Numerical investigations of flat punch molding using a higher order strain gradient plasticity theory

In this work we have revisited the problem of molding a deformable substrate with a rigid flat punch. The work is motivated by the recent experiments by Chen et al. (Acta Mater 59:1112−1120, 2011) where it was shown that systematically determined characteristic molding pressure H increased significantly with decrease in punch width, for widths less than \(\sim 25 \; \mu m\). This size effect, akin to the indentation size effect observed in nano-indentation of metals, assumes importance in applications involving molding of metallic microstructures. Numerical simulations have been conducted within the framework of a finite deformation higher order strain gradient model. While classical plasticity predicts almost uniform stress with severe plastic strain concentration at the sharp corners to prevail just beneath the punch, our simulations present a significantly different picture. Very narrow punches have fairly uniform plastic strain with severe concentration of strain gradients and large contact stresses close to the edges. Wider punches however, behave in a manner closely resembling the predictions of classical plasticity.