3D ductile crack propagation within a polycrystalline microstructure using XFEM

authored by: Steffen Beese, Stefan Loehnert, Peter Wriggers
Abstract: In this contribution we present a gradient enhanced damage based method to simulate discrete crack propagation in 3D polycrystalline microstructures. Discrete cracks are represented using the eXtended finite element method. The crack propagation criterion and the crack propagation direction for each point along the crack front line is based on the gradient enhanced damage variable. This approach requires the solution of a coupled problem for the balance of momentum and the additional global equation for the gradient enhanced damage field. To capture the discontinuity of the displacements as well as the gradient enhanced damage along the discrete crack, both fields are enriched using the XFEM in combination with level sets. Knowing the crack front velocity, level set methods are used to compute the updated crack geometry after each crack propagation step. The applied material model is a crystal plasticity model often used for polycrystalline microstructures of metals in combination with the gradient enhanced damage model. Due to the inelastic material behaviour after each discrete crack propagation step a projection of the internal variables from the old to the new crack configuration is required. Since for arbitrary crack geometries ill-conditioning of the equation system may occur due to (near) linear dependencies between standard and enriched degrees of freedom, an XFEM stabilisation technique based on a singular value decomposition of the element stiffness matrix is proposed. The performance of the presented methodology to capture crack propagation in polycrystalline microstructures is demonstrated with a number of numerical examples.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computational mechanics
Volume: 61
Pages: 71-88
No. of pages: 18
ISSN: 0178-7675
Publication date: 13.06.2017
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-017-1427-y (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{93f3c8cdabc444b89ef7cbb2b45e250b,
title = "3D ductile crack propagation within a polycrystalline microstructure using XFEM",
abstract = "In this contribution we present a gradient enhanced damage based method to simulate discrete crack propagation in 3D polycrystalline microstructures. Discrete cracks are represented using the eXtended finite element method. The crack propagation criterion and the crack propagation direction for each point along the crack front line is based on the gradient enhanced damage variable. This approach requires the solution of a coupled problem for the balance of momentum and the additional global equation for the gradient enhanced damage field. To capture the discontinuity of the displacements as well as the gradient enhanced damage along the discrete crack, both fields are enriched using the XFEM in combination with level sets. Knowing the crack front velocity, level set methods are used to compute the updated crack geometry after each crack propagation step. The applied material model is a crystal plasticity model often used for polycrystalline microstructures of metals in combination with the gradient enhanced damage model. Due to the inelastic material behaviour after each discrete crack propagation step a projection of the internal variables from the old to the new crack configuration is required. Since for arbitrary crack geometries ill-conditioning of the equation system may occur due to (near) linear dependencies between standard and enriched degrees of freedom, an XFEM stabilisation technique based on a singular value decomposition of the element stiffness matrix is proposed. The performance of the presented methodology to capture crack propagation in polycrystalline microstructures is demonstrated with a number of numerical examples.",
keywords = "Cracks, Crystal plasticity, Gradient enhanced damage, Microstructure, Polycrystal, Stabilisation, XFEM",
author = "Steffen Beese and Stefan Loehnert and Peter Wriggers",
note = "Funding information: The support of the German Research Foundation (DFG) within the framework of the Grant SFB TR 73 is gratefully acknowledged.",
year = "2017",
month = jun,
day = "13",
doi = "10.1007/s00466-017-1427-y",
language = "English",
volume = "61",
pages = "71--88",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "1-2",
}