A study of through-thickness texture gradients in rolled sheets

Abstract

A method to simulate shear effects and through-thickness texture gradients in rolled sheet materials is introduced. The strain history during a rolling pass is idealized by superimposing a sine-shaped evolution of the 13 shear component to a plane-strain state. These generic strain histories are enforced in a visco-plastic self-consistent (VPSC) polycrystal deformation model to simulate texture evolution as a function of through-thickness position. The VPSC scheme is deemed superior to a full constraints (FC) or relaxed constraints (RC) approach, because it allows one to fully prescribe diagonal and shear-strain-rate components while still accounting for grain-shape effects. The idealized strain states are validated by comparison with deformation histories obtained through finite-element method (FEM) calculations. The through-thickness texture gradients are accounted for by introducing a relative variation of the sine-shaped 13 shear with respect to the plane-strain component. The simulation results are validated, in turn, by comparison with typical examples of through-thickness texture gradients observed experimentally in rolled plates and in sheets of fcc and bcc materials.

A New Analytical Approach for the Velocity Field in Rolling Processes and Its Application in Through-Thickness Texture Prediction

“…The L xz component shows a sine-shaped type of curve, which was the assumption for shear in study of Engler et al [18] The sine-shaped function implies that due to the friction, the top layer first moves faster than the underlying layers, and later, when the frictional force works in the opposite direction, this layer moves slower compared to the underlying layers. This effects become more pronounced for higher values of a.…”

“…Equations [18] and [19] yield in following differential Eq. [20] for h as a function of 1 and its derivative…”

“…[13] An overview of these models is given by Qie et al [14] Numerous literature sources report on the calculation of the velocity gradient tensor coupled with polycrystal plasticity models. [15][16][17][18] Choi et al [15] used the FE method to calculate the local strain evolution. Van Houtte et al used an incremental texture updating procedure in a FE model of a cup drawing process.…”

“…[16] Segurado et al [17] reported on a multiscale model to embed the VPSC model in an implicit FE model of sheet rolling. Engler et al [18] imposed a sine-shaped 31 and 13 shear (where 1 represents the rolling direction, and 3 the sheet's normal direction) in the top layers to implement the shear between the rolls and the plate's surface. Alternatively, the deformation flow across the thickness in rolled materials is described by analytical flow functions.…”

“…The non uniform velocity gradient field across the thickness of a rolled sheet explains the through-thickness texture gradient, as reported in numerous literature sources. [15,18,27] The flow line models are capable of reproducing the shear component in the rolling plane by assigning heterogeneous velocity distribution at the end of the flowline. However, current state of the art does not contain a streamline formulation with a continuous velocity field homogeneous outside of the deformation zone, and which can alter when different frictional conditions applied between the rolls and the plate's surface.…”