Magnetic Response Field of Spherical Defects Magnetic Response Field of Spherical Defects within Conductive Componentswithin Conductive Components

M. M. KreutzbruckKreutzbruck , H., H.--M. ThomasM. Thomas , R. , R. CaspersonCasperson , V. , V. ReimundReimund and M. and M. BlomeBlome

Federal Institute for Materials Research and Testin g, BAM Berlin

Division VIII.4, Acoustical and Electrical Nondestructive Methods

Progress in NDT 2009, 12th -14th October, Prag

1. Examples of different electromagnetic NDE Problems to detect inclusions using dc or ac currents

2. FEM – Modelling and influence of

- different conductivity of matrix and inclusion- sensor-to-inclusion separation- inclusion size- Development of an analytical description

3. Experimental results

4. Summary and outlook

Overview and Introduction

Inclusion Detection in Microwave Cavities

- Accelerating microwave cavity made from high purity niobium. - tantalum inclusions are common defects, which must not be larger than

100 µm in diameter- Methods to be used: Eddy Current Testing, Current Injection and

thermomagnetic methods.

b)

(Courtesy W. Singer, TESLA-Accelerator, DESY, Hamburg)

Pore Detection within Electrical Contacts

b)

Cross-section of the contactContact from outside,

- Testing electrical contacts- usually tested by measuring the electrical resistance

- The injected current can be used to detect the magnetic field variation due toadditional geometrical changes within the contact

10 mm

arising of pores sheet: AlMg3 [3% Mg], 1 mm thickpore-Ø average ~300 µm

rdef = 300 µm: SNR: 69

rdef = 100 µm: SNR: 7.5

27.6 mm

Bz

MR- linear-array

• 64 single sensors• 50 µm strips Permalloy• Sensitivity 1 nT / √Hz• Ppatial resolution 125 µm

Testing Al-laser welds and its porosity

Technical Application of Superconducting Wires

Magnetic Resonance Tomograph(MRI)Cu/NbTi: 45 Filaments, ∅ 0.6 -2.4 mm, 2 - 5 Tesla at 4.2 K∆I <1.5 ppm/ year

NbTi

Cu

High Energy Physics,Magnets for particle acceleratorsCu/NbTi: 8670 Filaments, ∅ 1.065 mm, Ic= 540 A (7 Tesla at 4.2 K)

NMR- and Lab-MagnetsCu/NbSn: 6000 - 18000 Filaments, ∅ 0.7 -1.4 mm, 10 - 15 Tesla at 4.2 K

15 Tesla- Magnet, JLU-Gießen (IAP)

Courtesy DESYCourtesy EAS GmbH

Courtesy Bruker GmbH

Testing the SC-Wire using 4 GMR-Sensors

Magnetic field strength of the radial component of each GMR sensor as function of the axial position of the wire.

defect size: about 60 µm diameter in 200 µm depth below the surface.

∅D = 0.7 mmf = 10 kHz

Rauschen:∆Bpp = 0.01 µT

S/N ration : 7 - 445

FEM-Modelling as a Suitable Tool forCurrent and Magnetic Field Calculations

High intrinsic accuracy requires large FEM-mesh with sufficient number of elements (> 2.5 Mio, > 1 Mio nodes).

Substraction method of reference model and defect model for a better determination of the inclusion’s tiny field variation up to nine orders of magnitude smaller than the excitation field.

Circular excitation coil located above a metal plate containing inclusions with sizes between 50 µm and 800 µm.

Example for a gradiometiccurrent excitation

FEM-Modelling as a Suitable Tool forCurrent and Magnetic Field Calculations

Spherical tantalum inclusion within a metal plate with eddy current distortion in cross-section plane. FE-mesh composed of several nested spheres.

Current distribution in the vicinity of the inclusi on

Spherical tantalum inclusion within a metal plate with eddy current distortion in cross-section plane. FE-mesh composed of several nested spheres.

Current distribution in vicinity of the inclusion

Current Density in the vicinity of the defect

Inclusion diameter: 200 µm, z = 0, uniform current flow passes along x-axis. Conductivities: Ti: 2.34 MS/m, Cu: 59.6 MS/m, Al: 37.7 MS/m.

If σΙ > σΜ : increased current flow within the inclusion

If σΙ < σΜ : increased current flow outside the inclusion

Iσ

Mσ

j

Iσ

Mσ

j

Perturbation current flow generates a 2D magnetic flux distribution above the surface, inclusion conductivity σΙ is zero, location: 1 mm below the surface, diameter: 100 µm, hosted in Al-alloy-matrix (σΜ =20 MS/m)

Magnetic Flux Density distribution above the plate caused by the Inclusion

IσMσ

j

Magnetic Flux Density Response for DifferentConductivity of Inclusion and Host

Inclusion diameter: 200 µm, located 2 mm below the surface, sensor-to-inclusion separation: 5 mm

Simulation shows:

( )( ) 2

lim

lim

0

−=→

∞→

β

β

β

β

z

z

B

B

with

M

I

σσβ =

σσσσDef < σσσσMat σσσσDef > σσσσMat

103 104 105 106 107 108109

-7.5

-5

-2.5

0

2.5

5

10

Leitfähigkeit Einschluß [S/m]

Bz

[µT

]

Nb-Matrix, 6.93 MS/m

Ti-Matrix, 2.34 MS/m

Ta

σσσσDef < σσσσMat σσσσDef > σσσσMatσσσσDef < σσσσMat σσσσDef > σσσσMat

103 104 105 106 107 108109

-7.5

-5

-2.5

0

2.5

5

10

Leitfähigkeit Einschluß [S/m]

Bz

[µT

]

Nb-Matrix, 6.93 MS/m

Ti-Matrix, 2.34 MS/m

Ta

y

Z = 0

Response for Different Conductivity of Inclusion and Host – error function of the fit

105 106 107 108

-2

-1

0

1

Conductivity [S/m][Hz]

erro

r [%

]

108 109103 104 105 106 107

-20

0

20

Inclusion Conductivity [S/m]

Mag

netic

fiel

d B

z [µ

T]

-40

Al-hostNb-hostTi-host

Inclusion diameter: 200 µm, located 2 mm below the surface, sensor-to-inclusion separation: 5 mm

+−

=+−

2

12

~ββ

σσσσ

MI

MIzBFit function: (FEM: red, green, blue dots)

(Fit: solid lines)

Fall-off characteristic for the flux density calculated for different inclusion diameter r and separations z

Inclusion with zero conductivity (air) located in a titanium matrix (conductivity: 2.34 MS/m).

)(zB 2

1

z~

Fall-off characteristics

above platewithin plate

Current distribution at the vicinity of the inclusions calculated for different inclusion diameter rInclusion with zero conductivity (air) located in a titanium matrix

Current Distribution for Different Inclusion Sizes

800 µm

400 µm

200 µm

100 µm

50 µm

-1.0 -0.6 -0.2 0.2 0.6 1.00.0

0.4

0.8

1.2

1.6

2.0

X [mm]

Cur

rent

den

sity

[A/m

m²]

800 µm

400 µm

200 µm

100 µm

Fall-off characteristic calculated for different inclusion diameter r and separations z

Inclusion with zero conductivity (air) located in a titanium matrix

)(zB ~ 3r

Magnetic Flux density for Different Inclusion Sizes

800 µm

400 µm

200 µm

100 µm

50 µm

1

2

3

4

5

6

7

8

9

0.01 0.1 1 10 100

Sensor -to-inclusion separation [mm]

B(z

,r=

400

µm)

/ B(z

,r=

200

µm)

B(z,r) ~ r

B(z,r) ~ r 3

77,27,47,67,8

88,28,48,68,8

9

1 10 100Sensor-to-inclusion separation [mm]

B (

r) /

B (

r/2)

B (r=100 µm) / B (r=50 µm)B (r=200 µm) / B (r=100 µm)B (r=400 µm) / B (r=200 µm)

( )

+−

⋅⋅⋅=2

1

354.1 2

3

00

ββµ

βz

rjB ppz

0

354.1k

µ=

Despite the high dynamic flux range between 30 pT and 7 µT, the constant varies in a range of a few percent only.

Analytical expression for the response field

4

Frequency Dependence of the Results

For dc current flow jo describes the current density at the defect. This is also the case for ac applications including the skin effect. In our case the distortion field caused by the defect is than attenuated on its way back to the surface. This makes jo a frequency dependent property

variation of k(f) as a function of the frequency and as a function of the normalized penetration depth).

Different inclusions (σ, r)

located in a Ti-matrix, z = 2 mm.

k(f) is an universal functionfor the frequency dependence.

)(354.1

)( 00 fjfk

µ=⇒

Experimental Results Tantalum inclusions in Nb-plates

− 2 − 1 1 2

1.01

1.02

1.03

1.04

1.05

1.06

Current density [A/ mm²]

Distance y [mm]

Current distortion of a 2 mm-deep circular tantalum inclusion (dia. of 800 µm) in a planar niobium sheet (FEM simulation),

Low perturbation effect due to similar conductivity:

Tantalum: 7.6 MS/mNiobium: 6.9 MS/m

Eddy current distortion along the dashed line in the left figure.

Experimental Results Tantalum inclusions in Nb-plates

- Eddy current response of a 1 mm-deep, 200 µm dia. circular inclusion with varying conductivity in a planar niobium sheet

- FEM simulations, Sensor-to-sample separation: 1 mm). The maximum achievable magnetic field 1 mm above the sample is about 1.7 nT for a tantalum inclusion(0.8 mT excitation field)

10 102 103

104 105.

10

20

30

40

50

Ti

Pb

Nb Ta

Al

Ag

Mag

net

ic in

duc

tion

Bz pp [

nT]

Electrical conductivity σ [S/mm]

Niobium plate

Experimental Results

11 Tantalum spheres each about 100 µm in dia. were embedded into a 30 cm x 30 cm niobium sheet. EC field distribution above the niobium plate shows a field amplitude in the order of 20 pT.

⇒

Bz =1.7 nT (FEM) for z = 2mm and r = 100µm

In case of r =50 µm -> 1/8and z = 7.9 mm -> 1/16

We thus expecta signal strength of 14 pT