Session: 04-24-01: Advancing Composite Materials through Integrated Multiscale Modeling and Experimental Techniques

Paper Number: 147282

147282 - Comparison of Volume Element Sizes for Elastic and Plastic Properties in Polycrystalline Steels 

In this work, we compare the volume element (VE) sizes for elastic and plastic properties to determine the converged representative volume element (RVE). RVE refers to a large volume element that is used to homogenize the microstructural heterogeneity to the macroscale. The macroscopic domain is partitioned into several small VEs that are smaller than RVEs but in a continuum length scale. We introduce the concept of statistical volume element (SVE), where variation and mean-based criteria are proposed for the convergence of elastic and plastic properties to achieve the RVE limit from the SVEs. This proposed SVE-based homogenization framework ensures local heterogeneity in the microstructures which enables us to capture the relationship between microstructural descriptors and mechanical responses. The present work attempts to predict the homogenized properties of macroscale using crystal plasticity finite element (CPFE) simulations and statistical analysis of different ensembles of SVEs. Microstructural SVE models are generated using the statistical descriptor of grain morphology (grain sizes and shapes), crystallographic texture (crystallographic orientations), and volume fraction of dual-phase (DP) steels. The RVE size for elastic and plastic properties varies with the volume fraction of each constituent phase and texture. We implement a dislocation-based crystal plasticity constitutive model in the CPFE framework. The meshing used in VEs for this research is voxel-based. Firstly, we compare the statistics of generated microstructural VE with the original. We implement boundary conditions based on Hill-Mandel conditions to the SVEs. After that, we calculate the average stress and strains for each SVE realization and compare the results. We consider bulk and shear modulus for isotropic and full elasticity tensors for anisotropic cases of elastic properties. We also calculate plastic flow stresses and plastic dissipations as plastic properties. The macroscopic materials are isotropic for the non-textured (random) microstructures. However, textured microstructures represent anisotropy even in the macroscales. During the loading of the SVEs, all the grains do not exhibit the same plastic behavior since some grains remain in the elastic regime. Thus, DP steels represent a wide range of plastic flow behavior and variation in the yield points. We determine the convergence of the RVE limits using the proposed mean-based approach, where the convergence rate using the proposed variation-based approach in the apparent properties of SVE sizes. The current research aims to establish a relationship between RVE size, volume fraction, and texture to estimate the effective homogenized properties from the SVE-based approach. This statistical framework can easily be extended to cyclic loading, fatigue, and fracture in polycrystalline steels.

Presenting Author: Anik Das Anto The University of Tennessee, Knoxville

Presenting Author Biography: Anik Das Anto is a PhD Student in Mechanical Engineering at the University of Tennessee, Knoxville. He completed his MS in Structural Engineering from North Dakota State University in 2022. His research interests lie in the broad areas of Computational Mechanics and Machine Learning. Currently, he is working on developing constitutive and phase Field Fracture modeling for Finite Element Analysis (FEA) codes.

Authors:

Anik Das Anto The University of Tennessee, Knoxville
Robert Fleishel The University of Tennessee, Knoxville
Stephanie Termaath The University of Tennessee, Knoxville
Reza Abedi The University of Tennessee, Knoxville