Characterization of formability in cold-rolled steel sheets using electromagnetic acoustic tranducers
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I.
INTRODUCTION
I T has long been known that ultrasonic velocities exhibit anisotropy in polycrystalline metals; that is, the velocities vary, depending on the propagation and polarization directions with respect to the sample geometry. Ordinarily, the magnitude of anisotropy is very small, and the relative velocity differences are observed in the order of 10 -2 at most. The elastic anisotropy is attributed to the presence of texture or preferred orientation of crystallites making up the polycrystals. During the thermomechanical processes, the crystallites rotate, and the lattice orientation tends to be aligned in a certain manner. The grain shape has no notable influence on the anisotropy. The dislocation structure is not considered to be the principal source either, because the annealing at a temperature lower than the recrystallization temperature does not diminish the anisotropy. Velocity measurements on cube specimens cut from rolled plates show that the elastic anisotropy is of orthotropic symmetry, and its full description needs nine independent elastic constants. Recently, a mathematical formalism was given for discussing the texture-ultrasonic relationship quantitatively. Using Voigt's averaging scheme, Sayers t~j derived polycrystalline elastic constants and noted that only six are independent among nine elastic constants. They are three independent elastic constants of the single crystal (in the case of cubic crystals) and three texture parameters called the lowest-order orientation distribution coefficients (ODC's). Texture causes the elastic anisotropy simply through three ODC's. Because these fundamental ODC's determine the major part of macroscopic material anisotropy 12.3j and they are measurable with considerable ease, the ultrasonic techniques are eligible for the means of nondestructive charM. HIRAO, Research Associate, and H. FUKUOKA. Professor. are with the Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan. K. FUJISAWA, Staff Manager. and R. MURAYAMA. Assistant Staff Manager, are with the System Engineering Division, Sumitomo Metal Industries, Ltd., Amagasaki, Hyogo 660, Japan. Manuscript submitted December 28, 1988. METALLURGICAL TRANSACTIONS A
acterization of the texture and texture-induced anisotropy. Many promising experimental results have been reported. Three ODC's evaluated by ultrasonics compared favorably with those evaluated by the conventional measurements, such as X-ray and neutron diffraction techniques, t4-TJ Ultrasonic pole figures provide a good approximation in visualizing texture, when the texture can be decomposed into its main ideal orientations. I8-'21 As a more practical application, an ultrasonic technique is currently under development for monitoring plastic anisotropy of rolled thin sheets of steel and aluminum.[~ ~.~2.13]The sheet formability, which arises from the plastic anisotropy, is one of the typical texture-dependent properties. These sheets are plastically stretched and drawn to produce automobile body parts, beverage cans, etc., a
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