Modeling Ultrasonic Grain Noise within Ti-6Al-4V ... MODELING ULTRASONIC GRAIN NOISE WITHIN TI-6A1-4V

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  • MODELING ULTRASONIC GRAIN NOISE WITHIN TI-6A1-4V FORCINGS

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

    Andrei Degtyar United Technologies Pratt&Whitney, East Hartford, CT 06108,USA

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

    BACKGROUND AND OBJECTIVES

    Large variations of backscattered ultrasonic grain noise with position and inspection direction 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 local microstructural variations that arise from thermo-mechanical processing (TMP) [1]. Historically, TMP has been used as the primary means of changing the shapes and sizes of materials, transforming, for example, cast ingot into a desired wrought product. However, it has also become an increasingly common way of controlling the microstructure by imposing restrictions on the working temperature range and the amount of work [2]. A variety of microstructural characteristics of the final product (grain size, degree of recrystallization, grain aspect ratio, texture, etc.) are sensitive to the TMP details. For example, if there is negligible recrystallization during TMP, the grain aspect ratio is primarily determined by the initial grain structure and the directional metal flow.

    Aircraft engine forgings generally have complex geometries, and the strain magnitude and flow direction are different at different locations. It is thus expected that the microstructure will vary throughout a forging. Because such forgings are often large, it is difficult to get a detailed overall picture of how the microstructure varies by the traditional metallographic approach. Fortunately, some useful microstructural information can be deduced from forging simulation software, such as DEFORM, a commercial software package produced by Scientific Forming Technologies Corporation, Columbus, Ohio. One successful use of this software to correlate ultrasonic noise anisotropy within a forging with the 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-section in 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 engine forging produced from a cylindrical billet. The billet itself began as a cast ingot that was subsequently worked to reduce its diameter. Fig.la displays the "strain map", which illustrates 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 modified by the forging process. Here the 7:1 aspect ratio in the billet has been motivated by the general shape of billet macrograins [1]. Note in Figure Ib that the forging process changes both the elongations and orientations of the elements. The rectangular and circular boxes in the figure indicate the locations where coupons were cut for the UT property measurements described in Reference [1].

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

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  • REVIEW OF THE THEORY Because 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 physical properties of the microstructure. Using a single-scattering assumption and the Born approximation, Rose developed a rigorous stochastic theory for the backscattered noise power, 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's theory to the cases of duplex microstructures, which may contain texture and elongated microstructural features. The expressions used in our work are consistent with those in Reference [13].

    A commonly used measure of a microstructure 's noise generating capability is the backscattering power coefficient TJ, i.e., the differential scattering cross section per unit volume 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 to the noise voltage observed on an oscilloscope during UT inspection. In the theories of Rose, Han and Thompson, FOM and TJ for longitudinal waves propagating in the z = 3 direction 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, z is a particular component of r, ')> is the two-point correlation of elastic constant perturbations [13]. r and r9 are two points in the poly crystalline, 8C33is the local deviation of the elastic constant from its Voigt average (8C33=C33-Cvolgt33), and < > denotes an ensemble average. We will assume that the crystalline axes of our scatterers are randomly oriented (i.e., an untextured microstructure). In that case we have the simplifications:

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

    FOM 2 = t i (m) = 8C2 W 47TPF,2

    where 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 that s = 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 0JoJ A>

    (4)

    A = {1 + (R2 -1) cos

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

    10 12 Frequency (MHz)

    Predict FOM on Coupon #2 FromSideS and Side4 V=1.328E-06cmA3, =9.75 GPaA2

    8 10 12 Frequency (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, located in the web region. Note that coupons #2 and #8 have very different deformations, as can be seen 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 directionality is 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 PVMW X PVW5 x PVW6 - RA»7 oPVWS 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, as deduced from measured values for selected coupons, b). Comparison between measured and predicted average GPN amplitudes in each quadrant of each coupon.

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  • Full FOM-vs-frequency curves for all coupons are not yet