Part VII

Radiographic Inspection

Electromagnetic Spectrum

microwave IR light

cosmic rays

X-rays

γ rays

UV light

visiblelightradio frequency

Frequency [Hz]

10 1081064 10 1014101210 10 1020101816 1022 1024

Energy [eV]

10 10-610-8-10 10 10010-2-4 10 1061042 108 1010

Wavelength [m]

10 1001024 10 10-610-4-2 10 10-1210-10-8 10-14 10-16

typical lattice constant

cλ =

ν, E h eU= ν =

83 10 m/sc ≈ × , 346.63 10 J sh −≈ × , 191.6 10 Ce −≈ ×

Microwave Techniques

Electromagnetic WavesPlane waves:

in dielectrics:

( )0 i t k xy y yE E e ω −= =E e e ( )0

i t k xz z zH H e ω −= =H e e

0

0

E iH i

ωμη = =

σ+ ωε

( )k i i= − ωμ σ + ωε

in conductors:

/ ( / )0 x i t x yE e e− δ ω − δ=E e

/ ( / )0

x i t xzH e e− δ − ω − δ=H e

1 ik = −δ δ

1i iωμ +η = =

σ σδ

1f

δ =π μ σ

00

0377μ

η = ≈ Ωε

0 0

0 r nμ η

η = ≈ε ε

( / )0 i t x c yE e ω −=E e

( / )0

i t x czH e ω −=H e

kcω

=

0

0 0

1

r

ccn

= =μ ε ε

80

0 0

1 3 10 m/sc = ≈ ×μ ε

Complex Wave NumberPlane waves:

0 ( , )y E x t= ψE e 0 ( , )z H x t= ψH e

( )k i i= − ωμ σ + ωε

in dielectrics: in conductors:

1 ik = −δ δ0k = ω μ ε

( ) ( / )( , ) i t k x i t x c xx t e e eω − ω − −αψ = =

r i( , ) i k x k xi tx t e e e−ωψ =

Re{ }c f

kω

= = λPhase velocity:

Im{ }kα = −Attenuation coefficient:

' ''iε = ε − ε

PolarizationPlane waves propagating in the x-direction:

( ) ( )0 0i t k x i t k xy y z z y y z zE E E e E eω − ω −= + = +E e e e e

( ) ( )0 0i t k x i t k xz z y y z z y yH H H e H eω − ω −= + = +H e e e e

0 00

0 0

y z

z y

E EH H

η = = −

0 0 0 0y zi iy y z zE E e E E eφ φ= =

y

z

y

z

y

z

Ey

EzE

0 (or 180º)y zφ − φ =

linear polarization elliptical polarization

90º (or 270º)y zφ − φ =

circular polarization

E E

Reflection at Normal Incidence

x

y

incident

reflected transmitted

I( )i i0

i t k xyE e ω −=E e

Ii0 ( )i

Ii t k x

zE e ω −=η

H e

I( )r r0

i t k xyE e ω +=E e

Ir0 ( )r

Ii t k x

zE e ω += −η

H e

II( )t t0

i t k xyE e ω −=E e

IIt0 ( )t

IIi t k x

zE e ω −=η

H e

I medium II medium

Boundary conditions:

( 0 ) ( 0 )y yE x E x− += = = i0 r0 t0E E E+ =

( 0 ) ( 0 )z zH x H x− += = = i0 r0 t0H H H+ =

i0 r0 t0

I I II

E E E− =

η η η

r0 II Ii0 II I

ERE

η − η= =

η + η

t0 IIi0 II I

2ETE

η= =

η + η

Reflection from Conductors

x

y

incident

reflected transmitted“diffuse” wave

I dielectric II conductor

1 0f

δ = ≈π μσ

0II I

in

ηωμη = << η =

σ

II III I

1R η − η= ≈ −

η + η

• negligible penetration

• almost perfect reflection with phase reversal

Far-Field Measurement Configurations

detectorisolatoroscillatorcirculator

hornantenna

specimen

reflection (monostatic radar, pulse-echo)

detector

isolatoroscillator

hornantenna

specimen

reflection (bistatic radar, pitch-catch) scattering (bistatic radar, pitch-catch)

isolatoroscillator

hornantenna

specimen

detector detec

tor

Near-Field Inspection

detectorisolatoroscillatorcirculator

open-endedwaveguidespecimen stand-off

distance

air backing

foam coreadhesivesubstrateskin laminate

corrosion damage

coating

Lock-in Thermographyglass fiber-reinforced polymer plates (50 × 75 mm2)

(Diener, 1995)

detectorisolatoroscillatorcirculator

open-endedwaveguidespecimen stand-off

distance

infraredcamera

lock-inamplifier

modulator

microwave raster scan

lock-in thermography(phase image)

150-µm-thickdelamination

bondingdefects

Thermal Imaging

Heat Source

Testpiece

Film or CameraInfrared

Advantages: fast, inexpensive

large specimens without scanning remote sensing

reflection and transmission modes

Disadvantages: material sensitive poor sensitivity

poor penetration depth

Thermal Radiation

Planck’s law 2

5 /2

( 1)b hc KThcL

e λ=λ −

Lb spectral radiance of black body 3[W / m srad]

h Planck constant ( -34= 6.626 10 Js× )

c speed of light ( 8= 2.998 10 m/s× )

λ wavelength ( 0.1 100 m≈ ÷ μ )

K Boltzmann constant ( 23= 1.381 10 J/K−× )

T absolute temperature [K]

0

5

10

15

0.1 1 10 100Wavelength [µm]

Spec

tral R

adia

nce

[W/m

3sr

ad]

1000 K

300 K

3000 K

100 K

visible10

10

10

100

5

10

15

0.1 1 10 100Wavelength [µm]

Spec

tral R

adia

nce

[W/m

3sr

ad]

1000 K

300 K

3000 K

100 K

visible10

10

10

10

Stefan-Boltzmann Law of Thermal Radiation

4

0( )b bI L d kT

∞= π λ λ =∫

8 -2 -45.67 10 [Wm K ]k −= ×

Thermal Emissivity

Pincident

Ptransmitted

Preflected

Pabsorbed

Pradiated

Pradiated

incident reflected transmitted absorbedP P P P= + +

radiated absorbedP P=

emissivity absorptionε = =

4

0( ) ( )bI L d kT

∞= π ε λ λ λ ≈ ε∫

X-Ray Imaging

X-Ray SourceTestpiece

Film or CameraX-Ray

Advantages:

fast, relatively inexpensive large, awkward shaped specimens

good penetration

Disadvantages: poor sensitivity

only transmission mode (two-sided)

Gamma Ray Sources

unstable (radioactive) isotope

e.g., 60Cobalt

isotope

shielding

1/ 2/0 0( ) 2 t TtN t N e N −− δ= =

1/ 2/

0 0( ) 2 t TtI t I e I −− δ= =

1/ 2ln 2 0.693T = ≈δ δ

N number of unstable atoms

I radiation intensity (diverging beam) δ decay constant

1/ 2T half-life period

X-Ray Sources

Cathode(filament)

X-ray

electrons

High-VoltagePower

Supply

Low-VoltageHeater

Supply

PowerMains

Control &RectifierCircuit

V_

X-ray tube

Inte

nsity

[a. u

.]

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

Wavelength [Å]

20 kV

25 kV

30 kV

35 kV

40 kV

45 kV

Tungsten Target

min12,400 [VÅ]h c

eU Uλ ≈ ≈

Geometric Unsharpness

X-Ray SourceTestpiece X-Ray Film

F

Lo

og

FUL

=

F (focal) spot size

object-to-film distance Lo source-to-object distance

micro-focus ( 0.1 mF < μ )

2constantI

L=

oL L= + source-to-film distance

Absorption and Scattering

( )dI I x dx− = μ nμ = σ

0( ) xI x I e−μ=

I intensity μ attenuation coefficient

σ atomic scattering cross section

n number density of scattering atoms

n NA Aamuρ ρ

= =

ρ (mass) density

A mass number

N = 1/amu Avogadro's constant ( 23 16.02 10 mol−≈ × )

amu atomic mass unit (1/16th of oxigen atom, 241.66 10 g−≈ × )

2a rσ << = π

a geometrical cross section of the atom

r geometrical radius of the atom

Radiographic Imaging

t'tμ μ '

I0

I I' I

( ' )' t mI I e− μ − μ= , 0 tI I e− μ= , 'tmt

=

Den

sity

, D

0 .3 .6 .9 1.2 1.5 1.8 2.1 2.4 2.7 3.0

3.02.72.42.11.81.51.20.90.60.3

0

1

2

high-speedfilm

low-speedfilm

Exposure, log E

E I T= , ( ) log illuminating visible

transmitted visible

ID E

I=

Unsharpness, Resolution

exposed unexposed exposed unexposed

coarse-grain film fine-grain film

Uf

ideal

real film

Total unsharpness: 2 2t g fU U U= +

Optimum Source-to-Film Distance:

of g

FU UL

≈ =

F (focal) spot size, object-to-film distance, Lo source-to-object distance

(1 )optimumf

FSFD L tU

= ≈ +

Grating Diffraction

diffracted beam

incident beam

θi θd

d

d

d

d

transmitted beam

d >> λ

sin sini dd d nθ + θ = λ

n = 0, 1, 2, … i dθ = θ + θ ndλ

θ ≈

d n n

d d dΔ λ λ

Δθ ≈ − = ≈ −ε

Bragg Diffraction

[100]

[010]

[001]

[110]

[111]

incident beam diffracted beam

D(001) = a

θB θB

incident beamdiffracted beam

Θ(εp)“cold work”

θB(ε)

incident beam diffracted beam

D(001) = a

θBθB θBθB

incident beamdiffracted beam

Θ(εp)“cold work”

θB(ε)

2 sin BD nθ = λ , (n = 1, 2, ...)

2 2 2( ) = (cubic)aD hkl

h k l+ +, 2 10Å, 0.5 5Åa ≈ − λ ≈ −

3 410 10D

D− −Δ

ε = ≈ −

Application:

residual stress texture (Pole figure)

Residual Stress Distribution in Shot-Peened C11000 Copper Specimens

Depth [mm]

Res

idua

l Stre

ss [M

Pa]

-125

-75

-25

25

75

125

0 0.2 0.4 0.6

Almen 0

Depth [mm]

Res

idua

l Stre

ss [M

Pa]

-250

-200

-150

-100

-50

0

0 0.2 0.4 0.6

Almen 2

Depth [mm]

Res

idua

l Stre

ss [M

Pa]

-250

-200

-150

-100

-50

0

0 0.2 0.4 0.6

Almen 8

Depth [mm]

Res

idua

l Stre

ss [M

Pa]

-250

-200

-150

-100

-50

0

0 0.2 0.4 0.6

Almen 16

before stress release after stress release (30 min, 315 °C)

Pole Figures in C11000 Copper Specimens

plane (200) back-reflection

Almen 0 Almen 2

Almen 14 Almen 16

50-100 %, 100-200 % (relative to average)