Ultrasonic Characterization of Texture and Formability
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Introduction There are now theories which predict the effect of texture on elastic properties and hence on the velocities of bulk, surface, and guided ultrasonic waves. Furthermore, there is a relation between texture and formability. These relationships can be potentially exploited to make ultrasonic measurements of formability, and partial pole figures can be made with ultrasonic techniques. This article presents results of various ultrasonic measurements made to characterize the formability of rolled steel and aluminum alloy sheet. A good correlation generally exists between ultrasonic velocity measurements and formability. Furthermore, there is a good possibility of on-line formability measurement using a noncontacting ultrasonic transducer. The influence of texture on material properties has been long recognized, and several excellent texts have been wholly or partly devoted to the subject.12 Texture classically has been measured with either x-rays or neutron diffraction. Lately, there has been interest in characterizing texture with ultrasound (high-frequency sound) as well. Ultrasound has several potential advantages over x-ray and neutron diffraction techniques. Ultrasonic systems are nondestructive, can rapidly scan large volumes of material, require no radiation sources, and can be devised to measure either surface or bulk textures. There is a distinct possibility .that ultrasonic texture monitoring can be implemented in real-time in a production environment such as a rolling mill. To date, most ultrasonic texture measurements have been applied to partial 40
pole figures and determination of mechanical properties such as formability. The following briefly reviews the theoretical link between texture, formability, and ultrasonic velocity and then describes results of several experimental investigations which highlight the potential of ultrasonic texture measurements, especially for on-line applications. For simplicity, the discussion is restricted to theoretical results to the technologically important cases of rolled plates of cubic metals (e.g., aluminum, steel).
. The t r a n s f o r m e d m o d u l i are weighted by OJ(£, \\i, ), which gives the probability that this orientation will occur. The result is then integrated over all values assumed by £, i/;, . Because of the symmetries involved, only the ODC co4„,0, where m = 0, 2, 4, influence the moduli and hence the ultrasonic velocity.3'4 This result holds for surface waves,5"7 guided waves in thin plates,8"10 and bulk waves (compressional, shear waves). 411 Consequently, "partial pole figures" can be made with ultrasonics and will be a good representation of texture provided that the dominant components are the The influence of texture on formability has also been studied. One measure of formability is the r-ratio, the ratio between width and thickness strains in specimens plastically deformed in uniaxial tension. For specimens cut at an angle a to the rolling direction in moderately textured steel sheet, it has been found experimentally12 that r(a)
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