Application of strain gradient plasticity in coining simulations of commemorative coins

Abstract

Size effect plays an important role in coining processes of commemorative coins. To deal with the size effect and improve the simulation accuracy, a constitutive model incorporating the conventional mechanism-based strain gradient (CMSG) plasticity theory was established in this study, with the nonlinear coupling between the statistically stored dislocation (SSD) density and the geometrically necessary dislocation (GND) density determined experimentally. Via the least square method, a bilinear equivalent plastic strain field was constructed for the evaluation of equivalent plastic strain gradient. In this way, the proposed constitutive model was implemented within a home-developed explicit finite element code for coining analyses. Uniaxial tensile tests and a nanoindentation test were conducted to obtain the mechanical properties of the Ag999 material, which was selected to verify the performance of the proposed constitutive model. By simulating the nanoindentation test and the coining process of a typical commemorative coin, it was demonstrated that the proposed constitutive model could provide accurate results in applications involving size effect, outperforming the classical plasticity constitutive model. Therefore, the proposed constitutive model based on strain gradient plasticity theory is suitable for coining simulations of commemorative coins.