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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 4715696, 14 pages
Research Article

Modeling Crack Propagation in Polycrystalline Microstructure Using Variational Multiscale Method

Department of Aerospace Engineering, University of Michigan, 3025 FXB Building, 1320 Beal Avenue, Ann Arbor, MI 48109, USA

Received 3 February 2016; Accepted 24 April 2016

Academic Editor: Zhiqiang Hu

Copyright © 2016 S. Sun and V. Sundararaghavan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Crack propagation in a polycrystalline microstructure is analyzed using a novel multiscale model. The model includes an explicit microstructural representation at critical regions (stress concentrators such as notches and cracks) and a reduced order model that statistically captures the microstructure at regions far away from stress concentrations. Crack propagation is modeled in these critical regions using the variational multiscale method. In this approach, a discontinuous displacement field is added to elements that exceed the critical values of normal or tangential tractions during loading. Compared to traditional cohesive zone modeling approaches, the method does not require the use of any special interface elements in the microstructure and thus can model arbitrary crack paths. The capability of the method in predicting both intergranular and transgranular failure modes in an elastoplastic polycrystal is demonstrated under tensile and three-point bending loads.