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# Discussion of Experimental Data for 3D Crack Propagation on the Basis of Three Dimensional Singularities

E. Schnack1, W. Weber2, Y. Zhu3

Karlsruhe Institute of Technology (KIT), Institute of Solid Mechanics, Bldg. 10.91, 3rd Floor, Kaiserstr. 12, 76131 Karlsruhe, Germany. eckart.schnack@kit.edu
Institute of Applied Mechanics, University Erlangen-Nuremberg, Egerlandstr. 5, 91058 Erlangen, Germany. weber@ltm.uni-erlangen.de
Karlsruhe Institute of Technology (KIT), Institute of Solid Mechanics, Bldg. 10.91, 3rd Floor, Kaiserstr. 12, 76131 Karlsruhe, Germany. yao.zhu@kit.edu

Computer Modeling in Engineering & Sciences 2011, 74(1), 1-38. https://doi.org/10.3970/cmes.2011.074.001

## Abstract

Three dimensional fracture mechanics was done by several groups in the past. One topic for these three dimensional fracture mechanics is to consider re-entrant corners or wedges for isotropic material. An algorithm was developed in the past to compute the dominant eigenvalues for those problems with high accuracy. Based on Kondratiev's Lemma for elliptic boundary value problems it is started with the asymptotic for the displacement and stress distribution around these three dimensional corners. By considering the mixed boundary value problem, the field quantities in the vicinity of corner points are computed by using a special finite element formulation, which is here the Petrov-Galerkin method. On that basis the quadratic eigenvalue problem is formulated and the dominant singularity exponent λ is determined iteratively by the Arnoldi method. Besides that, there are some new formulations in 3D crack propagation considering curved crack surfaces. They have been outlined as mode I, mode II and mode III formulations. In the fracture mechanics group of the University of Erlangen-Nuremberg, some experiments have been done especially for this 3D fracture mechanics effect at re-entrant corners. Therewith, the numerical data are compared with the experimental one. Moreover, the results are interpreted and it is shown that there are coincidences between theoretical and experimental results for re-entrant corners.

## Keywords

Schnack, E., Weber, W., Zhu, Y. (2011). Discussion of Experimental Data for 3D Crack Propagation on the Basis of Three Dimensional Singularities. CMES-Computer Modeling in Engineering & Sciences, 74(1), 1–38.

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