Eddy Current Assessment of Near-Surface Residual · PDF fileP1: KVK Journal of Nondestructive...

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Journal of Nondestructive Evaluation [jone] pp1382-jone-496223 November 3, 2004 18:26 Style file version June 3rd, 2002

Journal of Nondestructive Evaluation, Vol. 23, No. 3, September 2004 ( C© 2004)

Eddy Current Assessment of Near-Surface ResidualStress in Shot-Peened Nickel-Base Superalloys

Mark P. Blodgett1 and Peter B. Nagy2,3

Received February 20, 2004; revised June 15, 2004

It is shown in this paper that, in contrast with most other materials, shot-peened nickel-basesuperalloys exhibit an apparent increase in eddy current conductivity at increasing inspectionfrequencies, which can be exploited for nondestructive residual stress assessment of subsurfaceresidual stresses. It has been found that the primary reason why nickel-base superalloys, whichare often used in the most critical gas-turbine engine components, lend themselves easilyfor eddy current residual stress assessment lies in their favorable electro-elastic behavior,namely that the parallel stress coefficient of the eddy current conductivity has a large negativevalue while the normal coefficient is smaller but also negative. As a result, the average stresscoefficient is also large and negative, therefore the essentially isotropic compressive planestate of stress produced by most surface treatments causes a significant increase in conductivityparallel to the surface. The exact reason for this unusual behavior is presently unknown, but therole of paramagnetic contributions cannot be excluded, therefore the measured quantity willbe referred to as “apparent” eddy current conductivity. Experimental results are presentedto demonstrate that the magnitude of the increase in apparent eddy current conductivitycorrelates well with the initial peening intensity as well as with the remnant residual stressafter thermal relaxation.

KEY WORDS: Eddy current; shot peening; residual stress.

1. INTRODUCTION

Shot peening is known to improve the resistanceto fatigue and foreign-object damage in metallic com-ponents due to its damage arresting qualities. This sur-face enhancement process, which introduces benefi-cial residual stresses and hardens the surface, is widelyused in a number of industrial applications, includinggas-turbine engines. Modern aircraft turbine enginecomponents are designed using a damage-tolerancephilosophy that allows the prediction of a given com-ponent’s useful service life based on fracture me-chanics and structural analysis. However, the fatigue

1 Metals, Ceramics, and NDE Division, AFRL, Wright-PattersonAir Force Base, Dayton, Ohio 45433-7817.

2 Department of Aerospace Engineering and Engineering Me-chanics, University of Cincinnati, Cincinnati, Ohio 45221-0070.

3 Corresponding author: E-mail: [email protected]

life improvement gained via surface enhancement isnot explicitly accounted for in current engine com-ponent life management processes. Therefore, thereis thought to be a significant potential for increasingthe predicted damage tolerance capabilities of com-ponents if beneficial residual stress considerations areincorporated into the life prediction methodology.Nondestructive inspection of components for near-surface flaws is a critical part of life assessment formany US Air Force engine applications. A major bar-rier to introducing subsurface residual stress informa-tion into the life calculation process is the necessity tomake accurate and reliable nondestructive measure-ments on shot-peened hardware. In this paper, we in-vestigate the effects of shot peening on the apparenteddy current conductivity (AECC) of several alloys,including Ti-6Al-4V and two nickel-base superalloys(Waspaloy and IN100). As a bridge to understanding

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108 Blodgett and Nagy

the eddy current results on shot-peened specimens, weexamine the effects of uniaxial mechanical loading onthe AECC using both directional (elliptical) and non-directional (circular) eddy current probes. The mainresult of this paper is the observation that the changesin AECC caused by shot peening and subsequent ther-mal relaxation are consistent with the effects result-ing from uniaxial tension and compression loading.Moreover, for certain nickel-base alloys, the AECCand the compressive residual stress arising from shotpeening appear to correlate uniquely, which leads usto believe the eddy current approach may provide awindow of opportunity for residual stress profiling.

The goal of this research is to develop non-destructive residual stress measurement techniquesfor a US Air Force research initiative known asEngine Rotor Life Extension.(1,2) Under this initia-tive, the Air Force Research Laboratory (AFRL) hasbeen sponsoring research to develop capabilities to,among other things, nondestructively measure subsur-face residual stresses in surface-treated titanium andnickel alloys. Shot peening is the main surface treat-ment of interest, along with laser peening and low-plasticity burnishing, which provide a deeper zoneof compression and significantly less cold work thanshot peening. For gas-turbine engines, fracture-criticalcomponents are currently shot peened in the (Almen)intensity range of 3A–8A, which results in a hardenedzone of near-surface compressive residual stress. Thedepth of compression is typically about 150–200 µmand the goal is to develop a nondestructive capabil-ity to measure the stress profile, with approximately25 µm depth resolution, over the entire compressivezone. A critical requirement is that the measurementmust be also capable of sensing small changes in thelevel of the remaining residual stress, since residualstresses may slowly relax over time as the componentis subjected to the harsh turbine engine environment.

Currently, the only reliable NDE method forresidual stress assessment is based on X-ray diffrac-tion (XRD) measurement that is limited to an ex-tremely thin (less than 20 µm) surface layer,(3−5)

which is approximately one order of magnitude lessthan the typical penetration depth of compressiveresidual stresses produced by currently used sur-face treatment procedures. Recent research effortsat AFRL have shown that stress relaxation in thisthin top layer occurs even at very modest tempera-tures and is essentially instantaneous at higher oper-ational temperatures. Therefore, without destructivesectioning, XRD cannot provide the sought informa-tion on subsurface residual stresses for life prediction

purposes. The commonly used hole-drilling methodis based on measuring the change in surface straincaused by relieving the prevailing residual stress bydrilling a hole in the specimen. Removing the stressedmaterial causes a readjustment in the surroundingmaterial to attain equilibrium, which can be quan-titatively measured by strain gauges mounted in thevicinity of the hole. Unfortunately, such destructivemeasurement techniques are not applicable to peri-odic maintenance of gas-turbine engine components.

Turbine engine components are designed to opti-mize aircraft performance, while accommodating theadverse effects of demanding service conditions. Dur-ing operation on an aircraft, many engine componentsare subjected to severe thermal and mechanical cy-cling conditions, which is presumed to cause dam-age and may also cause the residual stress and coldwork profiles to relax over time, thereby graduallylosing the protection afforded by shot peening. SomeUSAF engines are periodically disassembled and crit-ical components, such as turbine disks, are subjectedto intensive nondestructive inspections to ensure thatdimensional tolerances are met and surfaces are freefrom life-limiting flaws. Many individual componentsare cleaned and inspected by visual, fluorescent dye-penetrant, ultrasonic, and eddy current means in aneffort to detect surface-breaking fatigue cracks, fret-ting damage, foreign-object-damage, and other fea-tures such as dents and gouges.

Eddy current inspection is an obvious candi-date for use in characterizing the residual stressesresulting from shot peening, due to its frequency-dependent penetration depth.(6−14) Unfortunately, itis well known that eddy current conductivity is af-fected by a number of things beside residual stress,such as chemical composition, microstructure, hard-ness, surface roughness, temperature, etc. Therefore,it is essential to make an assessment of the relation-ship of the eddy current conductivity with stress, act-ing alone, on the alloys of interest. The sensitivityof eddy current conductivity to stress may be easilydemonstrated by putting a sample of the alloy into aload-frame and subjecting it to changing stress con-ditions over a fairly broad range of both compressiveand tensile loads within the elastic limits. Some ex-amples of the effect of stress on eddy current con-ductivity, the so-called electro-elastic effect, are pro-vided in this paper to help illustrate why we contendthat there may exist a window of opportunity for suc-cessful application of this type of eddy current-basedresidual stress measurement in some nickel-base su-peralloys. Eddy current conductivity measurements

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Eddy Current Assessment of Near-Surface Residual Stress 109

on shot-peened engine components, both prior andsubsequent to service, are currently not part of thestandard inspection protocol. However, with appro-priate calibration standards and tracking methods ofthe initial shot peening conditions and material pa-rameters, such as microstructure and alloy composi-tion, quantitative eddy current measurements couldbe made on the same critical engine components tocomplement routine eddy current flaw inspections.

The shot peening process involves impinging thesurface with a stream of uniformly sized spherical pro-jectiles. The plastic deformation generated by the shotimpact causes an instantaneous tensile stress in thedimple and a subsequent contraction, resulting in aremnant compressive residual stress zone beneath thedimple. By overlapping the dimple coverage, a moreor less homogeneous compressive residual stress zoneis created over a shallow surface layer in the shot-peened region. For engine components, shot peen-ing is controlled using specific guidelines on the shotdiameter and uniformity, shot velocity, impact angleof the shot stream, and the percentage of area cov-erage. Shot peening plastically deforms the surfaceof metal components, resulting in more or less uni-form but random surface roughness, a near-surfacelayer of compressive residual stress, and a shallowcold worked layer. Shot peening is performed on awide range of applications, including Ti- and Ni-basegas-turbine engine components, where the resultingcombination of hardening and compressive residualstress significantly improves resistance to fatigue andwear. Shot peening also serves as a surface finishingprocedure performed on parts to seal-up microscopicdamage and reverse tensile residual stress fields intro-duced by machining.

On actual engine hardware, the shot peening pa-rameters are based on fatigue and control samplestudies from identical alloys, where thermal and me-chanical interactions may be examined and the use ofdestructive residual stress profiling techniques, suchas X-ray diffraction, is feasible. However, suitablenondestructive techniques are absolutely required tosuccessfully implement residual stress protection as astrategy for component life extension, since the ac-tual degree of stress relaxation is especially difficultto predict because of the varying level of cold workpresent in surface-treated components, which exerts aprofound effect on the rate of stress relaxation. More-over, there are currently no adequate onboard en-gine monitoring or tracking devices to serve as a basisfor predicting the degree of protection loss for shot-peened engine components due to usage.

To the best of our knowledge, no nondestruc-tive profiling techniques are currently established thatcould meet the measurement needs for subsurfaceresidual stress in terms of component life extension.The eddy current approach is attractive for this pur-pose because it is presently the workhorse for nonde-structive inspection of military turbine engine com-ponents. Current periodic nondestructive inspectionsof engine components revolve around the detectionof near-surface flaws and often involve differentialeddy current techniques to optimize the probabil-ity of detection, rather than to map the eddy cur-rent conductivity. Eddy current based characteriza-tion of residual stress is also very attractive from thestandpoint of available instrumentation, since state-of-the-art eddy current instruments enjoy the benefitsof several decades of development. Currently, thereis already a substantial eddy current inspection in-frastructure geared for flaw detection in place, whichcould be easily branched over to residual stress char-acterization via AECC spectroscopy. However, theapparent eddy current conductivity is obviously in-fluenced by a number of different variables such assurface roughness, microstructure, magnetic perme-ability, etc. Therefore, great care must be taken inits measurement and interpretation and further re-search is needed to determine if the approach canbe made into a practical, quantitative means of as-sessing subsurface residual stresses for life predictionpurposes.

Most turbine engine components of interest arecomprised of either titanium alloys or nickel-base su-peralloys, which all have strict requirements on im-purity tolerances, heat treatments, and microstruc-ture characteristics to qualify as rotor-grade material.For titanium alloys, the material generally solidifiesin a hexagonally symmetric lattice structure for thealpha phase, which typically constitutes about 95%of the alloy volume. The processing of titanium al-loys typically results in the presence of bulk crystal-lographic texture due to limited availability of slipsystems and often there are macroscopic colonies ofgrains with similar crystallographic orientation. Thealpha phase in titanium alloys gives rise to local vari-ations in the AECC due mainly to the presence ofthese domains of crystallographic similarity, whichtypically affect the AECC to a larger extent than anyeffect due to stress. AECC variations as large as ±3%can be often observed in forged Ti-6Al-4V. Addition-ally, for Ti alloys, the surface roughness, cold work,and near surface compressive residual stress arisingfrom shot peening all cause similar decrease in the

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AECC as a function of frequency. Therefore, thereexists a uniqueness problem that prevents the eddycurrent conductivity approach from being used forresidual stress measurement in titanium alloys. Nev-ertheless, AECC mapping may prove to be a valuabletool to track other material properties, which evolveover time due to thermal and mechanical exposure. Incontrast, the AECC of alloys solidifying in cubic sym-metry, such as Ni-base superalloys, is not significantlyaffected by processing related material inhomogene-ity, such as crystallographic texture. The refined grainstructure and relatively even phase distribution ofthe microstructure essentially eliminates these char-acteristics as factors in the AECC signal since thesevariations are spatially averaged over the probe di-mensions, which are typically 2–3 mm or larger indiameter. Most importantly, there appears to be aunique relationship between the subsurface residualstresses in certain nickel-base superalloys and varia-tions in AECC, which is the main focus of this paper.

2. PRELIMINARY XRD AND EDDYCURRENT MEASUREMENTS

The main technical challenges to developing non-destructive techniques for characterization of subsur-face residual stresses are twofold: (i) achieving thehigh measurement sensitivity and accuracy requiredfor modest shot peening intensities (between Almen3A and 8A) typically applied to engine components,and (ii) separating the primary residual stress contri-bution from competing secondary factors in the mea-surement due to texture, hardness, microstructure,surface roughness, etc. As a first step towards meet-ing these challenges, several Ti-6Al-4V, Waspaloy, andIN100 sample sets of Almen intensities between 4Aand 16A were shot peened and tested by eddy cur-rent inspection. To get the necessary information onthe subsurface residual stresses, one set of samplesof each alloy was sacrificed for XRD stress measure-ments, using the destructive layer removal method.Figure 1 shows the residual stress profiles in shot-peened samples of three different engine alloys. Theseresults illustrate that the shot peening intensity has astrong effect on the depth of the compressive zone,but much less on the peak value of the compressiveresidual stress. Furthermore, the residual stress mea-surements all tend to cluster on the surface, indicatingone of the main reasons why surface only XRD mea-surements are probably insufficient for life predictionpurposes.

Fig. 1. Residual stress profiles in shot-peened samples of three dif-ferent engine alloys.

Existing scientific evidence indicates that evenwhen the eddy current measurements are conductedwith sufficient precision the obtained parameters areaffected by not only the existing residual stress profile,but also by the accompanying cold work(13) and sur-face roughness effects.(12,15,16) The penetration depthof the cold worked region is typically one third of thatof the compressive residual stress, therefore, just likethe surface roughness effect, cold work effects can-not be eliminated simply by an appropriate selectionof the inspection frequency. Generally, cold work ex-hibits itself through lattice imperfections, such as in-creased dislocation density, and localized anisotropycaused by crystallographic and morphological tex-ture. Separation of the residual stress and cold workeffects requires careful optimization of the inspec-tion method on a case-to-case basis. For example,crystallographic anisotropy strongly affects ultrasonic

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surface acoustic wave (SAW) measurements in allmetals except those of very low elastic anisotropy liketungsten or aluminum, but has no effect on eddy cur-rent and thermoelectric measurements in metals thatcrystallize in cubic symmetry, a broad category thatincludes essentially all engine materials with the no-table exception of titanium alloys.(17,18)

It should be emphasized that for the purposesof practical nondestructive assessment of thermo-mechanical relaxation in surface-treated metals, theseparation of residual stress and cold work effectsis less crucial than the elimination of surface rough-ness effects. The main reason for this is that in mostcases the decay of the subsurface residual stress ismore or less proportional to the parallel decay ofcold work, therefore their relative contribution to thenondestructively measured parameter is more or lessconstant. In comparison, the adverse effect of sur-face roughness is unaffected by thermo-mechanicalrelaxation, and might even increase as a result ofadditional roughening due to fretting, corrosion, orerosion, therefore its role is gradually increasing withrespect to the weakening residual stress.

The characteristic dependence of electrical con-ductivity on stress has been thought to be verypromising for residual stress measurements in met-als for a long time, though these expectations haveremained largely unfulfilled as far as surface-treatedcomponents are concerned. In most metals the stress-dependence of the electrical conductivity is ratherweak and the primary residual stress effect is ratherdifficult to separate from the secondary cold work ef-fect and, especially in shot-peened specimens, fromthe apparent loss of conductivity caused by the spu-rious surface roughness effect. In paramagnetic ma-terials the electrical conductivity typically increasesby approximately 1% under a maximum biaxial com-pressive stress equal to the yield strength of the ma-terial. However, the electrical conductivity measuredon shot-peened specimens typically decreases with in-creasing peening intensity, often as much as 1–2%,which indicates that surface roughness and cold workeffects dominate the observed phenomenon. We havefound that, in sharp contrast with most other materi-als, shot-peened Waspaloy and IN100 specimens ex-hibit an apparent increase in electrical conductivityat increasing inspection frequencies. This observationby itself seems to indicate that in these materials themeasured conductivity change is probably dominatedby residual stress effects, since surface roughness, in-creased dislocation density, and increased permeabil-ity are known to decrease rather than increase the

Fig. 2. Relative change in apparent eddy current conductivity(AECC) between the shot-peened sample and the unpeened equiv-alent for three different engine alloys over a frequency range of 1to 6 MHz.

apparent conductivity and the presence of crystal-lographic texture does not affect the electrical con-ductivity of these materials, which crystallize in cubicsymmetry.

Preliminary eddy current conductivity measure-ments were conducted on the remaining alloy samplesets using a Nortec 19eI I instrument and a 4-MHzUniwest absolute pencil probe to observe the changein AECC due to shot peening. Figure 2 shows someof these results over a range of frequencies from 1 to6 MHz. Of course the intrinsic electrical conductiv-ity of the material is independent of frequency overthis range. The observed frequency dependence ofthe eddy current conductivity is due to the depth-dependence of the electrical conductivity and the fre-quency dependence of the eddy current penetrationdepth. The apparent eddy current conductivity is cal-culated from the actually measured complex electricalimpedance of the probe coil by assuming a perfectlyflat and smooth homogeneous conducting half-spaceof zero magnetic susceptibility, therefore could be alsosignificantly affected by variations in magnetic ma-terial properties (permeability) as well as spuriousgeometrical effects (surface roughness). In order toindicate the potential influence of these uncorrectedeffects on the measured quantity, we will call it “ap-parent” eddy current conductivity or AECC.

The eddy current measurements shown in Fig. 2are based on the difference in the AECC between theshot-peened alloy and the unpeened equivalent alloy.The measurements were calibrated using two differ-ent conductivity standards (1.03% IACS and 1.45%

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IACS) in order to get the results in terms of percentchange in AECC. The results of Fig. 2 demonstratethat the AECC is affected by the Almen intensityand the inspection frequency, although the influenceof the inspection frequency is much clearer in thenickel-base superalloys than in the case of Ti-6Al-4V.It should be mentioned that in these preliminary mea-surements we used a rudimentary method to maintainlift-off consistency from sample to sample, which is es-pecially problematic for measurements at higher fre-quencies, and the data acquisition approach in generalwas rather crude. These measurements were subse-quently repeated in Waspaloy using a four-point lin-ear interpolation approach, which better elucidatedthe effect of frequency, over a larger frequency rangeas shown in Section 4.

Based on these preliminary results, the mostpronounced change in AECC occurs at the high-est peening intensities, where the compressive layeris the deepest, and at the highest inspection fre-quencies, where the penetration depth is the small-est. The alloys tested in this study are all relativelypoor conductors, with Ti-6Al-4V at approximately1% IACS and Waspaloy and IN100 both at approxi-mately 1.5% IACS. Hence, despite the high inspectionfrequencies, the standard penetration depth, whichis inversely proportional to the square root of thefrequency-conductivity product, is relatively large forthese alloys (e.g., approximately 200 µm at 6 MHzfor Waspaloy). The most important detail apparentfrom Fig. 2 is that the two nickel-base superalloysdemonstrate a frequency-dependent increase in theAECC over the shot-peened region, while Ti-6Al-4Vshows the opposite effect, which behaves like alu-minum alloys and other structural materials previ-ously studied in the literature.(6−14) This observationsuggests that the residual stress is most likely respon-sible for the observed increase in the AECC in shot-peened nickel-base superalloy samples because theother main effects of shot peening (i.e., increased dis-location density and surface roughness) are known tocause the apparent eddy current conductivity to de-crease.

There is some concern that this phenomenoncould be somehow related to subtle ferromagneticeffects caused by strong elastic and plastic strainsin these otherwise paramagnetic engine materials ofhigh iron and nickel content. However, we shouldmention that a thin ferromagnetic surface regionwould cause an apparent decrease rather than in-crease in the measured eddy current conductivity,therefore it is unlikely to play a dominant role in

the observed phenomenon. The possible influence ofmagnetic and microstructural variations in the cold-worked near-surface layer of shot-peened nickel-basesuperalloys will be separately investigated in order tobetter understand this phenomenon and to help de-velop the eddy current technique as a viable approachfor subsurface residual stress characterization.

3. ELECTRO-ELASTIC EFFECT

In direct analogy to the well-known acousto-elastic effect, a widely used NDE terminology for thedependence of the acoustic velocity on elastic stress,we are going to refer to the stress dependence ofthe electrical conductivity as the electro-elastic effect,which is often called in the literature as the piezoresis-tive effect. In the presence of elastic stress [τ ] the elec-trical conductivity tensor [σ ] of an otherwise isotropicconductor becomes slightly anisotropic. In principalcoordinates,

σ1

σ2

σ3

=

σ0 0 00 σ0 00 0 σ0

+

K‖ K⊥ K⊥K⊥ K‖ K⊥K⊥ K⊥ K‖

τ1

τ2

τ3

,

(1)

where σ0 denotes the electrical conductivity in the ab-sence of stress and K‖ and K⊥ are the so-called paralleland normal electro-elastic coefficients, respectively.

The simplest example of the electro-elastic effectis exhibited by ordinary strain gauges. Under uniaxialstress (τ1 = τ and τ2 = τ3 = 0), the so-called gaugefactor γ is defined as the ratio of the relative resistancechange δR/R0 and the axial strain ε = τ/E

γ = 1ε

δRR0

≈ (1 + 2ν) − 1ε

δσ

σ0= (1 + 2ν) − K‖

Eσ0

,

(2)

where δσ is the change in electrical conductivity andν and E denote Poisson’s ratio and Young’s modulus.It is well known that the gauge factor is usuallysignificantly higher than the first term 1 + 2 ν ≈ 1.6of purely geometrical origin, which indicates thatK‖ is negative. Of course, if the average electricalconductivity σ◦ is measured under uniaxial stressby a unidirectional circular eddy current probe, theeffective electro-elastic coefficient K◦ will be equalto the algebraic average of the parallel and normalelectro-elastic coefficients, i.e.,

δσ◦τ1

= K◦ = 12

(K‖ + K⊥). (3)

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Another example of the electro-elastic effectin conducting metals is the pressure dependence ofthe electrical conductivity under hydrostatic pressure(τ1 = τ2 = τ3 = −p), when

δσ

p= −(K‖ + 2K⊥). (4)

It is well known after the classic work of Bridgmanthat the pressure coefficient of the electrical conduc-tivity is negative in most structural metals, althoughsome exceptions do occur.(19) For our immediate pur-poses, the most important case is that of isotropicplane stress (τ1 = τ2 = τ and τ3 = 0), when the changein the measured average conductivity in the plane ofstress can be written as follows

δσ◦τ

= 2K◦ = K‖ + K⊥. (5)

Unfortunately, there is not much known in thescientific literature about the electro-elastic coeffi-cients of high-temperature engine alloys, thereforewe had to conduct a series of electro-elastic measure-ments to verify our working hypothesis that the in-creased apparent eddy current conductivity observedin shot-peened nickel-base superalloy specimenscould indeed be caused by the presence of com-pressive near-surface residual stresses. For this pur-pose we prepared a series of samples to be testedin a load-frame, where the effects of stress couldbe singled-out versus the other shot peening effects.Figure 3 shows a schematic diagram of the exper-imental arrangement used to measure the electro-elastic coefficients of different engine alloys in uni-axial compression and tension. Both non-directionalcircular and directional racetrack coil probes wereused for the load frame testing. The racetrack coilswere used in directions both parallel and normalto the loading direction to observe the directional

Fig. 3. A schematic diagram of the experimental arrangement usedto measure electro-elastic coefficients in uniaxial compression andtension.

dependence of stress on the apparent eddy currentconductivity.

Figure 4 shows examples of the axial stress andthe corresponding eddy current conductivity at par-allel orientation in IN718 as functions of time. Alter-nating axial load was applied to the specimens at acyclic frequency of 0.5 Hz. Although we are mainlyinterested in the effect of compressive stresses onthe electrical conductivity of the specimens, the max-imum tensile load was chosen to be twice as high asthe maximum compressive load in order to minimizethe possibility of buckling in the slender rectangu-lar bars used as specimens (w = 12.5 mm, t = 6.35mm, L ≈ 150 mm). Unless explicitly noted otherwise,these measurements were all made at f = 300 kHz,where the standard penetration depth (δ ≈ 1 mm) wasmuch smaller than the thickness of the specimens,therefore the spurious thickness modulation causedby the Poisson effect could be neglected. These mea-surements were conducted over a sustained period ofapproximately 2 minutes so that the adverse effects ofrandom noise and thermal drift could be sufficientlyreduced via averaging. However, it is clear even fromthe somewhat noisy raw data shown in Fig. 4 that theparallel electro-elastic coefficient of IN718 is negative,that is the conductivity increases in compression.

Figures 5, 6, and 7 show eddy current con-ductivity versus stress results for Ti-6Al-4V, IN718,and Waspaloy, respectively, at both parallel and nor-mal orientations. The symbols represent experimen-tal data while the solid lines are best fitting linearregressions. It is apparent from these results thatthe behavior of parallel eddy current conductivityis quite different between Ti-6Al-4V and the twonickel-base superalloys. In the case of Ti-6Al-4V, un-der compressive loading the AECC in the load di-rection (parallel orientation) progressively decreases,while for IN718 and Waspaloy, under similar loadingconditions, the AECC progressively increases. As wementioned above in connection with Eq. (5), the ef-fective electro-elastic constant under isotropic planestate of stress is the sum of the parallel and normalelectro-elastic coefficients, K‖ + K⊥. Therefore, it isvery important that in nickel-base superalloys bothcoefficients are negative so that they act together toprovide a relatively large increase in the apparenteddy current conductivity in shot-peened specimens.

Figure 8 demonstrates for ten repeated measure-ments each how the difference in signs of the paralleland normal stress coefficients results in a destructiveeffect on the average stress coefficient value in thecase of Ti-6Al-4V (a) versus IN718 (b) where the

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Fig. 4. An example of (a) the axial stress and (b) the eddy currentconductivity at parallel orientation as functions of time in IN718.

likeness in signs of the stress coefficients leads to aconstructive effect on the average value. These re-sults demonstrate that the anticipated role of stressin AECC measurements of shot-peened samples isexpected to be marginal in the case of Ti-6Al-4V, butquite significant if not dominant, for the case of IN718.

In nickel-base superalloys there is a possibilitythat a thin ferromagnetic surface layer forms dueto mechanical, microstructural, or chemical effects.For example, we found that the commercial qualityWaspaloy used in some of our experiments, which wassurface-treated by pickling (a type of chemical etch-ing to remove the top layer), did exhibit an approx-imately 0.1-mm-deep ferromagnetic surface layer inthe as-received state before machining and shot peen-ing. Chemical analysis revealed that this layer was sig-nificantly depleted of Ni, Mo, and Co and rich in Cr,C, and Fe. Measurements conducted on these spec-imens before removing the spurious ferromagneticsurface layer by grinding showed more than one or-der of magnitude increase in the electro-elastic coeffi-cients, which also showed strong signs of nonlinearity,hysteretic behavior, and frequency dependence. In or-der to verify that the measured electro-elastic effects

Fig. 5. Electro-elastic measurements in Ti-6Al-4V using a direc-tional eddy current probe (a) parallel and (b) normal to the applieduniaxial load.

in nickel-base superalloys were not significantly af-fected by the presence of such spurious ferromagneticsurface layers, we measured the electro-elastic coef-ficients in low-stress ground specimens over a widefrequency range. As an example, Fig. 9 shows the par-allel and normal electro-elastic coefficients measuredin engine quality Waspaloy between 100 and 800 kHz.Within the experimental uncertainty of the measure-ment, both electro-elastic coefficients are frequencyindependent, which clearly indicates that the resultsare not affected significantly by spurious surfaceeffects.

The fundamental reason for the difference inelectro-elastic behavior between nickel-base super-alloys and Ti-6Al-4V is currently unknown, but ofthe large number of different materials we havetested to date, the former case appears to be theexception, rather than the rule, which is probably

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Fig. 6. Electro-elastic measurements in IN718 using a directionaleddy current probe (a) parallel and (b) normal to the applied uni-axial load.

why eddy current-based evaluation of residual stresshas not been successfully demonstrated before forshot-peened specimens. Fortunately, the small groupof structural metals that exhibit this beneficialelectro-elastic behavior appears to include someof the most critical nickel-base superalloy mate-rials for gas-turbine engine components, includingWaspaloy, IN100, IN718, and likely many others.Table I lists the electro-elastic coefficients of varioushigh-temperature alloys tested to date. Clearly, thethree critical precipitation hardened gasturbine en-gine alloys (Waspaloy, IN100 and IN718) all demon-strate the potential window of opportunity for resid-ual stress assessment by eddy current means due totheir relatively large negative average electro-elasticcoefficients.

Table II lists the relevant electro-elastic, electri-cal, and mechanical properties of high-temperature

Fig. 7. Electro-elastic measurements in commercial Waspaloy us-ing a directional eddy current probe (a) parallel and (b) normal tothe applied uniaxial load.

alloys, which are useful as a basis for assessing theconsistency between the electroelastic effect and theAECC change observed in shot-peened specimens.The maximum expected relative change in the appar-ent eddy current conductivity can be estimated from

S = −2K◦τmax

σ0(6)

where K◦ is the non-directional average electro-elastic coefficient, σ0 is the unstressed electrical con-ductivity, and τmax is the maximum compressive resid-ual stress due to shot peening, which is estimatedfrom the nominal yield strength of the material. Innickel-base superalloys, the maximum relative con-ductivity change is predicted to be on the order of0.5–1%, which is reasonably close to the maximumAECC increase observed in shot-peened specimens.However, there are some minor discrepancies in the

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Fig. 8. A comparison the electro-elastic stress coefficients of(a) Ti-6Al-4V and (b) IN718.

results, requiring further research to better under-stand the physics of this approach in order to reliablyand accurately characterize shot peening relaxation inturbine engine materials. Specifically, for the case ofWaspaloy we would anticipate only a 0.5–0.6% change

Fig. 9. Parallel and normal electro-elastic coefficients measured inengine quality Waspaloy over a wide frequency range.

Table I. Combined Results of Stress Coefficient Measurements inHigh-Temperature Alloys (the Average and Standard Deviation

Values Are Given in 10−6% IACS/MPa)

1/2Alloy K‖ K⊥ (K‖ + K⊥) K◦

Ti-6Al-4V +5.73/0.15 −4.79/0.09 +0.46/0.07 +0.45/0.09Hastelloy X −0.62/0.06 +2.97/0.22 +1.17/0.09 +1.42/0.10IN718 −5.64/0.09 −4.38/0.09 −5.02/0.06 −5.31/0.07IN100 −6.90/0.16 −2.09/0.23 −4.50/0.09 −5.32/0.29Commercial −3.39/0.19 −1.54/0.12 −2.47/0.10 −2.63/0.15

WaspaloyEngine −2.93/0.10 −1.10/0.10 −2.02/0.07 −2.28/0.15

Waspaloy

in the electrical conductivity due to stress, but in a 16Ashot peened Waspaloy sample we actually measuredapproximately 1.8% increase at 10 MHz, relative tothe unpeened equivalent alloy. The discrepancy is notso apparent for the case of the 8A shot-peened Was-paloy, where we measure only about a 1.2% changeat 10 MHz, but there is still about a factor of 2 differ-ence in terms of the anticipated change due to stress.There could be a number of reasons for this, e.g., theknown fact that the presence of microstructural de-fects significantly increases the stress dependence ofconductors,(20,21) which will be separately investigatedin a follow-up project. Despite the small discrep-ancy for Waspaloy, we show later in this paper thatthe agreement between the eddy current results forcharacterizing shot peening stress relaxation is quitegood as judged by the established XRD layer removalstress measurement technique. On the other hand,IN100 and IN718 appear to be excellent candidatesfor this kind of nondestructive stress measurementapproach considering the nearly exact agreement be-tween the anticipated effect of stress on conductiv-ity and the actually measured effect in shot peenedspecimens.

Table II. Electro-Elastic, Electrical, and Mechanical Propertiesof High-Temperature Alloys, Which Are Useful as a Basis for As-sessing the Consistency Between the Electro-Elastic Effect and the

AECC Change Observed in Shot-Peened Specimens

K◦ [10−6% σ0 τmaxAlloy IACS/MPa] [%IACS] [MPa] S [%]

Ti-6Al-4V +0.45 1 680 −0.07Hastelloy X +1.42 1.6 410 −0.08IN718 −5.31 1.4 1370 +1.03IN100 −5.32 1.3 1370 +1.12Commercial −2.63 1.5 1720 +0.60

WaspaloyEngine −2.28 1.5 1720 +0.52

Waspaloy

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In summary, more research is essential to fur-ther understand this phenomenon, including the pos-sible role of slight permeability changes due tomarginal ferromagnetism and shot peening inducedmicrostructural effects, but the demonstrated consis-tency between shot peening and load-frame testing inthese preliminary results appears to reinforce our po-sition that retained stress is probably the main factorresponsible for the increase in frequency-dependentAECC for shot-peened nickel-base superalloys.

4. ABSOLUTE VERSUS RELATIVEAECC MEASUREMENTS

Since our specimens were shot-peened only overhalf of their surface, the unpeened half could be read-ily used for comparison purposes. Scanning the spec-imens parallel to their surface allowed us to directlydetermine the AECC difference between the peenedand unpeened parts at each inspection frequency. Weare going to refer to this technique as relative mea-surement. The surface of the specimen is first alignedwith the scanning plane of a motorized x − y table,the probe is adjusted to a constant nominal lift-offdistance (typically � = 0.1 mm), then the compleximpedance plane is rotated by changing the phase an-gle so that the lift-off direction appears horizontal,and the vertical component of the impedance varia-tion is used to assess the AECC. The adverse effectsof inevitable lift-off variations during scanning are ef-fectively reduced by this choice of the phase angle.The relative sensitivity of the system is determinedat each inspection frequency using similar measure-ments on a pair of appropriately chosen calibrationblocks. Because of its automatic scanning capability,this technique allow us to quickly inspect relativelylarge areas and obtain either two-dimensional AECCimages of the surface or simply calculate the averagedifference between the peened and unpeened parts.

In spite of its obvious advantages, relative mea-surements of the AECC based on direct compari-son of peened and unpeened parts is not practical inreal applications when usually there is not such refer-ence surface available. Instead, we have to measurethe absolute AECC of the specimen as a function offrequency and compare the near-surface propertiesmeasured at high frequencies to those at larger depthmeasured at low-frequencies. In order to clearly dis-tinguish this technique from the above described rel-ative measurement, we are going to refer to it as ab-solute measurement.

First, additional AECC measurements were con-ducted on intact shot-peened Waspaloy samplesin order to verify whether point-by-point absolutemeasurements using manual scanning or large-arearelative measurements using automated scanning arebetter suited for the subsequent inspection of ther-mally relaxed specimens. These measurements weremade by a Staveley Nortec 2000S eddy current instru-ment with three different probes to assure optimalsensitivity over a wide frequency range from 100 kHzto 10 MHz. The four-point calibration procedure usedin absolute measurements is slightly more compli-cated than the two-point calibration used in our pre-liminary measurements. Figure 10 shows a schematicrepresentation of the coil impedance in the complexplane before (a) and after (b) zoom-in and roation.For a given set of gains and phase rotation, the realx = x(σ , �) and imaginary y = y(σ , �) components ofthe measured impedance are determined by the con-ductivity of the specimen σ and the lift-off distance �.First, the four reference points are measured on twoappropriate calibration blocks with (� = s) and with-out (� = 0) a polymer foil of thickness s between theprobe coil and the specimens.

As we discussed before, complications such asinhomogeneity, permeability effects, surface rough-ness, etc., are neglected during inversion of thecoil impedance, therefore the measured frequency-dependent quantity is referred to as apparent eddycurrent conductivity or AECC. The coil impedancemeasured on the shot-peened specimens is evalu-ated in terms of apparent conductivity and lift-offusing simple linear interpolation (though the lift-offdata was subsequently discarded). It should be men-tioned that the linear interpolation technique, whichis known to leave much to be desired over larger

Fig. 10. A schematic representation of the coil impedance in thecomplex plane before (a) and after (b) zoom-in and rotationdemonstrating the four-point linear interpolation procedure for ac-quisition of the AECC data.

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measurement ranges, was quite sufficient over therelatively small conductivity range considered in thisstudy. Because of the high precision requirements ofthese measurements, efficient rejection of inevitablelift-off variations is of the utmost importance. It wasalso necessary to periodically repeat the calibrationprocedure during manual scanning in order to re-duce the adverse effects of thermal drift caused bythe weak, but still perceivable instability of the probeand the instrument. The statistical variations over the50.8 mm × 50.8 mm shot-peened areas were keptunder control by repeating all measurements at 50different locations and averaging the data for eachfrequency, which also reduced the incoherent scatterin the data caused by thermal oscillations, electricalnoise, imperfect lift-off rejection, etc. With such mea-sures, the accuracy of the averaged data is expectedto be better than ±0.002% IACS, i.e., approximately±0.15% relative to the 1.5% IACS baseline conduc-tivity of nickel-base superalloys.

For the following absolute measurements the ex-perimental system was calibrated at each inspectionfrequency using two standardized reference blocksof σ1 = 1.34% IACS and σ2 = 1.48% IACS and ans = 0.076-mm-thick polymer foil for controlling lift-off (above 4 MHz the thickness of the polymer foilwas reduced to 0.025 mm). Figures 11a and 11b showthe results of the eddy current measurements on thesmooth untreated and the shot-peened surfaces, re-spectively, for each of the four different peening in-tensities over a range of 100 kHz to 10 MHz. Theseresults were collected using manual scanning taking50 randomly located individual measurements (awayfrom the edges) at each frequency from both the un-treated and shot-peened surfaces and averaging thedata. The measurements from the untreated surfacesshow only a very mild decrease in AECC with increas-ing frequency, while the shot peened surfaces exhibitan increasing AECC as a function of frequency foreach peening intensity.

Figure 12 shows the difference between the un-treated and shot-peened surfaces for each peening in-tensity using two different methods. Figure 12a showsthe difference between the corresponding absolutemeasurements obtained by manual testing, whichwere previously shown in Fig. 11. Figure 12b showsthe results of the relative AECC measurements ob-tained by computer-controlled automatic scanning.A comparison between these results reveals a mi-nor discrepancy in the magnitudes of the AECC dif-ferences between the manual versus automated test-ing approaches. At this point, the exact reason for

Fig. 11. Absolute AECC taken manually from the (a) smooth orunpeened and (b) shot-peened halves of the intact Waspaloy sam-ples from 100 kHz to 10 MHz.

this discrepancy is not known, but we found thatmost of it is due to lift-off variations. During auto-matic scanning, additive errors due to inevitable lift-off variations are effectively rejected by measuringonly the component normal to the lift-off directionin the complex impedance plane. However, multi-plicative errors due to the decreasing sensitivity atincreasing lift-off distances still could affect the data.We conducted an experiment to determine the effectof varying the lift-off, which was measured using adial-gauge with approximately 2.5 µm accuracy, onthe sensitivity of the AECC measurement. The re-sults shown in Fig. 13 illustrate that for a 1.5-mm-diameter probe coil ±25-µm lift-off uncertainty re-sults in a relatively small ±4% error at 100 kHz, but asmuch as ±15% error at 10 MHz, which could accountfor most of the differences we observed between man-ual versus automated testing, considering that therecould have easily been ±25-µm lift-off uncertainty

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Fig. 12. Eddy current results after taking the difference in AECCbetween the peened and unpeened surfaces for (a) manual testingand (b) automated scanning.

in the AECC difference measurements during auto-matic scanning. Undoubtedly, this technical issue willhave to be solved before the eddy current method be-

Fig. 13. A comparison of the effect of varying the lift-off at100 kHz and 10 MHz on the normalized eddy current measure-ment sensitivity of a 1.5-mm-diameter probe coil.

comes a reliable quantitative tool for residual stressassessment, but for the limited purposes of the presentstudy we can conclude that the absolute and relativeAECC measurements are at least consistent. There-fore the following extensive measurements on ther-mally relaxed specimens were all made by the muchsimpler relative technique using automatic scanning.

5. MEASUREMENTS AFTER THERMALRELAXATION

As previously mentioned, an essential featureof the sought measurement capability is that it mustbe capable of sensing changes in the residual stressprofile after relaxation takes place in order to beuseful for life prediction purposes. To determine ifthe eddy current approach meets this requirement,additional AECC measurements were conducted onshot-peened samples after different levels of thermalrelaxation in order to verify the close correlation be-tween the observed increase in the apparent eddy cur-rent conductivity at high frequencies and the retainedresidual stress.

The first question is whether the AECC differ-ence between peened and unpeened surfaces dimin-ishes with thermal relaxation or not. To answer thisquestion, we inspected four shot-peened Waspaloyspecimens of different peening intensity both beforeand after full thermal relaxation. Figure 14a shows theresidual stress profiles as measured by XRD. An im-portant byproduct of the XRD stress measurementis the cold work distribution over depth in terms ofplastic strain as shown in Fig. 14b, which is based onthe width of the particular diffraction peak of inter-est (the 311 peak was used for these Waspaloy mea-surements). We can conclude that the peening inten-sity has a relatively strong affect on the degree anddepth of the resulting cold work in shot-peened sam-ples, with the highest degree of plastic strain occur-ring just below the surface at each peening intensity.In addition to the XRD data obtained from intactspecimens (solid symbols), Figs. 14a and 14b alsoshow the corresponding data obtained after full re-laxation for 24 hours at 900◦C (empty symbols). It isevident that essentially complete stress relaxation oc-curred in the specimens. In comparison, roughly one-fifth of the original cold work effect, which can befully eliminated only by actual recrystallization, sur-vived below the surface. Figure 15 shows the AECCdifferences recorded on these intact and fully re-laxed Waspaloy specimens. Within the uncertainty

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Fig. 14. X-ray diffraction (a) residual stress and (b) cold work pro-files in a series of shot-peened Waspaloy samples before and afterfull relaxation (24 hours at 900◦C).

of the eddy current measurement, the AECC dif-ference completely vanished, which indicates that itis not only very sensitive to thermal relaxation, butalso that it is mostly sensitive to the residual stresscontribution since the cold work effect did not entirelydisappear.

The next question is whether the AECC differ-ence decays gradually with thermal relaxation or not,which is extremely important from the point of viewof detecting partial relaxation. To answer this ques-tion, a Waspaloy specimen of Almen 8A peening in-tensity was gradually relaxed by repeated heat treat-ments of 24-hour each at increasing temperatures in50◦C steps from 300◦C to 900◦C in protective nitrogenenvironment. Figure 16 shows the decaying AECCdifference between the peened and unpeened partsafter each heat treatment. These results clearly in-dicate that the measured AECC difference gradu-ally decreases during thermal relaxation and almost

completely disappears after the 13th 24-hour heattreatment at 900◦C, which is very promising for thepossibility of sub-surface residual stress assessmentin shot-peened Waspaloy.

The most crucial question is whether the AECCdifference is proportional to the remaining residualstress throughout thermal relaxation or not. To an-swer this question, we subjected a couple of Waspaloyspecimens of Almen 16A peening intensity to differ-ent thermal conditions, followed by eddy current con-ductivity and X-ray diffraction stress and cold workmeasurements. These samples were treated with threedifferent thermal profiles at (i) 600◦C for 24 hours, (ii)600◦C for 24 hours followed by 650◦C for 24 hours,and (iii) 900◦C for 24 hours and then compared tothe original, as-received, shot peen condition. TheXRD residual stress and cold work profiles for eachcase are shown in Fig. 17. There is a rather strongrelaxation after the first heat treatment of 24 hoursat 600◦C, which is somewhat surprising as one wouldthink that the shot peening induced residual stresswould be more persistent in Waspaloy. However, wealready found in the previous series of measurementson a Waspaloy specimen of Almen 8A peening inten-sity, which is supposed to be thermally more stablebecause of the lower level of cold work present in thespecimen, that significant relaxation occurs at temper-atures as low as 500◦C (see Fig. 16), therefore theseXRD results are not entirely unexpected. To the bestof our knowledge, such early thermal relaxation inshot-peened Waspaloy has not been reported in theliterature before and this phenomenon will have to befurther investigated in the future. One possible expla-nation for this early relaxation is that these Waspaloyspecimens were stress annealed prior to shot peening,which typically puts the material in its softest state.Another unexpected result is shown in the XRD coldwork profiles where the degree of cold work is slightlyhigher in case (ii) than in case (i). This discrepancy isunusual, but the precise pedigree of the Waspaloy weused is unknown and samples may have come fromplate stock with different rolling conditions.

For each case, eddy current conductivity mea-surements were performed between 100 kHz and10 MHz. As before, differential measurements weremade between peened and unpeened surfaces usingautomatic scanning. As shown in Fig. 18, the eddycurrent measurements are consistent with the XRDdata in that the 600◦C, 24-hour thermal treatment, i.e.,case (i), caused a dramatic change in shot peen con-dition, as compared to the original. A comparison ofthe eddy current data for case (i) and case (ii) suggests

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Fig. 15. AECC differences recorded on intact (solid symbols) and fully relaxed (emptysymbols) Waspaloy specimens.

only a modest change in condition between the two,and case (iii) indicates virtually complete eliminationof shot peen effects in the measured AECC. Over-all, the decay of the AECC difference between thepeened and unpeened specimens is roughly propor-

Fig. 16. The decay of AECC difference between the peened andunpeened parts of a Waspaloy specimen of Almen 8A peeningintensity during gradual thermal relaxation.

tional to the decay of the sub-surface residual stress,although a more quantitative comparison has notbeen attempted yet. It should be mentioned that thereare numerous analytical and numerical methods thatcould be exploited to invert the frequency-dependentAECC.(22−25) The conductivity profiles obtained fromsuch inversion then could be used directly to assessthe existing residual stress profile based on the em-pirically determined electro-elastic coefficient of thematerial. These efforts will be part of our follow-upstudy.

6. CONCLUSIONS

Our experiments indicate that there exists aunique “window of opportunity” for eddy currentNDE in nickel-base superalloys. At least six factorscontribute to this fortunate constellation of materialproperties. First, the parallel stress coefficient of theelectrical conductivity has a large negative value whilethe normal coefficient is smaller but also negative. Asa result, the average stress coefficient is also large andnegative, therefore the essentially isotropic compres-sive plane state of stress produced by most surface

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Fig. 17. X-ray diffraction (a) residual stress and (b) cold work pro-files in a series of Waspaloy samples of Almen 16A peening intensityafter different levels of thermal relaxation.

Fig. 18. Eddy current conductivity measurements in shot-peenedWaspaloy of Almen 16A intensity (each heat treatment was 24hours).

treatments causes a significant increase in the electri-cal conductivity parallel to the surface. Second, theelectrical conductivity in nickel-base superalloys israther low (≈1.5% IACS) therefore the penetrationdepth is relatively high at a given frequency (≈180 µmat 10 MHz). Therefore, at typical inspection frequen-cies we can detect the increasing conductivity due tothe highly persistent residual stresses at larger depthsthat cannot be measured in a nondestructive way byX-ray diffraction, which is sensitive to the very unsta-ble near-surface residual stresses only. Third, the hard-ness is relatively high therefore the spurious surfaceroughness is relatively small for typical Almen inten-sities (3A–8A) used on engine components, thereforethe apparent conductivity drop due to this artifact isalso relatively small. Fourth, for the same reason, theeddy current conductivity is not reduced significantlyby increased dislocation density and other types of mi-crostructural defects due to cold work, which causethe thermal instability of the near-surface residualstress in the first place. Fifth, these materials crystal-lize in cubic symmetry, therefore the electrical con-ductivity does not exhibit crystallographic anisotropy,and therefore the spurious crystallographic texturebelow the surface does not affect the measurement atall. Sixth, in spite of the very high nickel and iron con-tent of these superalloys, neither the intact materialnor the cold-worked surface layer exhibit perceivablemagnetic permeability beyond slight paramagnetism,which otherwise could easily overshadow the muchweaker electro-elastic effect due to piezoresistivity.

On intact shot-peened specimens we found thatthe excess AECC was proportional to the peeningintensity. On partially relaxed shot-peened Waspaloyspecimens we found that the measured AECC differ-ence changed more or less proportionally to the re-maining sub-surface residual stress. On fully relaxedWaspaloy specimens, the AECC completely vanished,which indicates that it is fairly selective to the residualstress contribution since the cold work effect did notentirely disappear. The close qualitative resemblancebetween the eddy current conductivity and XRDresidual stress data leads us to believe that the eddycurrent approach has the potential to be exploited fornondestructive characterization of subsurface resid-ual stresses in certain surface-enhanced nickel-basesuperalloys. The frequency-dependence of the ex-cess apparent eddy current conductivity is consistentwith the penetration depth of the compressive resid-ual stress distribution and in a follow-up paper wewill demonstrate that quantitative inversion of thestress profile from the conductivity spectrum is also

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possible. However, it is obvious that further efforts areneeded to fully realize the quantitative potential of theeddy current approach in terms of the exact weight-ing of the different effects, the material-dependentcorrelation to residual stress, and the rendering ofresidual stress profiles based on the measuredfrequency-dependent AECC.

ACKNOWLEDGMENTS

This work was partially supported by the Depart-ment of the Air Force under Contract No. F33615-03-2-5210. The authors would like to acknowledgevaluable discussions with Waled Hassan of HoneywellEngines, Systems, and Services, Neil Goldfine andVladimir Zilberstein of JENTEK Sensors Inc., andNorbert Meyendorf of the University of Dayton. Theauthors also wish to thank Curtis Fox, Brian Minda,Mike Perrino, and Mary Locke of the Department ofAerospace Engineering and Engineering Mechanicsat the University of Cincinnati for their contributionsto some of the eddy current measurements reportedin this paper. The specimens used in this study weremachined at Metcut Research, Inc., the shot peeningwas performed by Metal Improvement Co., and theX-ray diffraction measurements were done byLambda Research.

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