Electromagnetic testing reading three

Electromagnetic Testing Reading-3 Fact Cards My ASNT Level III Pre-Exam Preparatory Self Study Notes 2nd April 2015

Charlie Chong/ Fion Zhang

Aerospace Applications

Charlie Chong/ Fion Zhang

Aerospace Applications

Charlie Chong/ Fion Zhang

Aerospace Applications

Charlie Chong/ Fion Zhang

Aerospace Applications

Charlie Chong/ Fion Zhang

Aerospace Applications

Charlie Chong/ Fion Zhang

Aerospace Applications

Charlie Chong/ Fion Zhang

Aerospace Applications

Charlie Chong/ Fion Zhang

Aerospace Applications

Charlie Chong/ Fion Zhang

Aerospace Applications

Charlie Chong/ Fion Zhang

Drone SDTI

Charlie Chong/ Fion Zhang

Drone SDTI

Charlie Chong/ Fion Zhang

Drone SDTI

Charlie Chong/ Fion Zhang

Wing Loong Drone

Charlie Chong/ Fion Zhang

Wing Loong Drone

Charlie Chong/ Fion Zhang

My Mickey Drone

Charlie Chong/ Fion Zhang

Charlie Chong/ Fion Zhang

Fion Zhang at Shanghai 2nd April 2015

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

Charlie Chong/ Fion Zhang

Reading 03-01 The TWI 31 – Eddy Current Methods for NDT

Charlie Chong/ Fion Zhang

Magnetic field is the magnetic effect of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H, where H is measured in units of amperes per meter (symbol: A·m−1 or A/m) in the SI. B is measured in Teslas (symbol: T) and Newton per meter per ampere (symbol: N·m−1·A−1 or N/(m·A)) in the SI. B is most commonly defined in terms of the Lorentz force it exerts on moving electric charges.

Magnetic fields can be produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. In special relativity, electric and magnetic fields are two interrelated aspects of a single object, called the electromagnetic tensor; the split of this tensor into electric and magnetic fields depends on the relative velocity of the observer and charge. In quantum physics, the electromagnetic field is quantized and electromagnetic interactions result from the exchange of photons.

Charlie Chong/ Fion Zhang

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

In everyday life, magnetic fields are most often encountered as a force created by permanent magnets, which pull on ferromagnetic materials such as iron, cobalt, or nickel, and attract or repel other magnets. Magnetic fields are widely used throughout modern technology, particularly in electrical engineering and electromechanics. The Earth produces its own magnetic field, which is important in navigation, and it shields the Earth's atmosphere from solar wind. Rotating magnetic fields are used in both electric motors and generators. Magnetic forces give information about the charge carriers in a material through the Hall effect. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits.

Charlie Chong/ Fion Zhang

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

φ Magnetic Flux Magnetic flux φ is the product of the average magnetic field times the perpendicular area that it penetrates. It is a quantity of convenience in the statement of Faraday's Law and in the discussion of objects like transformers and solenoids. In the case of an electric generator where the magnetic field penetrates a rotating coil, the area used in defining the flux is the projection of the coil area onto the plane perpendicular to the magnetic field

B = magnetic flux density φ in weber (Wb) (in derived units: volt-seconds)

Charlie Chong/ Fion Zhang

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcon.html#c1

Magnetic Flux Illustrations

The contribution to magnetic flux for a given area is equal to the area times the component of magnetic field perpendicular to the area. For a closed surface, the sum of magnetic flux is always equal to zero (Gauss' law for magnetism). No matter how small the volume, the magnetic sources are always dipole sources (like miniature bar magnets), so that there are as many magnetic field lines coming in (to the south pole) as out (from the north pole).

Charlie Chong/ Fion Zhang

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcon.html#c1

Magnetic Field Strength H The magnetic fields generated by currents and calculated from Ampere's Law or the Biot-Savart Law are characterized by the magnetic field B measured in Tesla (symbol:T) and newtons per meter per ampere [symbol: N·m−1·A−1 or N/(m·A)] . But when the generated fields pass through magnetic materials which themselves contribute internal magnetic fields, ambiguities can arise about what part of the field comes from the external currents and what comes from the material itself. It has been common practice to define another magnetic field quantity, usually called the "magnetic field strength" designated by H A·m−1 or A/m. It can be defined by the relationship:

H = B0/μ0 = B/μ0 - M

and has the value of unambiguously designating the driving magnetic influence from external currents in a material, independent of the material's magnetic response. The relationship for B can be written in the equivalent form:

B = μ0(H + M) H and M will have the same units, amperes/meter. To further distinguish B from H, B is sometimes called the magnetic flux density or the magnetic induction. The quantity M in these relationships is called the magnetization of the material.

Charlie Chong/ Fion Zhang

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcon.html#c1

Inductance of a Coil Coil's reaction to increasing current. For a fixed area and changing current, Faraday's law becomes Since the magnetic field of a solenoid is

then for a long coil the emf is approximated by

From the definition of inductance

we obtain

Charlie Chong/ Fion Zhang

Inductors Inductance is typified by the behavior of a coil of wire in resisting any change of electric current through the coil. Arising from Faraday's law, the inductance L may be defined in terms of the emf generated to oppose a given change in current:

Charlie Chong/ Fion Zhang

Inductor AC Response You know that the voltage across an inductor leads the current because the Lenz' law behavior resists the buildup of the current, and it takes a finite time for an imposed voltage to force the buildup of current to its maximum.

Charlie Chong/ Fion Zhang

Inductive Reactance The frequency dependent impedance of an inductor is called inductive reactance.

Impedance = Angular frequency x Inductance

Charlie Chong/ Fion Zhang

Capacitor AC Response You know that the voltage across a capacitor lags the current because the current must flow to build up the charge, and the voltage is proportional to that charge which is built up on the capacitor plates.

Charlie Chong/ Fion Zhang

Capacitive Reactance The frequency dependent impedance of a capacitor is called capacitive reactance.

Charlie Chong/ Fion Zhang

Resistance The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current which flows through it:

If the resistance is constant over a considerable range of voltage, then Ohm's law, I = V/R, can be used to predict the behavior of the material. Although the definition above involves DC current and voltage, the same definition holds for the AC application of resistors.

Whether or not a material obeys Ohm's law, its resistance can be described in terms of its bulk resistivity. The resistivity, and thus the resistance, is temperature dependent. Over sizable ranges of temperature, this temperature dependence can be predicted from a temperature coefficient of resistance.

Charlie Chong/ Fion Zhang

Resistivity and Conductivity The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made. Experimentally, the dependence upon these properties is a straightforward one for a wide range of conditions, and the resistance of a wire can be expressed as

The factor in the resistance which takes into account the nature of the material is the resistivity .

Although it is temperature dependent, it can be used at a given temperature to calculate the resistance of a wire of given geometry.

It should be noted that it is being presumed that the current is uniform across the cross-section of the wire, which is true only for Direct Current. For Alternating Current there is the phenomenon of "skin effect" in which the current density is maximum at the maximum radius of the wire and drops for smaller radii within the wire. At radio frequencies, this becomes a major factor in design because the outer part of a wire or cable carries most of the current.

The inverse of resistivity is called conductivity. There are contexts where the use of conductivity is more convenient.

Electrical conductivity = Ďƒ = 1/ Ď Charlie Chong/ Fion Zhang

Electrical conductivity or specific conductance is the reciprocal of electrical resistivity, and measures a material's ability to conduct an electric current. It is commonly represented by the Greek letter σ (sigma), but κ(kappa) (especially in electrical engineering) or γ (gamma) are also occasionally used. Its SI unit is Siemens per meter (S/m) and CGSE unit is reciprocal second (s−1).

Charlie Chong/ Fion Zhang

IACS The International Annealed Copper Standard (IACS) establishes a standard for the conductivity of commercially pure annealed copper. The standard was established in 1913 by the International Electrotechnical Commission.

The Commission established that, at 20째C,commercially pure, annealed copper has a resistivity of 1.7241x10-8 ohm-meter or 5.8001x107 Siemens/meter when expressed in terms of conductivity. For convenience, conductivity is frequently expressed in terms of percent IACS. A conductivity of 5.8001x107 S/m (58 x 106 S/m) may be expressed as 100% IACS at 20째C. All other conductivity values are related back to this standard value of conductivity for annealed copper.

Therefore, iron with a conductivity value of 1.04 x 107 S/m, has a conductivity of approximately 18% of that of annealed copper and this is reported as 18% IACS. An interesting side note is that commercially pure copper products now often have IACS conductivity values greater than 100% IACS because processing techniques have improved since the adoption of the standard in 1913 and more impurities can now be removed from the metal. Wire of high purity has been produced having a conductivity of slightly over 103% IACS, which is very near the value expected for copper without any impurity.

Charlie Chong/ Fion Zhang

Leading and lagging in AC current There are three options in a circuit for current. It can be leading, lagging, or in phase with voltage. These can all be seen when one maps current and voltage of alternating (AC) circuits against time. The only time that the voltage and current are in phase together is when the load is resistive. If at some point in the phase shift the current leads the voltage by more than 90 degrees, it can then be stated that the current lags that voltage by 180 degrees minus the phase shift. Ninety degrees phase shift is the determining point if the current is either leading or lagging the voltage.

Each of the main components of a circuit (resistor, capacitor, and inductor) can be seen as an impedance. All of them produce resistance in either fractional or exponential ways. Here are their complex number forms: Resistor, R = R Capacitor, Zc = 1/jω C Inductor, Zl = jωL ω =2 π f Charlie Chong/ Fion Zhang

Lagging Voltage against current- Capacitive

Current

Voltage

XC= 1/ ωC

Charlie Chong/ Fion Zhang

Leading Voltage against current - Inductive

Voltage Current

XL= ωL

Charlie Chong/ Fion Zhang

Capacitive Reactance

Charlie Chong/ Fion Zhang

http://www.electronics-tutorials.ws/filter/filter_1.html

Inductive Reactance

Charlie Chong/ Fion Zhang

http://www.electronics-tutorials.ws/inductor/ac-inductors.html

Resistance

2

R

Charlie Chong/ Fion Zhang

Inductive Reactance

XL

2

Impedance

Z

2

Defect Detection – Perturbation of Eddy current

Magnetic Field From Test Coil Magnetic Field From Eddy Currents Crack Eddy Currents

Charlie Chong/ Fion Zhang

Impedance Phasor Diagrams

Charlie Chong/ Fion Zhang

and

Charlie Chong/ Fion Zhang

and

Charlie Chong/ Fion Zhang

Charlie Chong/ Fion Zhang

and 10

100

Charlie Chong/ Fion Zhang

and

Charlie Chong/ Fion Zhang

and

Charlie Chong/ Fion Zhang

and

Charlie Chong/ Fion Zhang

and

Charlie Chong/ Fion Zhang

Conductivity vs Impedance constant frequency

1 Titanium, 6Al-4V

Normalized Reactance

0.8

Inconel Stainless Steel, 304

0.6

Copper 70%, Nickel 30%

0.4 Lead

0.2 Copper

Magnesium, A280 Nickel Aluminum, 7075-T6

0 0

Charlie Chong/ Fion Zhang

0.1

0.2 0.3 Normalized Resistance

0.4

0.5

Apparent Eddy Current Conductivity

magnetic field probe coil specimen

Normalized Reactance

1.0 0.8 lift-off curves

0.6 0.4

conductivity (frequency) curve

0.2 0 0

eddy currents

0.1 0.2 0.3 0.4 Normalized Resistance

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

Normalized Reactance

 4

 3 =0

=s

 

2

1

Normalized Resistance Charlie Chong/ Fion Zhang

0.5

Lift-Off Curvature

inductive (low frequency)

ℓ =0

ℓ =s

σ2

“Vertical” Component.

lift-off

ℓ =0

σ2

conductivity σ σ1

“Vertical” Component.

lift-off

ℓ =s

capacitive (high frequency)

conductivity

σ

σ1

“Horizontal” Component

Charlie Chong/ Fion Zhang

“Horizontal” Component

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

low susceptibility 1.0

4 Âľr = 4

3

permeability

3

2

2 1

frequency (conductivity)

1 0

Normalized Reactance

Normalized Reactance

permeability

0.8 lift-off

0.6

frequency (conductivity)

0.4 0.2 0

0

0.2

0.4 0.6 0.8 1 Normalized Resistance

1.2

0

0.1 0.2 0.3 0.4 Normalized Resistance

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

0.5

Thickness versus Normalized Impedance scanning probe coil

thickness loss due to corrosion, erosion, etc.

1 0.8

1

thinning lift-off

0.6 0.4

thick plate

0.2

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

0.8 Re { F }

Normalized Reactance

aluminum (σ = 46 %IACS)

0.6 0.4

F ( x )  e  x /  e i x / 

0.2

thin plate

0 -0.2 0

0

0

0.1 0.2 0.3 0.4 0.5 Normalized Resistance

0.6

1

2 Depth [mm]

3

Defect Detections 1

Normalized Reactance

0.8

conductivity (frequency)

lift-off 0.6 crack depth

ω1

flawless material

0.4 ω2 0.2

0

0

0.1

0.2 0.3 0.4 Normalized Resistance

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

0.5

Conductivity, Magnetic Susceptibility, AECL & AECC Responses Key: apparent eddy current lift-off (AECL) apparent eddy current conductivity (AECC)

Conductivity VS Alloying & Temper IACS = International Annealed Copper Standard σIACS = 5.8107 Ω-1m-1 at 20 °C ρIACS = 1.724110-8 Ωm

60

Conductivity [% IACS]

2014

2024

6061

50 T0

T0

40

T6

T72 T6

30

T6

T8

T0

T0

T73 T76

T4

T3 T4 T3 T4

20 Various Aluminum Alloys

Charlie Chong/ Fion Zhang

7075

T6

Inductive Lift-Off Effect 4 mm diameter

8 mm diameter

2.0

2.0

1.5 %IACS

1.0 0.5 0.0 -0.5 -1.0

19.1 μm 12.7 μm 6.4 μm 0.0 μm

-0.5 -1.0 -2.0

100

0.1

1 10 Frequency [MHz]

100

80

80

70

70

63.5 μm

60

60

50.8 μm

50

50 40

38.1 μm 25.4 μm

30

19.1 μm

20

AECL [μm] . .

AECL [μm] .

0.0

-2.0

40 30 10

10

12.7 μm 6.4 μm

0

0

0.0 μm

-10

-10

20

0.1

Charlie Chong/ Fion Zhang

0.5

-1.5 1 10 Frequency [MHz]

63.5 μm 50.8 μm 38.1 μm 25.4 μm

1.0

-1.5 0.1

1.5 %IACS

1.5 Relative ΔAECC [%].

Relative ΔAECC [%] .

1.5

1 10 Frequency [MHz]

100

0.1

1 10 Frequency [MHz]

100

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

3.0

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

2.5

AECC Change [%] .

2.0 1.5 1.0 0.5 0.0 -0.5 0.1

1

10

100

Frequency [MHz]

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

Charlie Chong/ Fion Zhang

Magnetic Susceptibility versus Cold Work cold work (plastic deformation at room temperature) causes martensitic (ferromagnetic) phase transformation in austenitic stainless steels

Magnetic Susceptibility

101

SS304L SS302 SS304

100 10-1 10-2

SS305

10-3

IN718 IN625 IN276

10-4 0

10

20

30 Cold Work [%]

40

50

60

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

Conductivity [%IACS]

1.4

1.3

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

1.2

1.1

1.0 0.1

1 Frequency [MHz]

10

Non-conducting Coating probe coil, ao

non-conducting coating

ℓ t d

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

ao = 4 mm, simulated 63.5 μm 50.8 μm 38.1 μm 25.4 μm 19.1 μm 12.7 μm 6.4 μm 0 μm

1 10 100 Frequency [MHz]

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

AECL [μm]

lift-off:

AECL [μm]

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

ao = 4 mm, experimental

1 10 100 Frequency [MHz]

Conducting Coating probe coil, ao

conducting coating

z = δe z

ℓ t

Je

d

conducting substrate (µs,σs) approximate:

large transducer, weak perturbation equivalent depth:

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

  

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

analytical: Fourier decomposition (Dodd and Deeds) numerical: finite element, finite difference, volume integral, etc. (Vic-3D, Opera 3D, etc.)

Crack Contrast and Resolution Vic-3D simulation ao = 1 mm, ai = 0.75 mm, h = 1.5 mm

probe coil

austenitic stainless steel, σ = 2.5 %IACS, μr = 1 f = 5 MHz, δ  0.19 mm

crack 1

-10% threshold

Normalized AECC

0.8 0.6 0.4 0.2 0 semi-circular crack

detection threshold

0

1

2 3 Flaw Length [mm]

4

5

and

Charlie Chong/ Fion Zhang

Characteristic Parameters

Pc= ﾏ火ｼﾏビ -2

Charlie Chong/ Fion Zhang

 Characteristic Parameter dimensionless. It allows test coil operating point to be specified in terms of a single quantity rather than four independent variables.  Characteristic or Limit Frequency fg hertz,  Characteristic Frequency Ratio f/fg dimensionless. It allows the test coil operating point to be specified in terms of a single quantity rather than four independent variables.

Charlie Chong/ Fion Zhang

The Characteristic Parameter (Pc) is a means of determining the operating point on the impedance curve. The formula for Pc depends on the units used, but the following is recommended: PC = 4.6 × 10-3 f μr σr 2

(5.3a)

or f = PC /(4.6 × 10-3 μr σr 2)

(5.3b)

Where: Pc = characteristic parameter, f = frequency (kHz), μr = relative permeability, σ = conductivity (% IACS), r = mean coil radius (mm) Note that the unit of frequency used in this formula, as in the other ‘applied’ eddy current formulae (for f90 and f/fg) is kHz, unlike the basic theoretical formulae for depth of penetration and inductive reactance.

Charlie Chong/ Fion Zhang

Calculations of Pc are used in conjunction with FIG. 5.20, which relates the value of Pc to the operating point on the impedance curve for surface probes.

FIG. 5.20. Impedance diagram showing conductivity curves at a number of different values of lift-off to coil radius ratio (LO/r) (the solid curves) and a number of lift-off curves (dashed) Values of Pc are indicated for the zero lift-off conductivity curve. These values also apply to the corresponding locations on the other conductivity curves.

Charlie Chong/ Fion Zhang

Example: Calculate the optimum frequency for maximum sensitivity in sorting commercially pure titanium (conductivity approximately 2.5% IACS) from Ti6AI-4Valloy (conductivity 1% IACS), using a coil with outer diameter 10 mm wound on a 6 mm diameter plastic core.

Calculation: For maximum sensitivity to conductivity, and minimum response to lift-off, the operating point should be at or somewhat below the knee of the impedance curve. That is, Pc should be between 10 and approximately 200. The Pc value will be different for the two alloys, but, since Pc is proportional to conductivity, the two values will differ by a factor of 2.5/1 = I (the ratio of the conductivities).

Suitable values would be 30 for titanium and 75 for stainless steel, though other similar values within the range 10 to 200 could be chosen.

Charlie Chong/ Fion Zhang

That is: f = Pc /(4.6 × 10-3 μrσ r2) Pc = 30 (for titanium), r = (10 + 6)/2 = 8 mm, so r = 4 mm, μr = 1 σ = 1% IACS Inserting these values into equation gives: f = 30/ (4.6 × 10-3 × 1 × 1 X 42) = 407.6 kHz or, rounding to a convenient figure: = approximately 400 kHz

Charlie Chong/ Fion Zhang

When eddy current conductivity meters are used, this approach is normally not possible, because they operate at one or more fixed frequencies.

Normally, these instruments are designed to give an operating point in the region of the knee of the curve at the lowest frequency, normally 60 kHz, and higher frequencies are used only if the material is too thin for testing at the lowest frequency.

Charlie Chong/ Fion Zhang

Goal of Pc - For maximum sensitivity to conductivity, and minimum response

to lift-off, the operating point should be at or somewhat below the knee of the impedance curve. The Pc = ﾏ火ｼﾏビ -2 is chosen such that the operating point is below the knee where frequency of the coil could be selected.

Charlie Chong/ Fion Zhang

Characteristic Frequency

Charlie Chong/ Fion Zhang

Reading 03-02 J.Younas– Eddy Current Methods for NDT

Charlie Chong/ Fion Zhang

Fill Factor

Usually, 70-90% "fill-factor" is targeted for reliable inspection

Charlie Chong/ Fion Zhang

fill factor: For encircling coil electromagnetic testing, the ratio of the cross sectional area of the test object to the effective cross sectional core area of the primary encircling coil (outside diameter of coil form, not inside diameter that is adjacent to the object).

For internal probe electromagnetic testing, the ratio of the effective cross sectional area of the primary internal probe coil to the cross sectional area of the tube interior.

Charlie Chong/ Fion Zhang

NDT Handbook Vol5. Chapter 19

fill factor: ď Ž For encircling coil electromagnetic testing, the ratio of the cross sectional area of the test object to the effective cross sectional core area of the primary encircling coil (outside diameter of coil form, not inside diameter that is adjacent to the object). r2/Re2 ď Ž For internal probe electromagnetic testing, the ratio of the effective cross sectional area of the primary internal probe coil to the cross sectional area of the tube interior. r2/Ri2 Re Ri r

Charlie Chong/ Fion Zhang

NDT Handbook Vol5. Chapter 19

Standard Depth

 Eddy current density is greatest at surface  Reduces exponentially with depth  At standard δ = 1/e (37%) of surface value, δ = (ωμσ) -½

Charlie Chong/ Fion Zhang

Effects of Frequency on δ

Charlie Chong/ Fion Zhang

Effects of conductivity σ on δ

Charlie Chong/ Fion Zhang

Effects of permeability μ on δ

Charlie Chong/ Fion Zhang

Standard Depth δ

Depth

Depth

Standard Depth of Penetration (Skin Depth) 1/e or 37 % of surface density

Eddy Current Density High Frequency High Conductivity High Permeability

Charlie Chong/ Fion Zhang

Eddy Current Density Low Frequency Low Conductivity Low Permeability

Type of probes Surface Probe

Internal Probe

Charlie Chong/ Fion Zhang

External Probe

Absolute Probes

Differential Probes

Sensitive to both sudden and gradual changes in properties.

Not Sensitive gradual changes in properties

Easy to interpret

Difficult to interpret

Show total length of long flaws

Detect only ends of long flaws

Sensitive to drift due to temperature changes

Less Sensitive to drift due to temperature changes

Sensitive to probe wobble

Less Sensitive to probe wobble

Single Coil

Pair of coils

Absolute value of impedance and induced Changes in impedance or induced voltage is measured voltage is measured

Charlie Chong/ Fion Zhang

Reading 03-03 UKHSE– Evaluation of the effectiveness of non-destructive testing screening methods

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Electromagnetic / Electrical Techniques SLOFEC Saturated Low Frequency Eddy current (SLOFEC) senses changes in permeability of steel plates for detection of corrosion. It uses strong magnets and eddy current coils. This combination generates magnetic field line and eddy current field line distribution to detect flux density changes within the material.

Testing field line changes within the material gives more sensitive results than conventional MFL techniques. The use of the eddy current technique allows variation of settings and analysis of signal amplitude & signal phase. Good for local defect detection such as detecting pitting corrosion and localised microbiological corrosion (which is mainly present as localised corrosion but can rarely appear as general corrosion). Even small isolated pits are detected.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

SLOFEC can detect & distinguish both internal and outer surface breaking defects. SLOFEC is suitable for inspection of ferritic and non-ferritic materials.

Suitable for inspection of pipes, tank floors, vessel Wall thickness up to 30 mm, coatings up to 10 mm for tankfloors, vessels and drums. Wall thickness up to 25 mm, coatings up to 7 mm for pipes and pipelines (1”+ diameter) Sensitive for corrosion detection but not used for absolute wall thickness determination “Gradual” defects (greater than 300- 00mm in length) are not as easily detectable. Findings should be complemented by conventional ultrasonic inspection.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

SLOPEC

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Pulsed Eddy Current – PEC PEC is a screening tool for inspecting remaining wall thickness under coatings and insulations. Not considered rapid. A coil is placed over the insulated pipe / vessel and a current pulse is sent through the coil. When the current is interrupted eddy currents are generated in the material, which decay in time. Measuring the rate of decay of the eddy currents determines the wall thickness. High wall thickness results in a slower decay. The PEC wall thickness is an average over its ‘footprint’, i.e. the area where eddy currents flow. The size of the footprint area depends on the distance between probe and metal surface. The footprint is approximately a circle with a diameter depending on the distance between probe and steel surface.

The PEC wall thickness readings are an average value over this footprint area. As a result, PEC can only detect general wall loss.

Localised corrosion such as pitting is not detected by PEC.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

A rough rule of thumb is smallest detectable defect diameter is 50% of the liftoff, i.e. in 50mm of insulation the smallest detectable defect diameter is around 25mm. In principle PEC cannot differentiate between internal and external defects. PEC can be deployed on- tream for detection of erosion corrosion, flow accelerated corrosion and corrosion under insulation in carbon steel or low alloy ferromagnetic metals with wall thickness between 2-35 mm.

PEC Can measure through any kind of non magnetic insulation upto 200 mm thick (e.g. rockwool, foamglas, concrete, marine growth, dirt, cladding and scaling) It can be applied in wet or underwater conditions and no surface preparation necessary.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Pulsed Eddy Current – Incotest Incotest is a pulsed eddy current system. Its principle of operation, strengths and weakness are similar to pulsed eddy current system PEC described in above. It is a screening tool for inspecting remaining wall thickness under coatings and insulations. Incotest can detect erosion corrosion, flow accelerated corrosion and corrosion under insulation in carbon steel or low alloy metals with wall thickness between 6-65 mm through insulation thickness up to 200mm Incotest can measure through any kind of non ferritic insulation e.g. rockwool, foamglas, concrete, marine growth, dirt, cladding, aluminium, stainless steel or galvanised (up to 1 mm) sheeting. No surface preparation is necessary The accuracy is roughly 5% and repeatability is 2%.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Charlie Chong/ Fion Zhang

Pulsed Eddy Current

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

In-service inspection of column skirt through passive fire protection.

PEC deployed on extension pole. No scaffolding needed.

Charlie Chong/ Fion Zhang

Pulsed Eddy Current

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Offshore Topside PEC inspection of coated riser while in service, deployed by ropeaccess.100% inspection took 2 day

MFL MFL technique uses magnets for inducing a magnetic field in the component being tested. In defect-free material, this field remains trapped within the material. Changes in material properties or geometry (i.e. defects) force the magnetic field to leak out of the material, where it is detected by the Hall- ffect MFL sensors.

MFL can detect corrosion, particularly pitting, in materials up to 20 mm thick at speeds upto 0.5m/ sec Inspection can be carried out through nonconducting coating (upto 6 mm thick) at sensitivity upto 20% underfloor corrosion (as per supplier). Also suitable for ferritic vessels, pipes, boiler tubes, heat exchanger tubes.

MFL cannot differentiate between top side and bottom side corrosion.

Erosion defects may not be detected as the change between full wall thickness and the thinned area is gradual. MFL is a qualitative technique and requires use of ultrasound for estimation of wall loss and proofup.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

MFL Pipescan A MFL pipescan is a specially designed tool for inspection of pipes. A MFL scanning head is moved across the external surface of the pipe and will detect internal and external corrosion pitting. The system includes a separate electronics module with an operator adjustable alarm threshold control. The defect alarm consists of an audible alarm and L.E.D.s. Used as a screening tool, Pipescan is capable of detecting corrosion pitting originating from the internal and/or external surface of the pipe. The system has no sizing capabilities. Pipescan scanning heads cannot pass bends / elbows and severely distorted areas of pipe. Pipescan can inspect wall thickness up to 19 mm with coatings up to 6 mm.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

RFT ferromagnetic pipe

exciter coil

Remote Field

Near Field ln(Hz)

low frequency operation (10-100 Hz)

 

1  f  r 0 

Exponentially decaying eddy currents propagating mainly on the outer surface cause a diffuse magnetic field that leaks both on the outside and the inside of the pipe.

Charlie Chong/ Fion Zhang

sensing coil

Remote Field

Without transition H z  H z 0 e z /  z

RFT

http://www.mdpi.com/1424-8220/14/12/24098/htm

RFT

Charlie Chong/ Fion Zhang

http://www.mdpi.com/1424-8220/14/12/24098/htm

Microwave Microwave signals readily penetrate inside non-conducting materials and may therefore be employed for defect detection within these materials.

Microwaves are radiated from the transducer to the specimen being tested. A detectable signal is returned at each interface where the dielectric constant changes (e.g. - where there are delaminations, cracks, holes, impurities or other defects).

The transducer may be moved relative to the specimen at any desired speed and the scanning speed need not be uniform. Once the data is collected, the software allows the image to be manipulated to enhance features. Also, since it is in digital form, the scan results can be stored and retrieved later to provide information on how a part or a defect has changed over time. This allows determination of the growth rate of a defect, which is critical to determining ultimate service life. Microwaves can be used for detection of defects such as delaminations, disbands and impact damage in dielectric materials such as fibre reinforced polymeric (FRP) materials. Full volumetric coverage can be obtained. Applicable to non-conductive materials only.

Moisture or liquid may affect results.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Microwave

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Others Non-Electromagnetic Techniques Thermography Thermography is a remote condition monitoring technique which identifies the surface temperatures by the measurement of the intensity of infra-red radiation emitted from a surface. The higher the temperature of the object, higher will be the emitted infrared energy. This is the energy detected by infrared cameras. Resolution up to 0.1째C can be detected depending on camera and extra options utilised. A low resolution Flir camera will measure hotspots from 10mm at 5 metres (and hotspots from the size of 6mm for the higher resolution option). Cameras with 0.02째C thermal sensitivity are used for dynamic images. Results can be distorted if hot pipes and shiny cladding are present close to inspection area - something that is likely to happen in reality.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

For CUI inspections a 30째C temperature gradient across the insulation (between pipe and environment) is desired to ensure detection. The presence of water will be measured in terms of temperature variations (e.g. variations of emitted infra red radiation) of the insulation weather proofing along the pipe, arising from a loss in thermal efficiency of the insulation system.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Neutron Backscattering Neutron backscattering uses the neutron slowing down property of hydrogen for detection of moisture. A radioactive source (Am 241/Be or Cf 252) emits high energy neutrons into the insulation. The neutrons are slowed down or “moderated� by collisions with light elements, in particular hydrogen. They then diffuse back to a thermal neutron detector where the slow neutrons are counted.

Moisture in, for example, insulation increases the density of hydrogen nuclei so the number of slow neutrons detected will rise. Detects moisture under thermal insulation on pipe work or vessels. Detection method also works on metal clad insulation. Effective moisture detection capability even where insulation is several centimeters thick. Hand operated instrument giving online readout of results within a few seconds for each location.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Detector is sensitive to presence of hydrogen so can be used to detect presence of oil and other liquids with a high hydrogen content. Detector is very sensitive to water very close and almost completely insensitive to the presence of water farther away. This means that any water within the pipe or vessel will not effect the results. This claim is made by FORCE’s Moisture Probe only. Not suited for outdoors use during rainfall. Not suited for use on foam insulation and plastic cladding or any insulation with high hydrogen content. Radiological hazards associated with use of neutron source.

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Neutron Backscattering

Charlie Chong/ Fion Zhang

http://www.hse.gov.uk/research/rrpdf/rr659.pdf

Reading 03-04 Fact Sheets

Charlie Chong/ Fion Zhang

Skin Effect / Standard Depth of Penetration (SDP) Eddy current density in a material is not uniform in the thickness (depth) direction. It is greatest on the material surface and decreases monotonously with depth (skin effect) and the eddy currents lag in phase with depth, allowing employ phase discrimination method to locate size and differentiate defects and disturbing variables. "Standard depth of penetration" (SDP) equation given above can be used to explain the capability of eddy current testing. For a uniform, isotropic and very thick material, SDP is the depth at which the eddy current density is 37% of its surface value. From the SDP equation, one can easily interpret that depth of penetration (delta) decreases with increasing frequency, conductivity, permeability (see flux line contours below). Thus, in order to detect very shallow defects (cracks, flaws) in a material and also to measure thickness of thin sheets, very high frequencies are to be used (see flux line contours below). Similarly, in order to detect suburface buried defects and to test highly conductive/ magnetic/ thick materials, low frequencies are to be employed.

Charlie Chong/ Fion Zhang

Eddy Current - Skin Effect

Charlie Chong/ Fion Zhang

Eddy Current - Skin Effect

Charlie Chong/ Fion Zhang

Probes/Sensors for ECT Appropriate selection of probe coil is important in eddy current testing, as even an efficient eddy current testing instrument can not achieve much if it doesn’t get the right (desired) information from the coils. The most popular coil designs are:  Surface probes or pancake probes (with the probe axis normal to the surface), are chosen for testing plates and bolt-holes either as a single sensing element or an array - in both absolute and differential (split-D) modes.  Encircling probes for inspection of rods, bars and tubes with outside access and  Bobbin probes for pre-and in-service inspection of heat exchanger, steam generator, condenser tubes & others with inside access.  Phased array receivers also possible for enhanced detection and sizing.

Charlie Chong/ Fion Zhang

Probes

 Absolute  Differential  Reflection

Charlie Chong/ Fion Zhang

Probes Considerations sensitivity

ferrite-core coil

air-core coil

high coupling

low coupling

high coupling

high coupling

eddy current

flat air-core coil

high coupling

eddy current

eddy current

thermal stability I2

I1

I

V  Z I V

Z  i  L*  Rwire

V1

V2

12 , 21

22

topology

flexible, low self-capacitance, reproducible, interchangeable, economic, etc.

Charlie Chong/ Fion Zhang

Z12  Z 22 

* Z12  i  L12 11



V1   Z11 V    Z  2   12

 I1  I   2

Probes Configurations voltmeter

voltmeter

oscillator

oscillator

excitation coil

excitation coil

voltmeter

~~

oscillator

~

Zo

~

coil

sensing coil testpiece

Hall or GMR detector testpiece

testpiece

differential coils

parallel

Charlie Chong/ Fion Zhang

coaxial

rotated

These three types of probes can be operated in absolute or differential (left, last). They can also operate in send-receive mode (reflection mode) (separate coils for sending and receiving [again absolute or differential]). The EC probes consisting of a single sensing coil for excitation and reception are called absolute probes. Such probes are good for detection of cracks (long as well as short) as well as gradual variations. However, absolute probes are sensitive also to lift-off, probe tilt, temperature changes etc. Differential probes have two sensing coils wound in opposite direction and investigating two different regions of the material. They are good for high sensitive detection of small defects and they are reasonably immune to changes in temperature and probe wobble.

Charlie Chong/ Fion Zhang

Eddy Current Testing Signals An eddy current signal is the trajectory of coil impedance formed upon scanning the coil over a material surface. Eddy current (impedance change) signal / data are analyzed in time-domain (strip-chart) and also in impedance plane (CRT or computer screen). Typical time-domain and impedance plane signals for a plate tested using a surface probe (absolute mode) are given on the right hand side.

CRT Screen or Impedance Plane Display

Charlie Chong/ Fion Zhang

Electromagnetic Coupling (Lift-off / Fill-factor) Coupling of magnetic field to the material surface is important in ECT. For surface probes, it is called "liftoff“ which is the distance between the probe coil and the material surface. In general, uniform and very small lift-off is preferred for achieving better detection sensitivity to defects. Similarly, the electromagnetic coupling in the case of tubes/bars/rods is referred to as "fillfactor". It is the ratio of square of coil diameter to square of tube diameter, in the case of encircling coils and is expressed as percentage (dimensionless).

Usually, 70-90% "fill-factor" is targeted for reliable inspection.

Charlie Chong/ Fion Zhang

Eddy Current Testing Procedure Usual EC test procedure involves first calibration. Artificial defects such as saw cuts, flat bottom holes, and electro-discharge machining (EDM) notches are produced in a material with similar chemical composition and geometry as that of the actual component. Well-characterized natural defects such as service induced fatigue cracks and stress corrosion cracks are preferred, if available. The test frequency, instrument gain and other instrument functions are optimized so that all specified artificial defects are detected, e.g. by thresholding of appropriate EC signal parameters such as signal peak-to- eak amplitude and phase angle. With optimized instrument settings, actual testing is carried out and any indication that is greater than the threshold level is recorded defective.

Charlie Chong/ Fion Zhang

For quantification (characterization) master calibration graphs, e.g. between eddy current signal parameters and defect sizes are generated. In the case of heat exchanger tube ECT, calibration graph is between depth of ASME calibration defects (20%, 40%, 60%, 80% and 100% wall loss flat-bottom holes) and the signal phase angle. In order to detect and characterize defects under support plates multi-frequency EC testing which involves mixing of signals from different frequencies is followed and separate calibration graph is generated for quantification of wall loss.

Charlie Chong/ Fion Zhang

FIGURE-Magnetic flux line contours of an eddy current probe in air, in an Inconel tube and in the tube surrounded by a carbon steel support plate. Freedom-loving flux lines are constrained by the tube wall and the support plate. This constraint (manifested as distortion / perturbation of eddy currents and associated impedance change) is what is measured to advantage in eddy current testing!

Charlie Chong/ Fion Zhang

Advantages of Eddy Current Testing  Eddy current test can nearly tested all metallic materials High inspection speeds possible (~ 5 m/s)  Eddy current test can readily detect very shallow and tight surface fatigue cracks and stress corrosion cracks (~ 5 microns width and 50 microns depth)  High temperature and on-line testing is possible, even in shop floors Noncontact / remote / inaccessible testing is possible (Couplant is not required unlike in ultrasonic)  Recording and analysis of inspection data is possible (Computer based instruments / systems available with data acquisition, storage, analysis and database management)

Charlie Chong/ Fion Zhang

Limitations of Eddy Current testing Like any other NDT technique ECT too has certain limitations, which are overcome to a large extent by the recent advances in the technique. A few key limitations are:  Only electrically conducting (metallic) materials can be tested  Maximum inspectable thickness is ~ 6 mm (12 mm possible by tuning frequency, probes, instrumentation etc.)  Inspection of ferromagnetic materials is difficult using conventional eddy current tests (Saturation ECT and Remote field ECT are possible for tubes)  Use of calibration standards necessary  Operator skill is necessary for meaningful testing and evaluation

Charlie Chong/ Fion Zhang

Recent Trends / Advances in ECT  Pulsed EC testing for sub-surface defect detection,  Remote field EC testing for ferromagnetic tubes,  Eddy current imaging to produce images or pictures of defects and to automate inspection,  Signal and image processing methods to extract more useful information of defects for enhanced detection and characterization of defects,  Low-frequency eddy current testing,  Numerical modeling (finite element, boundary element / volume integral, hybrid etc.) for simulation of inspection technique / situation, prediction of ECT signals for inversion & optimization of probes / test parameters,  Design of Phased-array and special focused probes,  Realization of expert systems and data-base systems.

Charlie Chong/ Fion Zhang

Figure: Eddy Current Image of a Stainless Steel Weld

Charlie Chong/ Fion Zhang

Figure: This is an eddy current image of a small defect (hole) in a stainless steel plate. As compared to the time domain and impedance plane signals shown earlier, it is possible to have a visual feel of the defect and can have an idea about the spatial extent/shape/size of the defect.

Charlie Chong/ Fion Zhang

Eddy Current Images of Small Fatigue Cracks

probe coil crack

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

Charlie Chong/ Fion Zhang

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

Crystallographic Texture J  E generally anisotropic

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

hexagonal (transversely isotropic)

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

0   E1  0   E2  3   E3 

cubic (isotropic)

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

0   E1  0   E2   2   E3 

 E1  E   2  E3 

x1 θ σM

σn

x3 σm

basal plane

x2

surface plane

1  2

σ1

conductivity normal to the basal plane

n ()  1 cos 2   2 sin 2 

σ2

conductivity in the basal plane

θ

polar angle from the normal of the basal plane

m ()  1 sin 2   2 cos 2 

M  2 a ()  絒 1 sin 2   2 (1  cos 2 )] Charlie Chong/ Fion Zhang

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

average conductivity in the surface plane

Electric “Birefringence” Due to Texture 500 kHz, racetrack coil highly textured Ti-6Al-4V plate

equiaxed GTD-111 1.40

1.04

Conductivity [%IACS]

Conductivity [%IACS]

1.05

1.03 1.02 1.01

1.38 1.36 1.34 1.32 1.30

1.00 0

Charlie Chong/ Fion Zhang

30 60 90 120 150 180 Azimuthal Angle [deg]

0

30 60 90 120 150 180 Azimuthal Angle [deg]

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

solution treated and annealed

heat-treated, coarse

heat-treated, very coarse

heat-treated, large colonies

equiaxed beta annealed

Charlie Chong/ Fion Zhang

Eddy Current versus Acoustic Microscopy 1”  1”, coarse grained Ti-6Al-4V sample

5 MHz eddy current

Charlie Chong/ Fion Zhang

40 MHz acoustic

In-homogeneity AECC Images of Waspaloy and IN100 Specimens inhomogeneous Waspaloy

homogeneous IN100

4.2”  2.1”, 6 MHz

2.2”  1.1”, 6 MHz

conductivity range 1.38-1.47 %IACS

conductivity range 1.33-1.34 %IACS

±3 % relative variation

±0.4 % relative variation

Charlie Chong/ Fion Zhang

Conductivity Material Noise as-forged Waspaloy 1.50 1.48 1.46

AECC [%IACS]

1.44 1.42 1.40 1.38 1.36

Spot 1 (1.441 %IACS)

1.34

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

1.32

Spot 4 (1.382% IACS)

1.30 0.1

1 Frequency [MHz] no (average) frequency dependence

Charlie Chong/ Fion Zhang

10

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

0.51×0.26×0.03 mm3 edm notch

f = 0.1 MHz, ΔAECC  6.4 %

f = 0.1 MHz, ΔAECC  8.6 %

f = 5 MHz, ΔAECC  0.8 %

f = 5 MHz, ΔAECC  1.2 %

Charlie Chong/ Fion Zhang

Standards in Eddy Current Testing Reference standards are used for adjusting the eddy current instrument’s sensitivity detection of cracks, conductivity, permeability and material thickness etc. and also for sizing. Some commonly used standards in eddy current testing are: 1.

2.

3.

4.

5.

ASME, Section V, Article 8, Appendix 1 and 2), Electromagnetic (eddy current) testing of heat exchanger tubes BS 3889 (part 2A): 1986 (1991) Automatic eddy current testing of wrought steel tubes BS 3889 (part 213): 1966 (1987) Eddy current testing of non-ferrous tubes ASTM B 244 Method for measurement of thickness of anodic coatings of aluminum and other nonconductive coatings on nonmagnetic base materials with eddy current instruments ASTM B 659 Recommended practice for measurement of thickness of metallic coatings on nonmetallic substrates

Charlie Chong/ Fion Zhang

6.

7.

8.

9.

10.

11.

12.

13.

14.

ASTM E 215 Standardizing equipment for electromagnetic testing of seamless aluminum alloy tube ASTM E 243 Electromagnetic (eddy current) testing of seamless copper and copper alloy tubes ASTM E 309 Eddy current examination of steel tubular products using magnetic saturation ASTM E 376 Measuring coating thickness by magnetic field or eddy current (electromagnetic) test methods ASTM E 426 Electromagnetic (eddy current) testing of seamless and welded tubular products austenitic stainless steel and similar alloys ASTM E 566 Electromagnetic (eddy current) sorting of ferrous metals ASTM E 571 Electromagnetic (eddy current) examination of nickel and nickel alloy tubular products ASTM E 690 In-situ electromagnetic (eddy current) examination of nonmagnetic heat-exchanger tubes ASTM E 703 Electromagnetic (eddy current) sorting of nonferrous metals

Charlie Chong/ Fion Zhang

Specific Applications of Eddy Current Testing 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Quality assurance and in-service inspection of austenitic stainless steel tubes, plates and welds.

In-service inspection of heat exchangers, steam generators and condensers for - Detection and sizing of defects in tubes (single frequency) - Detection and sizing of defects near support plates (multi-frequency) Detection and sizing of defects in multi-layer aircraft structures (multifrequency & pulsed eddy current tests) Quality assurance and in-service inspection of ferromagnetic tubes.

Detection and characterization of intergranular corrosion (IGC) in stainless steel 316L/304L. Detection of weld centre line in austenitic stainless steel welds using eddy current C-scan imaging.

Measurement of thickness of plates as well as thickness of coatings using eddy currents.

Sorting of materials based on electrical conductivity and magnetic permeability.

On-line eddy current detection of defects in materials.

High temperature and non-contact testing of materials.

Charlie Chong/ Fion Zhang

Multiplexing time-multiplexed multiple-frequency

Signal

Signal

single-frequency

Time

Time

frequency-multiplexed multiple-frequency Signal

Signal

pulsed

Time

Time

D    2

excited signal (current) Charlie Chong/ Fion Zhang

detected signal (voltage)

Nonlinear Harmonic Analysis single frequency, linear response

Signal

ferromagnetic phase (ferrite, martensite, etc.)

B

Time nonlinear harmonic analysis

Signal

H

Time

Charlie Chong/ Fion Zhang

https://www.yumpu.com/en/browse/user/charliechong Charlie Chong/ Fion Zhang