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T metals produced by a combination of rolling and annealing have long been known to exhibit anisotropic mechanical properties. The anisotropy of sheet metals in a given angle to the rolling direction is normally characterized by the plastic strain ratio R, defined as R5

ew et

[1]

where ew and et are true plastic strains in the width and thickness directions, respectively, measured in a tensile test specimen after a certain amount of straining in the uniform elongation region. Due to the difficulties encountered in measuring thickness changes with sufficient precision, a constancy of volume is usually assumed. The R-value can then be calculated from longitudinal and transverse strains using the equation R5

ln ðww0 Þ ew 5
ðew 1 el Þ ln ðl0lww0 Þ

[2]

where l0 and w0 are the initial gage lengths in longitudinal and transverse directions, respectively, and l and w are the corresponding dimensions after straining. Although the determination of strain ratio is often claimed to be simple and accurate, appreciable differences in the values for corresponding specimens are often recorded. These differences suggest that universal agreeA. CHAMANFAR, Research Assistant, and R. MAHMUDI, Professor, are with the Department of Metallurgical and Materials Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran. Contact e-mail: [email protected] Manuscript submitted November 1, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A

ment on the measurement of strain ratio is not easily reached.[1] In pursuing a reliable technique for precise determination of R-value, several authors have studied the effect of various factors, such as elastic strains,[2] specimen type,[3–6] locations along the gage length for strain measurements,[1,4,6–10] angle between the tensile test axis and the rolling direction of the sheet,[11,12,13]and the amount of straining in the tension test.[14–20] Rao and Mohan[5] studied the effect of specimen geometry on the mechanical properties of commercial brass sheets and concluded that anisotropy values are similar in all ASTM E 8M-93 and 517 to 92a type A (dog-bone shaped) and type B (parallel strips) specimens. Liu[3] observed that R-values of AKDQ steel sheets obtained from both the parallel-sided and tapered specimens are indistinguishable. Liu and Johnson[8] observed that during tension testing of AA3004 aluminum specimens, width strain rate is not uniform within the gage length. Atkinson[1] reported that plastic strain ratios are related to the measurement locations in the test piece. Taylor and Scherrer[4] reported that in IF steel (high R-value) and DQSK steel (low R-value), because of differences in width reduction over the length of the reduced parallel section in ASTM E 517 type A and type A alternative specimens, the magnitude of calculated R-value depends upon the length of gage marks and width measurement locations. Ingelbrecht[7] reported that the R-values of Ti-6Al-4V sheet testpieces measured after superplastic strain were influenced by the effect of test piece heads on the width contrac