On the R -value measurements
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I.
1.76 1.26 2.17 1.61
-+ 0.04 +- 0.02 --- 0.04 -+ 0.03
1.82 1.24 2.15 1.61
INTRODUCTION
THE plastic strain ratio or planar plastic anisotropy, r, as initially introduced by Lankford et al 1 was defined as: /32
r = --
[11
83
where 62 is the natural width strain and E3 is the natural thickness strain in a uniaxially tensile-tested specimen. In the literature, this experimental method is known as the "direct method"] Because of the difficulties of measuring the thickness of a sheet specimen after plastic deformation with sufficient accuracy, an "indirect method ''3 was proposed by rewriting Eq. [1] as: r =
E2
-(e~ + e2)
[21
where e~ is the natural axial strain, on the assumption that the volume before and after deformation remains constant, i.e., 61 + 62 + 63 = 0
[3]
Since its introduction, the indirect method or Eq. [2] has been adopted internationally as the standard formulation in the determination of r-values. Despite its simplicity in both experimental procedures and computation, the r-value so determined in a given steel sheet scatters over a wide range. As quoted in Reference 4, in a cooperative test program conducted by the I.D.D.R.G. in England, the experimental results determined by different laboratories, on supposedly identical samples, showed variaY.C. LIU is a Research Scientist with the Metallurgy Department, Scientific Research Laboratories, Engineering and Research Staff, Ford Motor Company, Dearborn, MI 48121. Manuscript submitted August 18, 1982.
METALLURGICALTRANSACTIONS A
+- 0.12 -+ 0.07 --- 0.19 + 0.11
tions in rm-values* from 1.22 to 1.60 with a +-15 pct scatter *rm = (ro + 2r45 + r9o)/4 where the subscript refers to the angle in degree the tensile specimen makes with the rolling direction of the sample sheet.
from the mean value. It has been suggested that for a steel having an r,,-value up to 2, an accuracy of _0.13 cannot be readily achieved (see Reference 2). Atkinson observed that for tensile strains between 10 to 20 pct the extent of variation in the rm-value along a 23 cm (9 inch) gage length was +--0.2, and he concluded that the r-value determination was hypersensitive to measuring accuracy. 4 In ASTM E 517 Standard measuring accuracy of 0.025 mm (0.001 inch) was specified but a much more stringent requirement, 0.005 mm (0.0002 inch), was demanded in the I.D.D.R.G. recommendation. On this ground, an experimental attempt was made to improve the measuring accuracy to 0.0013 mm (0.00005 inch). 5 For the further refinement of the measuring accuracy new techniques, such as Moir6 method, have been suggested] In view of the increasingly required measuring accuracy, reliable determination of r-values, which are so important in both mathematical modeling and indexing of material drawability, are seemingly beyond the capability of most facilities which do not have the benefit of sophisticated instrumentation and trained personnel. A simple technique for accurately determining r-value of known confidence is therefore needed. The present investigation was carried out for that pur
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