CRYSTALLOGRAPHIC TEXTURE IN ROLLED ALUMINUM PLATES: NEUTRON POLE FIGURE MEASUREMENTS R. C. Reno and R. J. Fields National Bureau of Standards Gaithersburg, Maryland 20899 A. V. Clark, Jr. National Bureau of Standards Boulder, Colorado 80303

INTRODUCTION In crystalline materials with anisotropic elastic constants, the propagation of ultrasound is strongly dependent upon crystallographic texture. This dependence may provide investigators with a relatively rapid and economical method for monitoring texture in processed materials such as rolled plate [1-3]. We have made use of ultrasound to characterize texture in rolled aluminum plates that are to be used in the fabrication of cans [4]. Ultimately, it would be desirable to incorporate ultrasound-based texture monitors in the manufacturing process so that texture can be automatically controlled. Although ultrasound propagation is influenced by texture, it is also affected by impurities, grain boundaries, and other inhomogeneities. It is therefore desirable to compare ultrasound texture measurements with more direct crystallographic measurements. Neutron diffraction is an excellent method for studying texture in bulk samples directly. Neutrons penetrate deeply into materials, thus sampling the overall texture of specimens having volumes in excess of several cubic centimeters. The extremely high penetration in aluminum permits one to generate a complete pole figure without having to switch from reflection to transmission modes. Analysis of the pole figure results in orientation distribution function coefficients (ODC's) that can be compared to those measured with ultrasound. THEORY In this paper, we will utilize Roe [5] and Allen [6]. We begin by function (ODF) , w(e, ~,~). Angles relate crystallite orientation with Figure 1). In the case of aluminum

the notation and methods developed by defining an orientation distribution ~, and ~ are Euler angles which respect to bulk sample axes (See plate, crystallographic axes are

e,

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defined along the three cube directions of the aluminum unit cell and the sample axes are defined along the rolling, normal and transverse directions of the plate. The function w(e, ~, ~) gives the proportion of crystallites whose orientation is within 8e, 8~, and 8~ of the specified Euler angles. The orientation distribution function can be expanded in terms of generalized spherical harmonics, as given by Roe [5]: 1

DO

w(e,

~,

L

~)

L

1=0 m=-l

1

L

(1)

n=-l

where the W mn's are orientation distribution function coefficients (ODC's) which quantitatively describe the crystallographic texture of a sample. Values of the ODC's are determined by measuring pole figures, qi(~' ~) and fitting the data to an expansion in spherical harmonics:

x,A X3

Sample Axes

X3 Y3

X2

y,--L y, Y3

X, X2

Crystal Axes

Figure 1.

Euler angles used in orientation distribution function

DO

L

1

L

1=0 m=-l

(2)

Here the subscript i denotes a choice of Miller indices corresponding to a particular diffraction condition. ~ and ~ are polar and azimuthal angles describing the orientation of the sample (i.e. the plate normal) with respect to the scattering vector.

1440

The Q~m's obtained from a fit to the measured pole figure can then be used to determine the orientation distribution function coefficients (Wimn's) through the following relation: (21\")

2 ) 1/2 ( 21 + 1

1.

I

(3)

n=-1

The angles e and ~ are polar and azimuthal angles describing the orientation of the reciprocal lattice vector (hkl) with respect to the unit cell crystallographic axes .

EXPERIMENTAL DETAILS AND DATA ANALYSIS Neutron pole figures were taken on six samples of hot-rolled aluminum plate, each having a different rolling history. Complete pole figures were generated by placing the samples (0.5 inch diameter x 0.25 inch thick) in a beam of neutrons having a wavelength of 0.127 nm , selecting the appropriate detector orientation to observe diffraction from crystal planes defined by Miller indices (hkl) , and measuring beam transmission over a range of sample orientations which span the entire hemisphere above the plane of the plate. Experiments were done at the NBS Reactor and data were converted to pole figures using programs written by C. S. Choi at NBS . Samples of pole figures taken with two different scattering vectors are shown in Figure 2. Quantitative analysis of the pole figure data was accomplished with a program written by one" of us (RCR) which inverts equation 2 and uses measured pole figure data to compute the Q.lm' s up to a maximum of 1=10. The choice of maximum 1 was dictated by computational considerations and the fact that ultrasound measurements only sense the 1.=4 coefficients. In order to see how well the original pole figure structure is reproduced with a series that is truncated at 1=10, we have written a program that reconstructs a pole figure with specific Q~m's as inputs . Figure 3 shows reconstructed pole figures corresponding to the two measured pole figures shown in Figure 2 .

RD

RD

(111 )

(200) Figure 2.' Neutron pole figures of a rolled aluminum plate. Two different diffraction conditions are shown.

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RO I

RO

(200)

(111 )

Figure 3.

Reconstruction of pole figures shown in Figure 2 . All components up through 1=10 are included in the reconstruction.

The reconstructions show the salient features of the measured pole figures, but obviously lack the high spatial frequencies that would have been present without truncation. The truncation does not , however, affect the values of the coefficients reported herein. The inversion procedure provides us with coefficients (Q40 ' Q42' and Q44) that are necessary to deduce the 1=4 orientation distribution function coefficients . For the case of aluminum plates, we can use crystallographic and sample symmetries to reduce the number of independent W,mn's. Equation 3 then simplifies to the following linear relations between the 1=4 ODC ' s and the Q4m coefficients: For (111) pole figures: For (200) pole figures:

- 0 . 2387 Q4 m 0.1592 Q4m

RESULTS For each sample of aluminum plate, we generated two neutron pole figures and deduced the ODC's for 1=4 using the method described in the above section . Table I gives the mean value of the 1=4 coefficients for each of the plates tested. The uncertainties listed are standard deviations about the mean for the values derived from the two pole figures . The major source of uncertainty in the value of the coefficients is due to sample alignment ( i.e. the choice of r=O and q=O) . The cylinders used in the diffraction experiments were cut from plates that had a small amount of curvature and were, therefore, not perfect right cylinders. In addition, two specimens were mounted on top of one another in order to increase the effective thickness and encourage neutron absorption . Several independent measurements of the same pole figure on a sample which was not disturbed between measurements gave coefficients which varied by only 5%, thus confirming that variations due to neutron counting statistics are not significant. Figure 4 compares the results of neutron and ultrasound measurements (4) for W420 and W440 . (Values of W400 are, at present, only available from neutron measurements.)

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TABLE I

Orientation Distribution Coefficients (1=4) for Rolled Aluminum Plates

Sample temperature exiting rollers

331 Celsius

+ 0.0100

± 0.0011

- 0.0034

± 0.0003

+ 0.0065

± 0.0009

335 Celsius *

+ 0.0062

± 0.0009

- 0.0025

± 0.0010

+ 0.0039

± 0.0018

335 Celsius *

+ 0.0062

± 0.0005

- 0.0024

± 0.0001

+ 0.0015

± 0.0004

347 Celsius

+ 0.0075

± 0.0003

- 0.0025

± 0.0004

+ 0.0041

± 0.0012

357 Celsius

+ 0.0082

± 0.0007

- 0.0028

± 0.0001

+ 0.0038

± 0.0005

* Two different production runs

~

a ~

I

c

a ~

-3.0

= !

~

~

..,

....0 >C

C>

4.0

..,

....0

-2.0

: :. >C

~

:.

-3.0 W420

Figure 4.

6.0

~

c

X

-4.0

10 3 (neutron diffraction)

2.0

-1.0'--_-L..._ _. l - - _ - 1 . - J o 2.0 4.0 6.0 W 440 x 10 3 (neutron diffraction)

Comparison of neutron and ultrasonic measurements of orientation distribution coefficients for 1=4. a) W420 values b) WHO values.

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An excellent correlation is seen to exist between values deduced from the two methods. In all cases, however, the magnitude of an orientation distribution coefficient is slightly larger when measured with neutrons. This disagreement could be due to ultrasound scattering from grain boundaries, from inhomogeneities in the alloy, or from imperfect angular resolution in the diffraction experiments. However, as the dotted lines in Figure 4 show, the introduction of a constant offset brings both sets of measurements into excellent agreement. Since the goal of this project is to develop an ultrasound sensor which can detect changes in texture during fabrication, a constant offset can be introduced as a correction quite easily.

CONCLUSIONS The good agreement between ultrasound and neutron pole figure data indicates that the ultrasonic measurements are measuring primarily aluminum plate texture, and are not being adversely affected by scattering from inhomogeneities. This further strengthens our previous conclusion [4] that ultrasound may be a viable method for monitoring texture in aluminum plate. The neutron pole figure analysis provides values for W400 , as well as values for W420 and W440 discussed above. Although W400 does not affect plate formability in the same way that W420 and W440 do, it does have some affect on formability and it would be interesting to compare neutron and ultrasound measurements of this coefficient. Measuring W400 with ultrasound, however, requires absolute sound velocity measurements and a more sophisticated data analysis. This work has begun in our laboratories. ACKNOWLEDGEMENTS We wish to thank Dr. C. S. Choi (ARRADCOM/NBS) for his generous assistance during our early pole figure measurements. The work reported here was sponsored at NBS in part by the NBS Office of Nondestructive Evaluation. REFERENCES 1.

C. M. Sayers, "Ultrasonic velocities in anisotropic polycrystalline aggregates", J. Phys. D: Appl. Phys., 15 2157 (1982).

2.

R.B. Thompson, J.F. Smith, and S.S. Lee, "Inference of Stress and Texture from the Angular Dependence of Ultrasonic Plate Mode Velocities", in NDE of Microstructure for Process Control, H.N.G. Wadley, ed., ASM, Metals Park, OH, 73 (1985).

3.

P.P. Del Santo, R.B. Mignogna, and A.V. Clark, "Ultrasonic Texture Analysis for Polycrystalline Aggregates of Cubic Materials Displaying Orthotropic Symmetry," to be published in Proceedings of 2nd International Conference on Nondestructive Characteristics of Materials, Montreal, 1986.

1444

4.

A.V. Clark Jr., A. Govada, R. B. Thompson, J. F. Smith, G. V. Blessing, P. P. Delsanto and R. B. Mignogna, "The Use of Ultrasonics for Texture Monitoring in Aluminum Alloys", Review of Progress in Quantitative Nondestructive Evaluation, Vol. 6 ed. by D. o. Thompson and D. E. Chimenti (Plenum, New York, 1987) p. 1515. See also A. V. Clark Jr. et a1., these proceedings.

5.

Ryong-Joon Roe, "Inversion of Pole Figures Having Cubic Crystal Symmetry", Journal of Applied Physics, 1I 2069 (1966).

6.

A. J. Allen, M. T. Hutchings, C. M. Sayers, D. R. Allen and R. L. Smith, "Use of neutron diffraction texture measurements to establish a model for calculation of ultrasonic velocities in highly oriented austenitic weld material", J. App1. Phys., 54 555 (1983).

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