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3D Crack Growth by Considering Re-Entrant Corners

E. Schnack1, K. Kolk2, A. Dimitrov3

Institute of Solid Mechanics, Karlsruhe University, Geb. 10.23, 3. OG, Kaiserstr. 12, D-76128 Karlsruhe, Germany. Email:
Institute of Applied Mechanics, University Erlangen–Nuremberg, Egerlandstr. 5, 91058, Erlangen, Germany. Email:
Robert Bosch GmbH, Research Center Schwieberdingen, P.B. 30 02 40, 70442 Stuttgart, Germany. Email:

The International Conference on Computational & Experimental Engineering and Sciences 2008, 8(3), 107-114.


In fracture mechanics, corner and wedge singularities have to be considered for two- and three-dimensional problems in isotropic and layered anisotropic continua. To investigate the behaviour of crack propagation starting from corners and edges the information about stress asymptotics in the vicinity of three-dimensional corner points is needed [1]. Thus, in this paper two aspects are studied: the interface crack in layered anisotropic materials with re-entrant corners and surface cracks in homogeneous isotropic continua. Moreover a strategy is presented to model such surface breaking cracks efficiently within a numerical 3D simulation [2]. To study the effect of geometrical singularities generalized stress intensity factors are defined. Starting with KONDRATIEV's Lemma an elliptic boundary value problem has to be solved with homogeneous DIRICHLET/NEUMANN boundary data that is generating a singular field in the vicinity of corner points. Afterwards the weak form for the described problem is discretized by using the PETROV-GALERKIN finite element method resulting in a quadratic eigenvalue problem. The quadratic eigenvalue problem is solved iteratively by the ARNOLDI method [3], and finite element approximations of corner singularity exponents are computed. These eigenvalues are the basis for the definition of generalized stress intensity factors in the neighbourhood of corner points. For the a-posteriori control of the eigenvalues, an error estimator is developed on the basis of the ZIENKIEWICZ-ZHU algorithm. This approach to determine 3D singularities is tested herein for some typical applications in fracture mechanics. Known 3D singularities are a key input for the formulation of an advanced 3D crack growth criterion [2].


Cite This Article

Schnack, E., Kolk, K., Dimitrov, A. (2008). 3D Crack Growth by Considering Re-Entrant Corners. The International Conference on Computational & Experimental Engineering and Sciences, 8(3), 107–114.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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