PSI - Issue 71

Ayub Khan et al. / Procedia Structural Integrity 71 (2025) 461–468

462

A key challenge in designing and developing advanced engineering materials lies in accurately predicting and manipulating their mechanical behavior. Computational modeling, particularly at the mesoscale, has emerged as a powerful tool for uncovering the mechanisms that govern the behavior of polycrystalline materials. By bridging the gap between microscale deformation processes and macroscale behavior, these models provide valuable insights into phenomena such as texture evolution, strain localization, and damage initiation. Theoretical investigations into polycrystals have suggested that the inhomogeneous plastic deformation between neighboring grains may be responsible for the grain-size dependence (i.e., Hall – Petch relationship) of flow stress (Acharya and Beaudoin (2000); Dai and Parks (1997)). One can partition crystallographic dislocations into two types: geometrically necessary dislocations (GNDs), which are associated with the curvature of the crystal lattice and plastic strain field incompatibility, and statistically stored dislocations (SSDs), which arise from random trapping during homogeneous deformation. Consequently, part of the dislocation population in a crystal is linked to the plastic strain gradient (Cermelli and Gurtin (2001)). Our study employs a phenomenological Crystal Plasticity (CP) model (Kalidindi et al. (1992)) to capture the plastic deformation behavior of polycrystals with face-centered cubic (FCC) and body-centered cubic (BCC) crystal structures. Within this framework, the quantification of Geometrically Necessary Dislocations (GNDs) is achieved through the utilization of Nye's dislocation tensor (Nye (1953); Anahid et al. (2011)), which quantifies the gradients of plastic shear, to capture the additional hardening, specifically near the grain boundaries. To enhance the fidelity of our simulations, the constitutive equations are augmented with a diffused interface model. This model homogenizes the deformation behavior in the grain boundary (GB) region to capture more effectively the hardening due to dislocation pile-up. In order to simulate realistic polycrystals, Electron Backscatter Diffraction (EBSD) data obtained from pure iron is used. These experimental datasets serve as the basis for constructing cuboidal simulation domains representative of the polycrystalline microstructure. A biased mesh generation technique (Thondiraj et al. (2024)) is employed that uses coarser elements in the bulk of the grain, assuming it has lower gradients in response, and finer elements near grain boundaries to capture the large gradients. Experimental studies have explored the deformation behavior near grain boundaries, particularly by correlating grain misorientation with variations in displacement fields (Schroeter and McDowell (2003); Kamaya (2004)). However, there is a notable scarcity of experimental investigations that provide insights into the local stress-strain behavior near grain boundaries at such fine length scales. This limitation hinders the direct validation of local response obtained from computational models using available experimental data. Furthermore, the present study aims to predict regions of elevated normal and shear stresses near grain boundaries, which are hypothesized to play a critical role in phenomena such as crack nucleation, grain boundary diffusion, and migration, which are pivotal in understanding material behavior and failure mechanisms. By running CP Finite Element Method (CPFEM) simulations on the polycrystalline RVE, macroscopic response is captured and compared with the stress-strain data of pure iron (Pohl (2019)). 2. Theory and Methodology In this section, a CP model integrated with a diffused interface is proposed that homogenizes the plastic velocity gradient in the GB region. The quantification of extra hardening in the region of high gradients of strain is achieved with the help of an incompatibility parameter calculated from Nye's dislocation tensor. 1.1. Diffused interface CP model and FEM framework In the CP model, the 2 nd Piola-Kirchhoff stress tensor and the elastic Green-Lagrange strain tensor are related by = ∶ (1) where is the fourth order elasticity tensor and = 1 2 ( − ) (2) is the elastic Green-Lagrange strain tensor and is the elastic deformation gradient. The deformation gradient ( ) is multiplicatively decomposed as (Lee (1969)) = −1 (3) where is the plastic deformation gradient, that is related to the plastic velocity gradient as = ̇ −1 (4)