A study of through-thickness texture gradients in rolled sheets

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.