Modeling Deformation Texture and Anisotropy during the Tensile Test of an Interstitial-Free Steel Sheet by Means of a Se
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I.
INTRODUCTION
RECRYSTALLIZED interstitial-free (IF) steel sheets are widely used in the automotive industry because of their excellent capacity to be deep drawn. This quality comes from their exceptional texture achieved after cold rolling and annealing. This texture is produced because of selected recrystallization and grain growth of nuclei with (111)[hkl] orientation, growth that occurs at the expense of grains with (100)[hkl] orientation.[1,2] One of the main characteristics of this steel is that its final texture depends mainly on cold reduction, and not much on the annealing cycle. Moreover, this steel can be produced either in batch or continuous lines with similar results.[3] A way of quantifying the capacity of a strip to be deep drawn is through the r value, which is determined in a tensile test. The r value is calculated as the ratio between the width and the thickness deformation rates.[4] Because r depends on the angle formed between the tensile and the rolling directions of the strip, two parameters are usually defined to characterize the material anisotropy: rm = (r0 + 2*r45 + r90)/4 and Dr = (r0 – 2*r45 + r90)/2, where r0, r45, and r90 are the values measured when the tensile direction forms an angle of 0,45 and 90 deg. with the rolling direction.[5] In low carbon steels, the r value shows a slight decline as a function of the applied strain.[6] In previous studies, this dependence was attributed to the rotation of grains during deformation [6] after measuring the changes of the crystallographic texture produced by deformation. As far M.A.VICENTE ALVAREZ, Advanced Researcher, and T. PEREZ, Metallurgical Department Head, Metallurgy Department, are with the Center for Industrial Research, Siderca-Tenaris, 2804-Campana, Buenos, Aires, Argentina. Contact e-mail: [email protected] Manuscript submitted July 12, 2006. METALLURGICAL AND MATERIALS TRANSACTIONS A
as we know, no one has attempted to model the evolution of the r value as a function of strain in low carbon steels, with the aim of identifying the causes of such dependence. The viscoplastic model has already been used to evaluate the r value[7,8] after an infinitesimal deformation, focusing in the dependence of r with the angle formed between the tensile and the rolling directions. In this article, the evolution of the r value and the texture is calculated by means of a self-consistent viscoplastic approach, in which the anisotropy of the medium is taken into account. This approach has the advantage over other plasticity models (such as the Taylor model) that the interaction between neighboring grains is considered. In Section II, a brief description of the model is presented. In section III, the results of the calculation and a comparison with experimental measurements on an IF steel are shown. The roles of grain rotation and work hardening on the r value are identified. Finally, a comparison with other plasticity models is made. II.
THE MODEL
In this section, we briefly outline the VPSC model proposed by Molinari et al.[9] They assumed
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