Diagnostics of Degradative Changes

in Paramagnetic Alloys with the Use of

Low Frequency Impedance Spectroscopy

Zbigniew Hilary ZUREK1), Miroslaw WITOS2)

1) Silesian University of Technology 2) Air Force Institute of Technology

Poland

7th International Symposium on NDT in Aerospace 16 – 18 November 2015, Bremen, Germany

We5-A7

Outline: Introduction Motivation Low frequency impedance spectroscopy Drude model of metal LCR model of metal and its alloys Measurement equipment Some results Conclusion

Introduction

Safe aircraft operation requires the use of reliable non-destructive methods

(NDT) and structural health monitoring (SHM).

The NDT and SHM are specific in aeronautics due to complex load spectrum, influence of changing ambient conditions and variety of construction materials, among others : • ferromagnetic steels, • paramagnetic (austenitic) steels, • titanium alloys (ferro- and paramagnetic), • aluminum alloys, • magnesium alloys, • heat resistant alloys on the nickel and wolfram basis, • composites, • hybrid materials (metal - non-metallic filler - metal), • ceramics.

The materials of critical parts are different:

chemical composition,

microstructure,

mechanical and physical properties,

mechanisms of degradation.

For reliable diagnosis of the above mentioned materials the optimisation of

the NDT and SHM, so that the control actions do not disturb the main function of

the tested part of aeronautical engineering.

Motivation

During structural degradation D

of metals and their alloys the

following changes:

conductivity σ,

magnetic permeability μ,

electrical permittivity ε.

Impedances:

- Elektromagnetic Zm

- Electric Ze

- Wave Zw

Vilysa J., Kvedarasb V., Dislocation Structure of Near Surface Layers of Deformed Low-carbon Steel. 15th Int. Metallurgical & Material Conference METAL 2006 .

The impedance of the surface layer is different from the impedance of the core.

The difference gives the state of microstructure, including dislocation density.

Motivation

For all metals and their alloys the observation frequency band

may be narrowed to:

0 - 100 kHz (ferromagnetic alloys)

0 - 10 MHz (paramagnetic and ferromagnetic alloys in the state of magnetic saturation).

Low frequency impedance spectroscopy Metals and their alloys

The parameters ε, μ, σ and change in their values can be observed and analysed during

electromagnetic tests in radio frequency band from 3 Hz to 3 THz using various test

methods and techniques.

Metals and their alloys

Ferromagnetic 𝜇(𝐇, σ𝑖𝑗) 𝜇0 ≫ 10 ,

but 𝜇(𝐇𝑠𝑎𝑡) 𝜇0 ~ 1.0

Metastable paramagnetic 𝜇 𝜇0 ∈ (1.0, 2.0 > ,

but μ(εij, σij)/ μ0 >> 2

Paramagnetic 𝜇 𝜇0 ∈ (1.0, 2.0 >

Diamagnetic 𝜇 𝜇0 ∈ (0, 1.0)

Diagnostic symptoms

σ(0), ε(0), Δσ(t), Δε(t)

σ(0), ε(0), μ(0), Δσ(t), Δε(t), Δμ(t)

Low frequency impedance spectroscopy State observer

The fatigue degradation process of metals is described by a nonlinear simple

problem

state of the microstructure → electric and magnetic parameters of the material

where: 𝑍𝑚 = 𝑍𝑚 𝜀, 𝜎, 𝜇, 𝜔 - material impedance, aim of the tests;

𝑍𝑠 = 𝑍𝑠 𝑅𝑠, 𝐿, 𝐶, 𝜔 - impedance of measurement probe,

state observer element;

𝑍0 = 𝑍0 𝜔 - reference impedance;

𝑘𝑚 = 𝑘𝑚 𝜔, ℎ, 𝑃𝑆,𝑀 - coupling coefficient of the probe

with the tested object,

𝑍𝑚 = 𝑓 𝑍𝑆, 𝑍0, 𝑘𝑚 = 𝑓( 𝜔, ℎ 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠

, 𝜎, 𝜀, 𝜇𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠

, 𝑟 𝑑 , 𝐿, 𝑅𝑆, 𝑄, 𝑆𝑅𝐹𝑝𝑟𝑜𝑏𝑒

𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠

)

Reliable diagnosis of the material structure condition and

its degradation degree with coil requires correct solving of

a nonlinear inverse problem.

Low frequency impedance spectroscopy Methodology (5 steps)

1. Measurement of the measuring probe's impedance response 𝑍𝑠 𝜔 and

coupling coefficient 𝑘𝑚 𝜔 of the probe with a tested material in selected

frequency band 𝜔 ∈ 𝜔𝑚𝑖𝑛, 𝜔𝑚𝑎𝑥 → same as ET NDT and PMFT NDT.

2. Estimation of the frequency response of the material impedance 𝑍𝑚 𝜔

3. Quantitative and qualitative analysis of the impedance response 𝑍𝑚 𝜔 ,

with the reference impedance response 𝑍0 𝜔

Δ𝑍 𝜔 =𝑍𝑚 𝜔 − 𝑍0 𝜔

𝑍0 𝜔

4. Analysis of the material nonlinearity degree on the basis of the material

impedance distortion response

𝑇𝐻𝐷𝑍 𝜔 = 𝑍 𝑘 ∙ 𝜔 2𝑛𝑘=2

𝑍 𝜔 2 or Δ𝑍 𝜔, Δ𝐼 =

𝑍 𝜔, 𝐼 − 𝑍0 𝜔, 𝐼0𝑍0 𝜔, 𝐼0

5. Diagnostic reasoning:

Active experiment – building diagnostic criteria,

NDT & SHM: diagnosis on the basis of revised criteria.

Drude model of metal Assist in the development of diagnostic criteria

In general, complex conductivity is rank-2 tensors (9 of complex numbers)

𝜎 = 𝜎1 + 𝑗𝜎2 = 𝜎𝐷𝐶 +𝜔𝜀2 𝜔 + 𝑗𝜔𝜀1 𝜔

Note: The Drude conductivity considers only the conduction electrons in a metal (omits the

polarisation of the ion cores, which may occur at the final stage of material degradation).

The frequency response of conductivity of metals and its alloys is well

described by the Drude model (1900) – it is a simplistic model for conduction.

𝜎 = 𝜎1 + 𝑗𝜎2 = 𝜎𝐷𝐶 1 + 𝜔2𝜏2 + 𝑗 𝜔𝜏𝜎𝐷𝐶 1 + 𝜔

2𝜏2

In the 10 MHz frequency band

𝝈𝟏 ≅ 𝝈𝑫𝑪 and 𝝈𝟐 ≅ 𝝎𝝉𝝈𝑫𝑪 The value of the conductivity at the maximum is

𝜎1 0 = 𝜎𝐷𝐶 = 𝜔𝑝2𝜏 4𝜋

where: 𝜔𝑝 − the plasma frequency (a few THz),

𝜏 − the relaxation time (typically 10-14 second).

𝜎1

𝜎2 Silver

Low frequency impedance

spectroscopy

Dobrzański J.: Sposób szacowanie czasu dalszej bezpiecznej pracy materiałów pracujących w warunkach pełzania na przykładzie charakterystyk materiałowych stali 10CrMo9-10 po długotrwałej eksploatacji. XIV Konferencja Naukowo-Techniczna Projektowanie, Innowacje Remontowe i Modernizacje w Energetyce PIRE 2012,

t/tr

0,1 0,8 1,0 0,6 0,4 0,2

Electric model of metals and their alloys

When the electromagnetic radiation wave is many times longer than the size of microstructure

elements and plasma frequency 𝜔𝑝 in the Drude model, the local and global parameters of

a metal may be modelled as a real inductor.

𝑌𝑚 = 𝑌𝑅 + 𝑌𝐿 + 𝑌𝐶 =1

𝑅𝑝+1

𝑅𝑆 + 𝑗𝜔𝐿+1

𝑅𝐶 + 𝑗1𝜔𝐶

The admittance of LCR circuit (Ym = 1/Zm)

Measurement Contactless method (coil), near field

Wave impedance Zw is described by: source type of wave reflection losses , RE, RM absorption loss, A

The Hioki IM 3532-50 LCR HiTester offers:

wide testing frequency: 42 Hz to 5 MHz

testing frequency while delivering 0.08%

accuracy;

high-speed measurement of 5 ms,

measurement data transmission to a

computer via USB 2.0,

control of the testing programme from

an external computer.

Measurement instruments

1. Laboratory digital LCR bridge

2. Cheap handheld digital LCR bridges (< 350 $)

The UT 612 model is a typical representative of cheap RLC meters

which enable automatic measurement and transmission of

measurement data to a computer via USB 2.0.

It is primarily designed to measure capacitance, inductance, resistance,

DC resistance and their associated quality factor, dissipation and phase

angle using a serial or parallel measurement mode.

Measurement frequency: 100 Hz, 120 Hz, 1 kHz, 10 kHz and 100 kHz.

Best accuracy: 0.5%.

Measurement instruments

3. Low cost evaluation module (< 50 $)

The LDC1000 Inductance-to-Digital Converter TI company measures the parallel impedance of an LC resonator. It accomplishes this task by regulating the oscillation amplitude in a closed-loop configuration to a constant level, while monitoring the energy dissipated by the resonator. By monitoring the amount of power injected into the resonator, the LDC1000 can determine the value of: impedance Rp with 16-bit resolution inductance L with 24-bit resolution. LC frequency range (carrier frequency of LCRs tank): 5 kHz – 5 MHz.

The LDC1101 converter is similar in its functionality to the LDC1000. The LDC1101 features dual inductive measurement cores, allowing for > 150 ksps 16-bit Rp and L measurements simultaneous, with a high-resolution L measurement with can sample at > 180 ksps with a resolution of up 24-bit. LC frequency range (carrier frequency): 500 kHz – 10 MHz.

Measurement instruments Low cost evaluation module (<50$)

The AD5933/34 Analog Device is a high precision impedance converter system solution that combines an on-board: frequency generator with a 12-bit, and < 0.1 Hz resolution (27-bits) allows an external

complex impedance to be excited with a known frequency to a max. frequency of 100 kHz. analog-to-digital converter (ADC): 1 MSPS for AD5933, 250 kSPS for AD5934, DSP engine with DFFT. Impedance measurement range from 1 kΩ to 10 MΩ with 0.5% accuracy. The response signal from the impedance is sampled by the on-board ADC and a discrete Fourier transform (DFT) is processed by an on-board DSP engine. The DFT algorithm returns a real (R) and imaginary (I) data-word at each output frequency.

Rs

Rp

SRF

ωL

Q-factor

Results HCF of the ASTM 289 class C austenitic steel

Very small in impedance changes outside the scope resonance probe

Results Quality control of the aluminum alloy (AlSi13Mg1CuNi)

Very small in impedance changes outside the scope resonance probe

Diagnostic symptoms are available in the data of handheld LCR bridge!

Results Low frequency estimators Parj = f(Zs, Zs,0, Γ, ω)

HCF of the ASTM 289 class C austenitic steel Quality control of AlSi13Mg1CuNi)

Results Resonance method, which is used by LDC1000 and LDC1101

Very high sensitivity and orthogonality impact of change in μ and (σ, ε).

Artificial 2 defects

Artificial 2 defects

Results Resonance method – reference impedance Z0

Note: While precise data analysis should take into account the frequency

characteristics of the coil (Rs, Ls, Q-factor).

Rs value changes under the skin effect.

SRF of coil >> SRF of LCR circuit. LDC Reference Coils User’s Guide. User’s Guide TI. http://www.ti.com

Example:

PCB circular coil, Φ13 mm, 4 layers, 25turns/layer

SRF = 9.3 MHz

Conclusion

1. Taking above present results into account, the low frequency

impedance spectroscopy provides possibilities to diagnose the

degradation degree of structure of paramagnetic alloys,

including:

detecting early stages of material degradation (work

hardening, cyclic weakness)

verify the quality of the microstructure (the quality of

material production and supply of spare parts)

2. Low frequency impedance spectroscopy can be implemented

(as NDT and SHM applications) for metals and their alloys with

the use of cheap microprocessor devices (the unit cost of

electronics is below 50 $).

Diagnostics of Degradative Changes

in Paramagnetic Alloys with the Use of

Low Frequency Impedance Spectroscopy

Zbigniew Hilary ZUREK1), Miroslaw WITOS2)

1) Silesian University of Technology 2) Air Force Institute of Technology

Poland

7th International Symposium on NDT in Aerospace 16 – 18 November 2015, Bremen, Germany

We5-A7

Thank you for your attention

Any questions?

More info: http://www.researchgate.net/profile/Zbigniew_Zurek3 http://www.researchgate.net/profile/Miroslaw_Witos