Three-dimensional topography of the matt surface in aluminium pack rolling

A model has been presented in a companion paper (Utsunomiya et al., Int. J. Mech. Sci., in press) to predict the generation of roughness on the matt surface in pack rolling of aluminium foil. This model was based on a two-dimensional (2D) finite element analysis using an isotropic plasticity model for the material. The spread of crystallographic grain orientations was simulated by ascribing different material properties to each grain. The predictions showed good qualitative agreement with experiments. It was found that the formation of shear bands causes roughening of the matt surface. The effect of material properties was further explored in Utsunomiya et al. (Int. J. Mech. Sci., in press). current study the model for evolution of the matt surface roughness is extended to a three-dimensional (3D) analysis and compared with predictions using a 2D analysis, a full crystallographic 3D model and experiments. The amplitude of the predicted roughness for the 3D model is lower than for the corresponding 2D analysis. In the 3D model, grains deform more uniformly due to the homogeneous constraint from adjacent grains. The predicted roughness shows good quantitative agreement with experiments, as well as with the predictions of the crystal plasticity model. The influences of grain shape and deformation mode are investigated. It is found that peaks or valleys running perpendicular to the first principal axis of strain are generated at the matt surface, regardless of initial grain shape.