and monitoring of fatigue cracks at fasteners (note that (c) and (d) are examples of MWM-Arrays designed for permanent mounting).

Meandering Winding Magnetometer (MWM) is a novel eddy current sensor that can measure absolute magnetic and conducting properties of ferrous and nonferrousalloys on flat and curved surfaces

Features of MWM Sensors

.

MWM sensors and MWM-Arrays can be permanently mounted for crack detection and monitoring in difficult-to-access fatigue-critical locations on operating equipment, e.g. in fuel tanks on aircraft, or between layers in a lapjoint

MWM can detect precrack fatigue damage in austenitic

stainless steels.

MWM provides the capability for continuous on-line monitoring of

crack initiation and growth during fatigue tests of coupons,

components, and full-scale test articles.

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Example of MWM Sensor for Fatigue Damage Assessment

Detection of fatigue damage in Type 304 stainless steel by MWM bi-directional

permeability measurements.

Representative measurement grids relating the magnitude and phase of the sensor trans-impedance to the (a) lift-off and magneticpermeability for 4340 alloy steel and (b) lift-off and electrical conductivity for titanium and Type 304 stainless steel.

Pulsed ECT

(a) Schematic representation of the model for theoretical calculations. Coil impedances of two cases (with and without coating) are calculated and used to predict the time-domain current differences.

(b) The step-function voltage that was applied to excite the coils in the PEC measurements and the resulting current difference between the two cases.

Comparison of measured data and theoretical calculations using the PEC method: (a) non-magnetic coatings on magnetic base metal

(zinc on steel) and (b) magnetic coatings on non-magnetic base metal

(nickel on copper).

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Advantages are:

Crack detection (Sensitive to small cracks and other defects)

Detects surface and near surface defects

Material thickness measurements

Coating thickness measurements

Conductivity measurements for:Material identificationHeat damage detectionCase depth determinationHeat treatment monitoring

Equipment is very portable

Test probe does not need to contact the part

Inspects complex shapes and sizes of conductive materials

Advantages and Limitations of ECTSome of the limitations of eddy current inspection include:

Only conductive materials can be inspected

Surface must be accessible to the probe

Skill and training required is more extensive than other techniques

Surface finish and and roughness may interfere

Reference standards needed for setup

Depth of penetration is limited

Flaws such as delaminations that lie parallel to the probe coil winding and probe scan direction are undetectable