Plastic anisotropy of sheets with continuously varying anisotropic parameters and flow stress
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INTRODUCTION
THE press performance, in particular, the pure drawing ability, is superior in low-carbon steel sheets with high strain-hardening exponents and with high r valuesY -5] The previous studiest4,6-n] have shown that high r values result from the recrystallization textures with strong ND[I(1 11) and {554}(225) components, where ND is the normal of sheets. The recrystallization texture is ordinarily controlled through cold rolling and subsequent annealing. For economical reasons, replacement of some part of cold rolling by hot rolling is being attempted. The hot rolling is performed in the temperature range of the alpha phase in which recrystallization does not occur. Such rolling is often called warm rolling and is applied to Ti-bearing and Nb-bearing interstitial-free (IF) steels. If steel sheets are warm-rolled using large rolls under good lubrication conditions, the desired textures of NDIJ(I 11) develop uniformly from the surface to the center of the sheet, t12 17] After subsequent annealing, the sheets have high mean r values. On the other hand, if warm rolling is performed without lubrication, redundant shear deformation takes place beneath the surface up to the depth of around one-fourth of the thickness of the sheet because of high friction between the sheets and the rolls. In such sheets, NDII(lll} textures due to plane-strain compressive deformation develop only at the central region of the sheet, whereas NDI[(I10) or {110}(001} textures are formed in the severely sheared regions. The formation of NDll(1 10) textures reduces mean r values after annealing. Sakai et al. [14,15a61 have clarified that when sheets are warm-rolled without lubrication, the equivalent plastic strain is maximum in the severely sheared regions. If the rolled sheets are annealed, very fine recrystallized grains form in the severely sheared regions compared with those in the central region. Such sheets have through-thickness strength gradients in addition to texture gradients. After Bunge v81 and Roe t191proposed the crystallographic orientation distribution function (CODF) method, many auT. SAKAK/, Professor, and K. KAKEHI, Research Associate, are with the Department of Precision Engineering, Faculty of Technology, Tokyo Metropolitan University, Tokyo 192-03, Japan. G.J. WENG, Professor, is with the Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ 08903. S. HASHIMOTO, Assistant General Manager, is with the Iron and Steel Research Laboratories, Kobe Steel Ltd., Hyogo 675, Japan. Manuscript submitted November 8, 1993. METALLURGICALAND MATERIALSTRANSACTIONSA
thors predicted the r value and yield stress of various metals and alloys based on the combination of the CODF and the Taylor-Bishop-Hill theory[20-/3l or on the relaxed model, t241 Welch et aLt251 have studied the texture and the r value of Nb-bearing low-carbon steel sheets and have shown that the r values predicted from the global textures of the entire sheet agreed well with the experimental ones of the samples of full thic
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