A simple theory for the development of inhomogeneous rolling textures
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I.
INTRODUCTION
M A N Y metal forming processes involve forcing the material through a convergent channel, and this inevitably produces changes in displacement and velocity components. In a strain-hardening material, gradients of strain and strain rate in the process zone result in gradients of structure and properties, and because slip only occurs on a restricted number of slip systems, crystallographic texturing must also be produced. Each channel has a characteristic parameter A, which is defined as the mean thickness-to-length ratio of the plastic zone that fills it, and Backofen tl] and Mathur and Backofen I21 have demonstrated a correlation between A and the surface texture produced in cold drawing of mild steel strip. Through-thickness inhomogeneity of texture has been reported in cold-rolled niobium, E31and in this work, in contrast to Reference 2, it was demonstrated that no simple rotational relationship existed between the "normal" and transition textures, where this transition texture was not a surface texture. Through-thickness texture variations were shown by various authors c4-81 using face-centered cubic (fcc) metals and alloys of different purity and stacking fault energy (SFE). An early attempt by Hansen and Mecking t41 to explain the effect of deformation geometry on texture inhomogeneity relied on the introduction of shear s,3 into the strain tensor. Using texture simulation calculations based on conventional Taylor theory (i.e., not incorporating the "relaxed constraints" principle), they showed that an abnormal texture developed when e~3 attained a value equal to half of the rolling strain, 611. Work by Truszkowski et al. [5'6'71showed that inhomogeneous rolling textures were also affected by the materials used, and these effects they ascribed to material properties, specifically the yield strength and the work-hardening exponent. These factors of shear and
C.S. LEE, formerly a Croucher Studentship holder, Department of Mechanical Engineering, University of Hong Kong, is with the Department of Applied Science, City Polytechnic of Hong Kong. B .J. DUGGAN, Reader, is with the Department of Mechanical Engineering, University of Hong Kong. Manuscript submitted March 19, 1991. METALLURGICAL TRANSACTIONS A
material properties are dealt with more critically in the Discussion, after the theory has been developed. In rolling, it is often assumed that plane strain conditions apply, but in addition to shear caused by roll gap geometry, friction is of prime importance in producing shear. As shearing effects are maximized at the rolling surface, when these arise from either or both deformation geometry and friction, it is easy to understand qualitatively that surface and interior textures can be different, but the explanation of the well-established depth dependence ignores friction and thus needs further investigation. This article, by introducing both shear and friction into a simple model of rolling, seeks to explain both the observed texture inhomogeneities and their material dependencies. II.
THE
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