Prediction of exit profile distortion in forward extrusion process using Riemann mapping theorem and upper bound method

One of the substantial topics in the forward extrusion process is using theoretical methods to predict the exit profile distortion due to the non-symmetry of sections or the off-centricity of die cavity. In this paper, a new approach based on the Riemann mapping theorem and upper bound method is developed to obtain the velocity field and the strain distribution. Then, the strain distribution is determined for the die with off-centered square sections. Afterwards, the exit profile curvature is calculated using an approach based on elastic-plastic bending of beams. Theoretical results are compared to the results yielded through experimental and finite element simulation and validated. Subsequently, the effect of various parameters such as relative die length and friction factor is examined on the amount of the exit profile distortion. The results show that the obtained theory can be used to predict the strain distribution and the exit profile distortion in addition to the process pressure.