Tone Burst Eddy Current Thermography(TBET) for NDEApplications

C.V. Krishnamurthy, Krishnan Balasubramaniam , N. Biju, M.Arafat and N. GanesanCenter for Non Destructive Evaluation, and Department of Mechanical Engineering,Indian Institute of Technology Madras, Chennai-600 036, India.E-mail : balas@iitm.ac.in

AbstractThe Eddy Current Thermography is an evolving non-contact, non-destructive evaluation method with applications especially in aircraftindustries. It involves two approaches (a) the volumetric heating of the specimen and the observation of additional heating at defect locationsdue to Joule heating (called eddy-therm) and (b) the use of high frequency eddy current bursts for the transient surface/near surface heatingof the objects and sensing the propagation of a “thermal wave” using a high sensitivity infra-red (IR) camera (Tone Burst Eddy-currentThermography-TBET). In this paper, a study on the optimum frequency of eddy current excitation which will give a maximum temperaturerise for a given thickness has been conducted using both modeling and experimental techniques. COMSOL 3.5 was used to solve the coupledequations of electromagnetic induction and heat transfer. The dependency of this optimum frequency (peak frequency) on thickness, electricalconductivity, and thermal response of the sample (both plate and pipe geometries) are studied. The effect of thickness loss relative to thecoil inner radius is looked in to. The thermal responses of defective samples obtained by simulation are compared with experimental results.

Keywords: NDE, induction heating thermography, Tone Burst Eddy current Thermography (TBET), peak frequency optimization.

mathematical model for high frequency induction heatingand studied the effects of heating parameters such as thecoil lift of f, applied current, the frequency, and the turns ofthe coil on the temperature histories. The study pertains toa specimen without any defect. The results obtained bysimulation were verified by experiments. Recently, KiranKumar et al., [20,21] discussed the application of Tone BurstEddy current Thermography (TBET) that employs a surfaceheating using high frequency eddy currents and comparedit with the flash thermography method. The paper describesthe temperature profiles of non defective samples of differentmaterials and also of a sample with a flat bottom defect. In[13,14], the method of using induction based volumetricheating based thermography is being explored for surfaceand subsurface crack detection.

Most efforts on the use of eddy current heating forNDT have been concentrated on volumetric heating of thesample and observing the Joule heating at the crack surface.Recently, the use of high frequency for surface heating, andthe use of “thermal wave” that diffuses into the sample(similar to the pulsed thermal imaging) called the Tone BurstEddy current Thermography (TBET) is being explored. Forboth approaches, the surface and subsurface heating zonesand the efficiencies of material heating and the subsequentretrieval of relevant information for the non-destructiveevaluation of materials and components will require the useof optimum frequency of the eddy current excitation. In thepresent paper, the dependence of frequency on the thicknessof the material, on the electrical conductivity, and on theamplitude of thermal response of the sample has been studied

1. Introduction

The process of induction heating consists ofdevelopment of eddy currents in a conducting material byelectromagnetic induction and generation of heat by Jouleheating. The heat diffuses in the material and the temperatureon the surface of the specimen changes [1,2]. The transienttemperature behavior on the surface of the specimen, and theinfluence of the “thermal wave” that diffuses into the mediumon the surface temperature, is picked up by a sensitivethermal imaging equipment (such as an IR camera) and usedfor detecting and characterizing surface and sub-surfacedefects. Pulsed thermographic NDT has been previously wellreported [3-7] and is based on the rapid heating of thesurface of an object using either a laser or a flash lamp andtransient mapping of the surface temperature, either on thesame side or on the opposite side, using a high-speed, high-sensitivity, infrared (IR) camera. Heat diffusion into thematerial, when perturbed by the presence of a subsurfacedefect, causes a local temperature contrast (between thedefective and the non-defective regions) on the measuringsurface. This temperature contrast is detected by the thermalimaging equipment. Recorded images over several time framesare processed for extracting the internal flaw information.

An alternative method using induction based (eddy-currents) heating for thermography is being explored forsurface and subsurface crack detection [8-14], and forapplications in the lock-in thermography mode [15]. Severalanalytical/numerical models are reported on the inductionheating process [16-18].H. Chen et al., [19] used a

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in detail using a Finite Element model and verified usingexperiments. An attempt is made to find the thermal responseof a defective Aluminum sample by simulation and compareit with the experimental results. The study was done usinga specimen with sixteen EDM notches which simulate theeffects of wall thinning defects of different diameters anddepths. The influence of defect size on the temperaturehistory is studied and effect of coil diameter relative to thedefect diameter is also looked in to. The simulation is doneby COMSOL 3.2 multi physics software.

2. Mathematical Model

The mathematical model for the electro magneticinduction is given by the Maxwell’s equations together withthe constitutive equations and Ohm’s law.

Using the definition of potentials

(1)

the Ampere’s law can be written in the form

(2)

where E is the electric field intensity (V/m), B is the magneticflux density (T), A is the magnetic vector potential and V isthe electric potential, J is the external current density(A/m2), ε is the permittivity of the medium (F/m) = ε0εr, εr isthe relative permittivity, ε0 is the permittivity of free space =8.854x10-12 F/m, and σ is the electrical conductivity (S/m).

For axially symmetric structures with current passingonly in the angular direction, the problem is formulated byconsidering only the Aϕ component of the magnetic potential.The gradient of electric potential can be written as

(3)

since the electric field is present only in the azimuthaldirection. Vloop is the potential difference for one turn aroundthe z-axis. For time harmonic analysis A=Aϕejωt, (2) takes theform

(4)

The boundary conditions are magnetic insulation on thedomain boundary,

Aϕ = 0 (5)

and continuity of magnetic fields on the interior boundaries,

n × (H1–H2) = 0 (6)

The heat generated within the plate is taken as [22]

Q = ½σ|E|2 (7)

For an axi-symmetric problem, the heat transfer equationis expressed by

(8)

where ρ is the material density (Kg/m3), Cp is the specificheat (J/Kg. K), T is the temperature (K), and k is the thermalconductivity (W/m. K).

The boundary conditions used are prescribedtemperature at the domain boundaries,

T=Ta (Ambient Temperature) (9)

and heat flux at the other boundaries

(10)

Where h is the convective heat transfer coefficient(W/m2.K), T∞ is the ambient temperature (K), and ε is theemissivity, and σ is the Steffan-Boltzmann constant= 5.67x10--8 W/m2K4.

3. Experimental Set up

The experiments were performed on two Aluminumplates. One was of 1 mm thickness without any defect andthe other with thickness 1.7 mm with wall thinning defects of30m, 20mm 10mm, and 5 mm diameter with defect thicknessof 1.25 mm, 1.45 mm, 1.55 mm, and 1.65 mm in each case [23].The coil was made by winding copper wire of gauge 26 ona bobbin with around 100 turns. The lift off of the coil fromthe sample was approximately 2 mm. A current of 12 A waspassed through the coil for 3 s and the temperature historyof the surface was monitored for 6 s. A power amplifier PA52A was used to amplify the input power to the coil. Theexperiments were repeated for different frequencies. Aninfrared camera with a sensitivity of ~ ±0.1o was used tomeasure the temperature on the top surface of the specimen.The camera was placed on the same side of the coil (reflectionmode). A schematic diagram of the experimental set up isshown in Fig.1.

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Fig. 1 : Schematic diagram of the experimental set up

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4. Simulation Studies

The coupled electromagnetic and temperature fieldequations were solved using COMSOL 3.5 multi physicssoftware. Axial symmetry was made use of in the analysis.The loop potential was calculated from the current passingthrough the coil (in the experiment) and its resistance andwas approximately equal to 0.25 V. Simulation studies werecarried out for different time of heating and finally arrived ata time of heating of 3 s and the period of observation 6 s.The smaller the time of heating, the lesser the temperaturerise. Higher values for excitation time are not used to avoidover heating of the amplifier during experiments. The trialswere repeated for different frequencies. The coil was modeledby Copper wires of 0.3 mm diameter in 25 x 4 arrangementsas shown in Fig. 2. The specimen was made of aluminum.Both the coil and the specimen were placed in air domain.Simulation studies were carried out for both defective andnon defective samples. Figure 3 finite element discretisationof the model.

The material properties and constants used for thesimulation studies are listed in Table 1.

The Boundary conditions used for the electro magneticinduction were

1) Axial symmetry at r=0

2) Magnetic insulation at the air boundaries (Aϕ=0)

3) Continuity of magnetic fields at the interior boundaries(n × (H1–H2) = 0)

and for the heat transfer,

1) Axial symmetry at r=0

2) Temperature boundary condition at the air boundaries(T=Ta =300 K)

3) Heat flux at the other boundaries

[ ].

The thermal signatures of the sample were monitored atpoint1.

5. Results and discussion

5.1 Simulation studies on an Aluminium plate without defect

Figure 4 shows the simulation temperature history ofpoint 1 on the top surface of 1mm thick Aluminum samplewithout any defect for different frequencies of excitation. Itis observed that there is an optimum frequency (fm) at whichthe temperature rise is the maximum.

Peaking takes place for 1 s duration pulse as well as forany higher value say 3 s duration. The peak temperatureincreases with duration. The frequency at which peakingtakes place is the same for any duration pulse. All thesetrends are observed in volume heating regime. For each

Table 1. Material properties and constants used for the simulation.

Material Property Air Aluminium Copper

Relative permeability, µr 1 1 1

Electrical Conductivity, σ(S/m) 0 3.774x10-7 5.998 x10-7

Thermal Conductivity, k (W/m. K) 0.026 160 400

Density, ρ(Kg/m3) 1.23 2700 8700

Specific Heat, Cp (J/kg. K) 1005 900 385

Constants

Convective Coefficient, h (W/m2. K) 5

Emissivity, ε 0.3

Ambient Temperature(K) 300

Fig. 2 : Model used for simulation study.

Fig. 3 : The discretised domain showing the Finite Elementmeshing, the coil mesh is provided as an insert.

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frequency fi, the local maximum temperature (Tfi) occurs at orgreater than the time at which heating takes place. The localmaximum temperatures (Tfi-) for each frequency was foundout and normalized with the highest value (Tmax) of the Tfi‘sand the normalized maximum temperature is plotted as afunction of frequency in Fig.6 and a comparison is madebetween simulation and experiment. A small input voltagewas found to be sufficient to produce a measurable changein temperature.

For high electrical conductivity values, the peakfrequency is more clearly observable . For low electricalconductivity values, the peak is less predominant. There canbe a wide range of frequencies for which there is noconsiderable temperature change. The simulations arerepeated with electrical conductivity values of 6.5x107 S/m(Silver) and 0.25x107 S/m (Zirconium). The optimum frequency(fm) is found to be 900 Hz and 4800 Hz respectively. The peaktemperature attained in each case with different loop potentialis shown in Fig.7. The effect of thermal diffusivity on theoptimum frequency is also studied. It was noticed that thethermal diffusivity has little influence on the optimumfrequency because of volume heating and because of longexposure, heat diffuses several times across the thickness.

5.2 Variation of optimum frequency (fm) with differentthickness and electrical conductivity values of the sample

The optimum frequency values for different samplethicknesses and electrical conductivities of the material,keeping all other parameters same, are plotted in Fig. 8. Threeelectrical conductivity values used are that of Silver (6.5x107

S/m), Aluminium (3.774x107 S/m), and Iron (1.1 x107 S/m) Thevalues of peak frequencies are plotted against the non-dimensional log (δ/T) values. Here, skin-depth (d) is computed

Fig. 4 : Simulation results of the temperature history of point1 on the top surface of 1 mm thick Al sample withoutany defect for various frequencies of eddy currentexcitation.

Fig. 5 : Simulation results of the temperature history at point 1on the top surface of a 2 mm thick Al sample, withoutany defect, for various excitation frequencies. Theheating time was 3 s and excitation voltage was 0.25 V.

Fig. 6 : Experimental verification of optimum frequency in a)1 mm aluminum plate

Fig. 7 : Peak Temperature vs. Loop Potential curve for materialsof high and low electrical conductivity values.

Fig. 8 : Simulation results of variation of peak frequency withlog(δ/T) for different electrical conductivity values.K=160 W/m. K, Cp=900 J/Kg. K, density=2700 Kg/m3

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using the standard expression where f is the

frequency of excitation, σ is the electrical conductivity of thespecimen, and µ is the permeability of the specimen.

For volumetric heating (δ>t i.e. where the skin depth isgreater than the thickness), the peak frequency (fm) isdependent on δ/T ratio as well as the electrical conductivityσ. For non-volumetric or surface heating (δ<t) this frequencyis found to be invariant to σ and t for a given coilconfiguration. The volume of heating, if the most efficientheating is desired, depends only on the skin depth andbecomes a function of the materials electrical conductivityonly. Any variations in the depth of heating can beaccomplished at sub-optimal frequencies i.e. only bysacrificing the efficiency of heating.

When the defect radius is more than the inner radius ofthe coil (dd > rd), a shift in the optimum frequency was alsoobserved (Fig.11). But when the defect radius is less than thecoil radius such a shift in optimum frequency was not visible.But there was a change in the peak temperature (Fig.11).Thus by observing the peak temperature and the optimumfrequency of excitation, one can detect the presence of metalloss/addition.

Experiments were conducted on an Aluminium plate of1.8 mm thickness with EDM notches simulating the effectsof metal loss. The defects were of 30 mm, 20 mm, 10 mm, and5 mm diameter with metal loss of 0.5 mm, 0.25 mm, 0.15 mm,and 0.1 mm in each case. The coil used had an inner diametergreater than the defect diameters. No shift in the optimumfrequency was observed. But the peak temperature changewas observed to be linear.

6. Experimental study with defective plate

The optimum frequency shift was observable inexperiments also. Figure 12 shows the optimum frequencyvalue obtained when a coil of 10 mm inner radius (rc) wasplaced over a wall thinning defect of 14 mm radius (rd) and

Figure 9 shows the simulated peak frequency plotted

against for cases where δ/T>1. From this data, a

regression analysis was performed. From the regression, forthe case of volumetric heating (δ/T>1), a rule-of-thumb

relationship can be written as where fm is the

optimal frequency of excitation, and C=4652. This empiricalexpression will be useful in obtaining the optimum frequencyfor efficient heating with reasonable accuracy, without theneed for time consuming Finite Element calculations. Theexpression compares well with the Finite Element results forδ/T values ranging from 1 to 10. However, for higher valuesof δ/T, the errors were found to be greater than 10% (arbitrarilychosen) and deemed unacceptable. Hence, the empiricalexpression is considered to be valid only for δ/T rangingfrom 1 to 10.

5.3 Simulation studies with a defective plate

Simulations were done on 2 mm Aluminium plate withdifferent defects simulating the effects of material loss andmaterial deposit. The defect depth (dd) and defect radii (rd)were varied. The Peak temperature obtained during simulationwith an optimum frequency of 900 Hz is shown in Fig. 10.When the defect radius is less than the coil inner radius, thepeak temperature variation is linear. But, as the defect radiusbecomes more than the coil inner radius the variation of peaktemperature becomes non linear.

Fig. 9 : Simulated optimum frequency (fm) vs. for caseswhere δ/T >1.

Fig. 10: Peak Temperature variation in a 2 mm Aluminiumsample when there is a defect (metal loss/ addition)whose diameter is less than the coil radius (20 mm). Thesimulations were done at an optimum frequency(fm = 900 Hz).

Fig. 11: Shift in the optimum frequency (fm = 900 Hz ) whenthere is a defect in an Aluminium sample of 2 mmthickness

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1.25 mm defect thickness (td) made in an aluminum plate of1.7 mm thickness. For the no-defect case, the optimumfrequency value was 900 Hz which changed to 1200 Hz forthe defective plate.

7. Simulation studies with pipe geometry

Simulation studies were carried out with a 1 s tone burstsignal with 0.5 V excitation potential. The trials were repeatedfor different frequencies. The coil was modeled by 1 layer ofcopper wire of 0.25 mm diameter and was placed inside thepipe as shown in Fig. 13. The stand-off distance of the coilfrom the inner surface of the pipe was about 2 mm. The innerdiameter of the pipe was 12 mm and length 50 mm. Both thecoil and the specimen were placed in air domain. Copper wasselected as the material for the pipe. Axial symmetry wasmade use of in the analysis.

Simulations were done for different thicknesses ofcopper pipe starting from 0.1 mm to 10 mm with differentexcitation frequencies. For each thickness, there existed afrequency for which the temperature rise at the surface of thepipe is a maximum. As in the case of plate geometry, thisoptimum frequency (fm) was unchanged for thickness of thepipe greater than the skin depth (δ). Figure 14 shows the

variation of the optimum frequency with thickness of thepipe. The optimum frequency followed an inverse relationwith (√σd) for cases where δ<d as shown in Fig. 15. For pipethickness more than 2 mm, the optimum frequency was foundto be around 3250 Hz for this coil geometry.

The numerical study was repeated for an aluminum pipewith two different wall thicknesses. For half of the length,the thickness was 2 mm and for the other half 1.5 mm. Thetemperature contrast between the thicker and thinner regionswas found out for different excitation frequencies. At theoptimum frequency, the contrast was found to be themaximum (Fig.16).

Fig. 12: Experimental results showing the shift in the optimumfrequency when the coil is placed over the defect. Coilradius is 10 mm, the defect radius is 14 mm and defectthickness 1.25 mm, aluminum plate thickness 1.7 mm.

Fig. 13: Model used for simulation of pipe geometry.

Fig. 14: Simulation results showing optimum frequency fordifferent thicknesses of copper pipe.

Fig. 15: Optimum frequency vs. for cases δ > d in a copperpipe.

Fig. 16: Normalised temperature contrast between the thickerand thinner regions of an aluminum pipe for differentexcitation frequencies.

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8. Experiments with Pipe Geometry

A coil was designed for the induction heatingthermography of pipes of small diameter. The coil was woundwith copper wire of 36 SWG, along the length of a non-conducting central core. Figure 17 shows the coil and thestepped aluminum pipe and Fig. 18 shows the schematic of

the experimental set up. The excitation was given for 1 sduration. The temperature history of two points on the surfaceof the pipe, one each in the thicker and thinner sides, isshown in Fig. 19. The data were acquired at 200 Hz framerate. The temperature profiles clearly distinguish the regionswith thickness changes. Convective heat loss boundarycondition was used in the simulation model at the innersurface of the pipe and the coil. During experiments, it wasfound that the heat loss from the interior is very small,because of the small diameter of the pipe as well as thecentral core. Hence, the temperature profiles obtained aredifferent. It took more time to cool down during experiments.Therefore, only a qualitative comparison is made here.

9. Conclusions

Based on an axi-symmetrical FE model used forsimulating the temperature field developed during theinduction heating of an electrically and thermally conductingplate like material, the following conclusions can be made:

(a) Excellent correlation between simulation andexperimental results verifies the

(b) validity of the FE model.

(c) Simulation studies showed the existence of an optimumfrequency (fm) of excitation at which the temperaturereaches a maximum value, which was verified in theexperiments.

(d) The optimal frequency (fm) was found to be dependenton the the electrical conductivity. For low electricalconductivity values, the peak temperature occurs overa wide range of frequencies. As the electical conductiviyincreases this range narrows down.

(e) The optimal frequency (fm) significantly varies with theδ/t for the case of volumetric heating (δ/t>1). For thisregions, a rule of thumb empirical expression was derivedand found to be valid for the δ/t range from 1 to 10.

(f) The effect of thermal properties on this peak frequencywas found to be negligible.

(g) When there is a metal loss or deposit of radius less thanthe coil inner radius, the peak temperature varies linearly.But when it is of size larger than the coil radius, thevariation becomes non linear. Also a shift in the optimumfrequency was observed in the latter case. It was foundthat for defect radius(rd)<coil radius (rc), the sensitivityfor the detection of defect is relatively small whencompared to rd>rc.

(h) The optimum frequency depended on the electricalconductivity and thickness of the materials. When theskin depth is less than the thickness of the material(surface heating), the optimum frequency was found tobe independent of the material properties for a givencoil geometry. A rule of thumb relationship wasdeveloped to predict the optimum frequency in thevolume heating regime (skin depth is greater than thethickness of the plate). The presence of a wall thinningdefect, with diameter greater than the inner diameter ofthe coil, changed the optimum frequency.

Fig. 19: Experimental results giving the temperature profile attwo points (one each on the thinner and the thickerside) on the surface of the stepped diameter aluminumpipe.

Fig. 17: The coil and the aluminum stepped diameter pipe usedfor the experiment.

Fig. 18: Schematic of the experimental set up for pipe geometry.

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