Computational homogenisation of polycrystalline elastoplastic microstructures at finite deformation

authored by: Eva Lehmann, Stefan Loehnert, Peter Wriggers
Abstract: It is well known that metals behave anisotropically on their microstructure due to their crystalline nature. FE-simulations in the metal forming field however sometimes lack the right macroscopic anisotropies as their type can be unspecific. In order to find a suitable effective elastoplastic material model, a finite crystal plasticity model is used to model the behaviour of polycrystalline materials in representative volume elements (RVEs) representing the microstructure, taking into account the plastic anisotropy due to dislocations occurring within considered slip systems. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as the split of the elastic free energy into volumetric and deviatoric parts resulting in a compact expression of the resolved SCHMID stress depending on the slip system vectors. In order to preserve the plastic incompressibility condition, the elastic deformation gradient is updated via an exponential map scheme. To further circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. Through homogenisation and optimisation techniques, effective stress-strain curves are determined and can be compared to results from real manufacturing and fabrication processes leading to an effective elastoplastic material model which is suitable for metal forming processes at finite strains.
Organisation(s): Institute of Continuum Mechanics
Type: Conference contribution
Pages: 6213-6228
No. of pages: 16
Publication date: 01.12.2012
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Theory and Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1002/pamm.201110192 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@inproceedings{7bcaf6192e9a40628368a5d0878d54fc,
title = "Computational homogenisation of polycrystalline elastoplastic microstructures at finite deformation",
abstract = "It is well known that metals behave anisotropically on their microstructure due to their crystalline nature. FE-simulations in the metal forming field however sometimes lack the right macroscopic anisotropies as their type can be unspecific. In order to find a suitable effective elastoplastic material model, a finite crystal plasticity model is used to model the behaviour of polycrystalline materials in representative volume elements (RVEs) representing the microstructure, taking into account the plastic anisotropy due to dislocations occurring within considered slip systems. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as the split of the elastic free energy into volumetric and deviatoric parts resulting in a compact expression of the resolved SCHMID stress depending on the slip system vectors. In order to preserve the plastic incompressibility condition, the elastic deformation gradient is updated via an exponential map scheme. To further circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. Through homogenisation and optimisation techniques, effective stress-strain curves are determined and can be compared to results from real manufacturing and fabrication processes leading to an effective elastoplastic material model which is suitable for metal forming processes at finite strains.",
keywords = "Effective material model, Finite crystal plasticity, Homogenisation, Sheet bulk metal forming",
author = "Eva Lehmann and Stefan Loehnert and Peter Wriggers",
year = "2012",
month = dec,
day = "1",
doi = "10.1002/pamm.201110192",
language = "English",
isbn = "9783950353709",
series = "ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers",
pages = "6213--6228",
booktitle = "ECCOMAS 2012",
note = "6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 ; Conference date: 10-09-2012 Through 14-09-2012",
}