# Rolling Simulation

This simulation concerns the rolling of metal sheet, so as to reduce its thickness. Normally, this process is applied to relatively wide plate or sheet, so that plane strain conditions are created - ie the strain is confined to the sectional plane shown in the simulation, with the width of the sheet remaining unchanged as it is rolled. The length of the sheet therefore increases in proportion to the reduction in its thickness, since plastic deformation of this type occurs with no change in volume.

The predictions shown in the simulation (for stress and strain fields, and also for the rolling load and hence the average rolling stress) were obtained by running a Finite Element Model (FEM) for several pre-selected cases. In this type of model, the domain of interest is sub-divided into a number of volume elements, creating a mesh, with the overall deformation taking place such that the response of all of these elements conforms to the governing equations and the imposed boundary conditions.

The stress-strain behaviour of the material is pre-specified, and is displayed here for each case, characterised by a (uniaxial) Yield Stress (YS), a constant Work Hardening Rate (WHR) and no strain rate sensitivity. The effects of varying the YS and WHR, the (thickness) Reduction Ratio and the application of tension to the emerging sheet can all be explored by changing the case being displayed. The roll diameter, initial billet diameter and roll rotation rate are all fixed. It's assumed that the rolls are rigid and that there is sticking friction (no sliding) between roll and sheet. The displayed stress and strain fields, and the mesh deformation, relate to the steady state that is set up soon after rolling is started. In order to make the movement clearer, it has been slowed down - a timer is shown in the lower right of the display.

Outcomes that can be explored include the rolling load, the creation of residual stresses in the sheet, the distribution of plastic strain etc. The stress displayed can be either the von Mises stress (a scalar), which is given by the square root of half the sum of the squares of the three differences between the principal stresses - see Yield criteria for metals, or one of the normal stresses in rolling (1), through-thickness (2) or transverse (3) directions. There is also an option for displaying the equivalent plastic strain, which is the analogous strain parameter to the von Mises stress. Material properties are taken to be constant, homogeneous and isotropic. The display shown is that of the top half of the system - ie the dotted line at the bottom is a plane of symmetry.