A numerical study into element type and mesh resolution for crystal plasticity finite element modeling of explicit grain
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ORIGINAL PAPER
A numerical study into element type and mesh resolution for crystal plasticity finite element modeling of explicit grain structures William G. Feather1 · Hojun Lim2 · Marko Knezevic1 Received: 19 May 2020 / Accepted: 24 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A large number of massive crystal-plasticity-finite-element (CPFE) simulations are performed and post-processed to reveal the effects of element type and mesh resolution on accuracy of predicted mechanical fields over explicit grain structures. A CPFE model coupled with Abaqus/Standard is used to simulate simple-tension and simple-shear deformations to facilitate such quantitative mesh sensitivity studies. A grid-based polycrystalline grain structure is created synthetically by a phasefield simulation and converted to interface-conformal hexahedral and tetrahedral meshes of variable resolution. Procedures for such interface-conformal mesh generation over complex shapes are developed. FE meshes consisting of either hexahedral or tetrahedral, fully integrated as linear or quadratic elements are used for the CPFE simulations. It is shown that quadratic tetrahedral and linear hexahedral elements are more accurate for CPFE modeling than linear tetrahedral and quadratic hexahedral elements. Furthermore, tetrahedral elements are more desirable due to fast mesh generation and flexibility to describe geometries of grain structures. Keywords Solids · Finite element methods · Plasticity · Micromechanics · Mesh sensitivity
1 Introduction Modeling of polycrystalline metals often employs spatiotemporal domains of constituent grains interacting explicitly with each other, while achieving the state of stress equilibrium and strain compatibility [1–4]. Such modeling is referred to as full-field. The full-field microstructural modeling, especially in three-dimensions (3D), accounts for topological effects of microstructural evolution on micromechanical fields defined in term of stress and strain and facilitates better understanding of complex phenomena pertaining to material behavior. The stress equilibrium governing equations of mechanics in conjunction with a constitutive law describing the material behavior under deformation can be solved numerically using the finite element method (FEM) in terms of a work-conjugated stress–strain measures [2]. For the FEM, the microstructural domain must be discretized into
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Marko Knezevic [email protected]
1
Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA
2
Department of Computational Materials and Data Science, Sandia National Laboratories, Albuquerque, NM 87185, USA
finite elements. If a crystal plasticity-based constitutive law is embedded at every FE integration point, the mechanical fields are governed by crystallography including deformation mechanisms and crystal lattice orientation as well as the evolution of inter- and intra-granular misorientation, grain shape, and grain-boundary-character-distribution (GBCD). Beginni
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