Grain size impact on sheet metal behavior via CPFEM

Abstract

A novel multiscale computational framework based on Crystal Plasticity Finite Element (CPFE) modeling is proposed to investigate the effect of grain size on the mechanical behavior and ductility limits of thin metal sheets, featuring both uniform and gradient grain structures. This approach relies on designing unitcell models that reflect the microstructural characteristics of thin metal sheets. The overall response of the unit cell is obtained from that of its single crystal constituents using the periodic homogenization scheme. At the single crystal level, the mechanical behavior is modeled within a finite strain, rate-independent plasticity framework, where the plastic flow is governed by the classical Schmid law. The effect of individual grain size is incorporated at the single crystal scale by adjusting the critical resolved shear stress (CRSS) evolution, using a combination of the microscopic Hall–Petch relationship and a dislocation density-based hardening model. To efficiently solve the single crystal constitutive equations, a return-mapping algorithm coupled with the Fischer–Burmeister complementarity function is developed and implemented into ABAQUS/Standard through a user-defined material subroutine (UMAT). At the macroscopic level, the ductility limits are predicted by the Rice bifurcation theory. The performance of the proposed strategy is validated through a series of polycrystalline aggregate simulations. The numerical results demonstrate a significant influence of grain size on both the macroscopic strength and ductility limits of polycrystalline aggregates. Additionally, the introduction of gradient grain structures is shown to substantially enhance both strength and ductility. These findings provide valuable insights for optimizing material performance in engineering applications.