Steady-state numerical modeling of size effects in micron scale wire drawing

Abstract

Wire drawing processes at the micron scale have received increased interest as micro wires are increasingly required in electrical components. It is well-established that size effects due to large strain gradient effects play an important role at this scale and the present study aims to quantify these effects for the wire drawing process. Focus will be on investigating the impact of size effects on the most favourable tool geometry (in terms of minimizing the drawing force) for various conditions between the wire/tool interface. The numerical analysis is based on a steady-state framework that enables convergence without dealing with the transient regime, but still fully accounts for the history dependence as-well as the elastic unloading. Thus, it forms the basis for a comprehensive parameter study. During the deformation process in wire drawing, large plastic strain gradients evolve in the contact region. This creates a need for a higher order plasticity theory to accurately predict the material behaviour across the multiple scales involved. The present study reveals that the contribution from an energetic (recoverable) length parameter is limited, while the corresponding dissipative contribution dominates and tends to shift the drawing force to a higher level. As a direct consequence, the strain gradient hardening effect reduces the most favourable tool angle of a sharp tool with up to 50% (in terms of the required drawing force), whereas a circular shaped tool is proven less sensitive to scaling effects. By considering the contact force profile between tool and material it becomes clear that the strain gradients have a smoothing effect and both the magnitude and position of the peak pressure are affected significantly. A round tool is found to reduce the peak force, while the location of the peak is found to move from outlet to inlet depending on the tool geometry.