MODELING ULTRASONIC GRAIN NOISE WITHIN TI-6A1-4VFORCINGS

Linxiao Yu, R. B. Thompson and F. J. MargetanCenter for Nondestructive Evaluation, Iowa State University, Ames, IA 50011, USA

Andrei DegtyarUnited Technologies Pratt&Whitney, East Hartford, CT 06108,USA

ABSTRACT. Large variations of backscattered ultrasonic grain noise levels have been observed withinTi-6Al-4V forgings. Such noise variations are believed to be correlated with the microstructuralvariations that occur during the forging processing. A modeling effort is made to try to correlate theultrasonic grain noise with available microstructure information. One model input is the localdeformation caused by the forging process, as calculated using DEFORM software. From this localdeformation the elongations and orientations of microstructural scattering elements are determined. Othermodel inputs are the mean volume of a scattering element and a parameter that quantifies the elasticproperty variation between scatterers. For one particular forging, the grain noise levels predicted by themodel at various locations are compared with experiment.

BACKGROUND AND OBJECTIVES

Large variations of backscattered ultrasonic grain noise with position and inspectiondirection have been observed within Ti-6Al-4V forgings intended for use in rotating jet-engine components [1]. Such noise variations are believed to be correlated with the localmicrostructural variations that arise from thermo-mechanical processing (TMP) [1].Historically, TMP has been used as the primary means of changing the shapes and sizes ofmaterials, transforming, for example, cast ingot into a desired wrought product. However,it has also become an increasingly common way of controlling the microstructure byimposing restrictions on the working temperature range and the amount of work [2]. Avariety of microstructural characteristics of the final product (grain size, degree ofrecrystallization, grain aspect ratio, texture, etc.) are sensitive to the TMP details. Forexample, if there is negligible recrystallization during TMP, the grain aspect ratio isprimarily determined by the initial grain structure and the directional metal flow.

Aircraft engine forgings generally have complex geometries, and the strainmagnitude and flow direction are different at different locations. It is thus expected that themicrostructure will vary throughout a forging. Because such forgings are often large, it isdifficult to get a detailed overall picture of how the microstructure varies by the traditionalmetallographic approach. Fortunately, some useful microstructural information can bededuced from forging simulation software, such as DEFORM, a commercial softwarepackage produced by Scientific Forming Technologies Corporation, Columbus, Ohio. Onesuccessful use of this software to correlate ultrasonic noise anisotropy within a forging withthe ratio of scatterer projections onto the two inspection directions was reported earlier [1].

CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00

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Billet Forging

FIGURE 1. DEFORM simulation for a axisymmetric forged disk, showing one-half of the cross-sectionin the radial-axial plane, a). Strain map; b). Net map, starting from 7:1 ellipsoids in the billet.

Examples of DEFORM outputs are shown in Figure 1, for the case of an engineforging produced from a cylindrical billet. The billet itself began as a cast ingot that wassubsequently worked to reduce its diameter. Fig.la displays the "strain map", whichillustrates how the magnitude of the forging strain varies with position. Fig.lb displays a"net map", which indicates how 7:1 ellipsoid-like elements in the billet would be modifiedby the forging process. Here the 7:1 aspect ratio in the billet has been motivated by thegeneral shape of billet macrograins [1]. Note in Figure Ib that the forging process changesboth the elongations and orientations of the elements. The rectangular and circular boxesin the figure indicate the locations where coupons were cut for the UT propertymeasurements described in Reference [1].

In the current work, a model is developed to predict the variation of the absoluteultrasonic grain noise level within a forging. The model treats the forging as an effectivemedium containing scattering elements whose mean properties vary systematically withposition. One model input is the local geometry of a scattering element, including itselongation and orientation with respect to the incident ultrasonic beam. Such informationcan be deduced by DEFORM. Two additional model inputs are the mean volume of ascattering element (assumed to be fixed throughout the forging) and a parameter thatquantifies the mean elastic property variation between scatterers. These latter two"global" inputs are deduced by fitting to experimental data. For the Ti-6Al-4V forgingillustrated in Figure 1, the grain noise levels predicted by the model at various locations arecompared with experiment.

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REVIEW OF THE THEORYBecause of its great importance in nondestructive evaluation and materials

characterization, ultrasonic backscattering has been investigated by many authors [3-13].A series of papers by Rose [10,11,12] relate backscattered noise levels to the physicalproperties of the microstructure. Using a single-scattering assumption and the Bornapproximation, Rose developed a rigorous stochastic theory for the backscattered noisepower, which led to explicit expressions for randomly orientated, equiaxed, single-phase[11] and multi-phase [12] polycrystals. Han and Thompson's work [13] extended Rose'stheory to the cases of duplex microstructures, which may contain texture and elongatedmicrostructural features. The expressions used in our work are consistent with those inReference [13].

A commonly used measure of a microstructure 's noise generating capability is thebackscattering power coefficient TJ, i.e., the differential scattering cross section per unitvolume in the backward direction [14,15]. Some authors prefer to use the square root of TJ,the so-called grain noise figure-of-merit (FOM) [5-9]), since it is directly proportional tothe noise voltage observed on an oscilloscope during UT inspection. In the theories ofRose, Han and Thompson, FOM and TJ for longitudinal waves propagating in the z = 3direction are related to microstructure features by :

FOM 2 = i! = \ 8C33(r)8C33(r'), v(4 Tip V,2 /

where k is wave number, p is density, Vl is the longitudinal wave velocity, r is a vector, zis a particular component of r, <SC33(r)SC33(>')> is the two-point correlation of elasticconstant perturbations [13]. r and r9 are two points in the poly crystalline, 8C33is the localdeviation of the elastic constant from its Voigt average (8C33=C33-Cvolgt

33), and < > denotesan ensemble average. We will assume that the crystalline axes of our scatterers arerandomly oriented (i.e., an untextured microstructure). In that case we have thesimplifications:

< 6C 3 3 ( r )6C 3 3 ( r ' ) > = < 6C323 > W (r - r') (2)

FOM 2 = t i (m) = 8C2 W47TPF,2

where <8C233> is a constant representing the crystallite elastic anisotropy, and W(r - r') is

the probability that two points are in the same crystallite and o is frequency. W(r - r') is

FIGURE 2. Geometry of an ellipsoidal scattering element showing the parameters used in the theory [13].Sonic beam propagation is assumed to be parallel to vector k.

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assumed to exponentially decreases with |r - r'|, the separation between r and r'. Note thats = r - r' is a vector. For elongated ellipsoidal scatterers, depicted in Fig. 2, Equation (3)becomes:

2sin 9FOM 2 = n = -,-=•——»- < 8C323 > f (±21°rfe«H.

(4KPV,2)2 0

JoJ A>(4)

A = {1 + (R2 -1) cos <92 }1/2 /(3VK / 4;r)1/3 - 2flk(sin 9 sin (/) sin T + cos 0 cos r), (5)

aspect ratio

average scatter volume

(6)

(7)

In the theory summarized by Eqs. (l)-(7), the backscattered noise level isdetermined by the scatterers' geometric features and elastic property variations. Thegeometric features include the grain aspect ratio (R), the grain orientation with respect tothe incident beam (T), and the average volume (V). The elastic property variations enterthrough the factor <8C2

33>. Local values for R and T will be deduced from the deformationsimulation. Global values of V and <8C2

33> will be fit to experimental data. Note that Eq.(4) contains a complicated two-dimensional integral, which can only be evaluatednumerically. An adaptive algorithm using a recursive technique was developed to performthe numerical integration.

COMPARISON BETWEEN THEORY AND EXPERIMENT

The global model parameters V and <8C233>, which are assumed to be constant

throughout the forging, were chosen by fitting the model predictions to a limited subset ofthe available noise data. As shown in Figure 3, FOM-vs-frequency curves measuredthrough side 1 (radial) and side 5 (axial) of forging coupon #8 were used. The optimalaverage scatterer volume was estimated as V = 1.328e-06 cmA3 and the optimal elasticproperty variation factor was estimated as <8C2

33> = 9.75 GpaA2. The measured and fittedcurves are compared in Fig. 3a; notice the large noise difference in the axial and radialdirections that is well reproduced by the model.

Having fixed the global model parameters, we now compare model with experimentfor other locations in the forging. Fig. 4b shows results for the remaining two sides of thesame coupon(#8) that was used in optimization. It is not surprising to see good agreementbetween theory and experiment for this case, because the microstructure variations within a

F

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•it to the Experimental FOM Data from side 1 and side 5V=1.328E-06cmA3, <deltaC33A2>=9.75 GpaA2

*side1 Exp.-sidel fitting• SideS Fitting _ «^

*»**

******* 1 O 1•«* v«J

———— ̂ - ———————————————————————————— A 44444^^^^ ———

6 8 10 12 14 16Frequency (MHz)

FIGURE 3. a). Comparison of measured and predicted FOM-vs-frequency curves for the optimal choicesof the model parameters, (b) Optimization used experimental data from Coupon #8 sides 1 and 5.

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Predicted FOM in Coupon #8 From Side 2 and Side 4V=1.328E-06cm*3, <deltaC33A2>=9.75 6paA2

10 12Frequency (MHz)

Predict FOM on Coupon #2 FromSideS and Side4V=1.328E-06cmA3, <deltaC33A2>=9.75 GPaA2

8 10 12Frequency (MHz)

FIGURE 4. (a): Positions of selected forging coupons (background is the forging macroetch). (b-c):Comparison of model and experiment for sides 2 and 4 of coupon #8 (b) and sides 4 and 5 of coupon #2 (c).

given coupon are generally small. Fig. 4c shows results for two sides of coupon #2, locatedin the web region. Note that coupons #2 and #8 have very different deformations, as can beseen from the macroetch show in Fig. 4a and the DEFORM simulation shown in Fig.lb.Also note that for coupon #8 the measured noise level is highest for radial propagation,while for coupon #2 it is highest for axial propagation. This reversal of noise directionalityis well predicted by the model.

0.02

£ 0.02

C

Scaling Factor Relating FOM (10MHz) to Normalized GPN

—— Linear (Measured) •

y = 0.003987x /*R2 = 0.979930 .S

/S^r

.S*^r

(a)1 2 3 4 5 C

Normalized GPN

1 4.0

r!"•0

Predicted Vs. Experimental GPN (Normalized by#1FBH )

• PVW1 • PVW2 A PVMWX PVW5 x PVW6 - RA»7oPVWS x ° °

X o

«. • "

X. .*'»• J'";' - .• • : % -

(b)0 1.0 2.0 3.0 4.0 5.0 6.0

GPN by Prediction

FIGURE 5. a). An approximation scaling factor which relates average GPN with FOM at 10MHz, asdeduced from measured values for selected coupons, b). Comparison between measured and predictedaverage GPN amplitudes in each quadrant of each coupon.

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Full FOM-vs-frequency curves for all coupons are not yet available. However, inearlier work described in Ref. [1], average Gated-Peak Noise (GPN) amplitudes relative toa flat-bottomed hole reference were measured for C-scans over each quadrant of eachcoupon using a focused transducer. To a good first approximation, the average GPNamplitude within a quadrant will be proportional to the average FOM value near the centerfrequency of the transducer [16]. For selected coupons, measured FOM and GPN data areboth available. As shown in Figure 5a, these were used to find an approximate scalingfactor relating average GPN to FOM at 10 MHz. Using this scaling factor, GPNamplitudes could then be predicted from the model FOM values for each coupon quadrant.Predicted GPN amplitudes are compared with experiment in Figure 5b. Our simplifiedmodel treatment ignores the fact that ultrasonic attenuation varies throughout the forging[1], and effectively ignores the frequency dependence of FOM. Nonetheless, we find agood correlation between measured and predicted GPN amplitudes, which each vary by afactor of 5 within the forging. If the model were exact, the points in Figure 5b would all liealong a diagonal line though the plot region. The largest departures from this idealsituation generally occur for coupons #5 and #6, where the macroetch indicates that theflow lines have a "swirling" appearance. The model predictions are quite sensitive to the

360°

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"'O SO 100 ISO .200 2SO 300 3SO

Angle Between Grain Major Axis and Inspection beam (T in degree)

FIGURE 6. (a). Cylindrical coupon location and definition of the orientation angle T. (b). C-scan image ofgated-peak grain noise in the coupon, (c) Angular profiles of measured GPN and predicted FOM at 5 MHz.

scatterer orientation and shape parameters, T and R. Values for these deduced from

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DEFORM simulations may be less accurate in regions where the flowlines swirl. We alsonote that our specific model calculations have assumed 7:1 ellipsoidal volume elements inthe billet prior to forging. Choosing a different starting aspect ratio will also affect theappearance of Figure 5b.

To further test the model, another comparison was made centering on the angulardependence of FOM. A cylindrical coupon 1.25" in diameter and 2.0" long was cut fromthe web region of the forging, as indicated in Figure 6a. As seen from the DEFORMsimulation of Fig. Ib, the model microstructure at that location is expected to be elongatedin the radial direction. The predicted backscattered noise amplitude is largest when themodel scatterers present the largest cross-sectional area to the incident beam. Thus thepredicted FOM, regarded as a function of the orientation angle, T, is expected to have peaksat 90 and 270 degrees w.r.t. the forging's radial direction. The cylindrical coupon wasrotated on a turntable and scanned using a cylindrical-focused transducer (Centralfrequency 5MHz). The resulting C-scan image of GPN amplitudes from the coupon'sinterior is shown in Figure 6b. The angular profile of the GPN image, averaged over thelinear scan direction, is compared in Figure 6c to the predicted FOM-versus-T curve at5MHz. As before, the experimental and model quantities are expected to be approximatelyproportional to one another, although the scaling factor will be different from that usedearlier because of the effect of the curved entry surface and the fact that transducers aredifferent. Thus in Figure 6c we have simply scaled the predicted FOM curve to havesimilar amplitude to the measured GPN profile. The predicted curve is seen to havesomewhat sharper peaks, but the overall level of agreement is reasonably good.

From the comparison between experiment and theory shown in Figures 4-6, weconclude that our modeling approach, in which microstructural geometry features arededuced from DEFORM simulations, captured the main factors that control the variabilityof backscattered grain noise within our forging.

SUMMARY AND FUTURE WORK

A simple model was developed to correlate backscattered grain noise levels withmicrostructural variations that arise during forging. The model approximates the forgingmicrostructure as an effective medium in which the average grain volume is constantthroughout, and the crystalline axes of the grains are randomly oriented. The shapes andorientations of the grains are deduced from DEFORM simulations of material strain duringforging, and consequently vary throughout the forging. The two global model parameters,the mean volume of the scattering elements and the elastic property variability, wereobtained by fitting to noise data for one particular Ti 6-4 forging. Model testing was doneby comparing predictions with experimental data for: (1): FOM-vs-frequency for selectedrectangular coupons; (2) mean GPN amplitudes within a suite of 7 rectangular couponsfrom different regions of the forging; and (3) angular dependence of grain noise for onecylindrical coupon cut from the web region of the forging. Reasonable agreement betweenexperiment and theory was achieved.

In the current model, the metal grains in the effective medium are assumed to haverandomly oriented crystalline axes. However, large deformations during forging areexpected to cause partial alignment of crystallites by slip, twinning or their combination.Such deformation-dependent texture will cause the elastic property variability factor,<8Qi2>, to vary with position inside the forging. Efforts to incorporate such texturaleffects into the model are currently under way.

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ACKNOWLEDGEMENTS

This material is based upon work supported by the Federal Aviation Administrationunder Contract #DTFA03-98-D-00008, Delivery Order IA029 and performed at UnitedTechnologies Pratt&Whitney and at the Iowa State University Center for NDE as part ofthe Center for Aviation Systems Reliability program.

REFERENCES

1. Linxiao Yu, R.B. Thompson, Frank J. Margetan and Andrei Degtyar, in Review ofProgress in QNDE, Vol.21B, eds. D.O. Thompson and D.E. Chimenti (Plenum, NewYork, 1998), p.1510.

2. J. C. Williams and E. A. Starke, Jr., "Deformation, Processing, and Structure",ed. G. Krauss (Metals Park, OH: ASM, 1984), p.279-354.

3. K. Goebbles: Research Techniques in Nondestructive Testing, Academic Press, NewYork, NY, 1980, pp. 87-157.

4. B. R. Tittmann and L. Ahlberg: Review of Progress in Quantitative NDE, Vol. 2A, eds.D.O. Thompson and D.E. Chimenti (Plenum, New York, 1983) p. 129-145.

5. F. J. Margetan, T. A. Gray, and R. B. Thompson: Review of Progress in QuantitativeNDE, Vol. 10B, eds. D.O. Thompson and D.E. Chimenti (Plenum, New York, 1991) p.1721-1728.

6. F. J. Margetan and R. B. Thompson: Review of Progress in Quantitative NDE, Vol.11B, eds. D.O. Thompson and D.E. Chimenti (Plenum, New York, 1992) p. 1717-1724.

7. F. J. Margetan, R. B. Thompson and I. Yalda-Mooshabad: Review of Progress inQuantitative NDE, Vol. 12B, eds. D.O. Thompson and D.E. Chimenti (Plenum, NewYork, 1991) p. 1735-1742.

8. I. Yalda-Mooshabad, F. J. Margetan and R. B. Thompson: Review of Progress inQuantitative NDE, Vol. 12B, eds. D.O. Thompson and D.E. Chimenti (Plenum, NewYork, 1992) p. 1727-1735.

9. F. J. Margetan, R. B. Thompson and I. Yalda-Mooshabad: Journal of NondestructiveEvaluation, 1994,13(3),p. 111.

10. J. H. Rose: Review of Progress in Quantitative NDE, Vol. 10B, eds. D.O. Thompsonand D.E. Chimenti (Plenum, New York, 1991) p. 1715-1720.

11. J. H. Rose: Review of Progress in Quantitative NDE, Vol. 11B, eds. D.O. Thompsonand D.E. Chimenti (Plenum, New York, 1992) p. 1677-1684.

12. J. H. Rose: Review of Progress in Quantitative NDE, Vol. 12B, eds. D.O. Thompsonand D.E. Chimenti (Plenum, New York, 1993) p. 1719-1726.

13. Y. K. Han and Thompson, in Metallurgical and materials transactions, Vol. 28A, p.91.14. A. Sigelmann and J. M. Reid: /. Acoust. Soc. Am., 1973, Vol. 53, pp. 1351-1355.15. E. L. Madsen, M. F. Insana, and J. A. Zagzebski: /. Acoust. Soc. Am. 1984, Vol. 76,

pp912-923.16. FJ. Margetan, I, Yalda, R. Bruce Thompson, in Review of Progress in QNDE, Vol.

15B, eds. D.O. Thompson and D.E. Chimenti (Plenum, New York, 1996) p. 1509.

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