Grain size effect of FCC polycrystal: A new CPFEM approach based on surface geometrically necessary dislocations

A multiscale modeling methodology involving discrete dislocation dynamics (DDD) and crystal plasticity finite element method (CPFEM) was used to study the grain size effect in FCC polycrystalline plasticity. The developed model is based on the dislocation density storage-recovery framework and is expanded to the scale of slip systems. DDD simulations were used to establish a constitutive law incorporating the main dislocation mechanisms that are involved in the strain hardening process observed in monotonically deformed FCC polycrystals. This was achieved by calculating the key features controlling the accumulation of the forest dislocation density within the grains and the polarized dislocation density at the grain boundaries during plastic deformation. The model was then integrated with a CPFEM model at the polycrystalline aggregate scale to compute short- and long-range internal stresses within the grains. These simulations quantitatively reproduced the deformation curves of the FCC polycrystals as a function of grain size. Because of its predictive ability to reproduce the Hall–Petch effect in a physically justified approach, the proposed framework has significant potential for further applications. • Based on DDD simulation results, a governing relationship between surface GND density and long-range internal stress is established. • The computation of long-range internal stress at the scale of slip system is free of fitting parameters. • With a simple geometry of polycrystalline aggregate, the computed Hall–Petch effect agrees with the experimental data of pure polycrystalline copper. • Two history-related and grain size-dependent features are responsible for the Hall–Petch effect: initial dislocation density and surface GND density accumulated at grain boundaries.