Optimizing continuous annealing of interstitial-free steels for improving deep drawability
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I. INTRODUCTION
HIGH values of the average plastic sheet anisotropy, commonly described by the engineering parameter r, and minimum in-plane orientation dependence of the anisotropy parameter, usually referred to as ⌬r are among the predominant objectives in optimizing the properties of interstitialfree (IF) steel sheets. Beneficial combination of both parameters typically entails a high, in-sheet plastic isotropy and a good deep drawability. The plastic anisotropy parameter is for a given stressstrain state described by the ratio of broadening to thickness reduction of a flat sample. The kinematic portion of plastic anisotropy can be calculated from the crystallographic texture of the sheet. Calculation methods for plastic anisotropy parameters are commonly based on appropriate homogenization theory, such as Taylor–Bishop–Hill[1–3] and Bunge[3] and self-consistent approaches or discrete single-component based methods, such as crystal-plasticity finite element methods.[4] Crystallographically, plastic anisotropy originates from the discreteness of crystal slip in each of the grains constituting polycrystalline material. The directionality of crystal slip with respect to the external reference frame, imposed by the actual deformation state, is determined by the texture, which provides a quantitative relation between the crystal reference systems of all the individual grains and the external reference system exerted by the process. This implies that conventional deep drawing property quantities are only valid for one particular velocity gradient tensor. This aspect is of particular relevance when Taylor–Bishop–Hill-type or self-consistentbased strain-rate homogenization models serve for predicting deep drawing properties. In other words, it is conceivable PASI JUNTUNEN, Researcher, and PENTTI KARJALAINEN, Professor, are with the Materials Engineering Laboratory, Department of Mechanical Engineering, University of Oulu, Finland. DIERK RAABE, Director, and GERD BOLLE, Research Technician, are with the Department of Microstructure, Max-Planck-Institut fu¨r Eisenforschung, 40237 Du¨sseldorf, Germany. TERO KOPIO, Engineer, is with Product Applications, Strip Products, Rautaruukki Steel, Hameenlinna, Finland. Manuscript submitted August 20, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
that a given texture may provide beneficial deep drawing properties for one particular deformation state while it might have worse properties for another. Deep drawability for intricate deformation paths is, thus, better computed by use of discrete crystal plasticity theory. Optimum deep drawing behavior of IF steels under ideal, homogeneous, plain-strain conditions is obtained by a strong and homogeneous {111}具uvw典 fiber texture (␥-fiber).[5–8] Textures of steel sheet products are affected by all production steps, i.e., by hot rolling, cold rolling, and final continuous annealing. Cold rolling textures of body centered cubic (bcc) transition metals have been widely investigated by experiment[5–10] and simulation.[6–17] In recent years,
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