Open Access

ABSTRACT

On Three-dimensional Effects in Propagation of Surface-breaking Cracks

E. Schnack¹, A. Dimitrov², F.-G. Buchholz³

1 Institute of Solid Mechanics, Karlsruhe University, Geb. 10.23, 3. OG, Kaiserstr. 12, D-76128 Karlsruhe, Germany. e-mail: eckart.schnack@imf.mach.uka.de
2 Robert Bosch GmbH, Research Center Schwieberdingen, P.B. 30 02 40, 70442 Stuttgart, Germany. e-mail: atanas.dimitrov@de.bosch.com
3 Lagesche Str. 76B, 32657 Lemgo, Germany. email: fus.buchholz@t-online.de

The International Conference on Computational & Experimental Engineering and Sciences 2007, 1(4), 139-146. https://doi.org/10.3970/icces.2007.001.139

Abstract

In fracture mechanics, we have to discuss corner and edge singularities for two- and three-dimensional problems in isotropic and layered anisotropic continua. To say something about the behavior of crack propagation starting from corners and edges, we need the information about stress asymptotics in the vicinity of three-dimensional corner points. Thus, in this paper we can study two aspects: the interface crack in layered unisotropic materials with re-entrant corners and surface cracks for the homogeneous isotropic continua. To study the effect of geometrical singularities on the stress intensity factors, we have to define generalized stress intensity factors. We are starting with KONDRATIEV's Lemma and starting from that, an elliptic boundary value problem with homogeneous DIRICHLET/NEUMANN boundary data which produce a singular field in the vicinity of corner points. In the next step, the weak form for the previous problem is discretized by using PETROV-GALERKIN finite element method and, as a result, we are getting a quadratic eigenvalue problem. The quadratic eigenvalue problem is solved iteratively by the ARNOLDI method, and finite element approximations of corner singularity exponents λ_I are computed. These eigenvalues λ_I are the basis for the definition of generalized stress intensity factors in the neighborhood of the corner points. For the a posteriori control on λ_I, an error estimator is developed on the basis of ZIEKIEWICZ-ZHU algorithm. The method is tested for some typical problems in fracture mechanics.

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Keywords

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