A comparison of ultrasonic and X-ray determinations of texture in thin Cu and Al plates
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I.
INTRODUCTION
THE
texture of metal sheets and plates plays an important role in determining their subsequent formability into such finished parts as beverage cans and automotive and aircraft components. 11'21 Traditionally, X-ray diffraction techniques are employed to measure texture. I3,41 However, these generally suffer from requirements for long measurement times and special samples and, in their most common implementation, only sense the texture in a very near-surface layer. Neutron diffraction techniques sense the bulk texture that would be expected to influence formability, but they require special instrumentation that is only available at a few laboratories. Therefore, there is considerable motivation to develop alternative techniques for nondestructive texture characterization. Ultrasonic techniques have long been candidates for such a role, due to the relative ease with which measurements can be made. The basic principles of such techniques, the anisotropy of the polycrystalline aggregate elastic constants in the presence of preferred grain orientation, and their potential application to texture measurement have been known for twenty years, tS-sl Several subsequent advances have suggested that those techniques could be put on a more quantitative basis with potential practical application. The first is the development of a mathematical description of the preferred grain orientation in terms of a set of orthonormal basis functions, t4'9,1~ This was rapidly followed by the derivation of the relationship of the polycrystalline aggregate elastic constants to the O D C ' s of that expansion.I4" 1-~31More recently, it has been noted that these elastic constants and, hence, the coefficients of the orientation distribution functions, could be deduced from ultrasonic meaR.B. THOMPSON, Professor and Associate Director, and J.F. SMITH, Emeritus Professor. are with the Department of Materials Science and Engineering and Ames Laboratory, Iowa State University, Ames, IA 50011. S.S. LEE, formerly a Graduate Student with Ames Laboratory, is now with the NDT Laboratory, Korea Standards Research Institute, P.O. Box 3, Taedock Science Town, Taejon, Ch'ungam 30031, Korea. G.C. JOHNSON, Professor. is with the Department of Mechanical Engineering, University of California, Berkeley. CA 94720. Manuscript submitted June 8, 1988. METALLURGICAL TRANSACTIONS A
surements made with a simple apparatus. 114] A more detailed discussion of this background may be found in a recent survey, tl51 One possible application of ultrasonically determined texture is in the prediction of sheet metal formability. The foundations of this application also were laid a number of years ago with the work of Stickels and Mould t~61 and Mould and Johnson, ll71 who reported a correlation between the Young's modulus (including its anisotropy) and the plastic-strain ratio (and its anisotropy) of steel sheet. Although this correlation between elastic and plastic properties was somewhat unexpected, Davies e t a l . HsJ identified the underlying principles. T
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