Relaxed grain cluster (RGC) homogenization scheme

Abstract

An efficient homogenization scheme for polycrystals is presented. The scheme is based on a generalization of the grain interaction (GIA) model. A volume element consisting of eight (= 2 × 2 × 2) hexahedral grains is considered. The kinematics of the relaxed grain cluster (RGC) scheme is formulated within a finite deformation framework, where the relaxation of the local deformation gradient of each individual grain is described by interface relaxation vectors. In the present model, the relaxation vectors are determined such that the total energy (or work) density of the cluster is minimum. A penalty term is added into the energy minimization landscape, which accounts for an energy density associated to the mismatch at the grain boundaries due to relaxations. Effectively, this penalty term mimics the kinematical condition of deformation compatibility at the grain boundaries. Furthermore, simulations have been performed for a polycrystalline sample. The overall behavior of the sample undergoing uniaxial tension and simple shear, is studied for various microstructural configurations. The prediction of the RGC scheme is compared with predictions using other averaging schemes, as well as the result of finite element (FE) simulation.

Current Challenges and Opportunities in Microstructure-Related Properties of Advanced High-Strength Steels

“…However, only a few multiscale forming simulations have been conducted for the case of AHSS. [34,35,37,474,515,516] Tjahjanto et al [517,518] conducted uniaxial tension simulations by using the relaxed grain-cluster (RGC) model in which a dual-phase microstructure was considered. Roters et al [454,478] further applied the RGC model to cup drawing simulations of dual-phase steel.…”

Quantifying the Contribution of Crystallographic Texture and Grain Morphology on the Elastic and Plastic Anisotropy of bcc Steel

“…Moreover, as full-field crystal plasticity simulations are often based on microstructures consisting of only a few hundred grains in an attempt to minimize the computational efforts, there is a danger of using "non-representative volume elements". Established mean-field homogenization approaches [52] such as the Grain Interaction Model (GIA) [53], the (A)LAMEL model [54], the Relaxed Grain Cluster (RGC) model [55,56] or self-consistent approaches [48,49] are, therefore, better suited as their computational performance does not require significant compromises on the number of crystallographic orientations. In many cases they also correctly predict the texture evolution after large deformation in good agreement with experimental results [49,54], a task that is especially challenging for full-field approaches due to the severe mesh deterioration.…”