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

A. Dimitrov1, F.-G. Buchholz2, E. Schnack3
Robert Bosch GmbH, FV/PLM2, Postfach 30 02 40, 70442 Stuttgart, Germany
Institute of Applied Mechanics (FAM), University of Paderborn, Pohlweg 47-49, 33098 Paderborn, Germany
Correspondence author. Institute of Solid Mechanics, University of Karlsruhe, Kaiserstr. 12, 76128 Karlsruhe, Germany, email: eckart.schnack@imf.mach.uka.de

Computer Modeling in Engineering & Sciences 2006, 12(1), 1-26. https://doi.org/10.3970/cmes.2006.012.001

### Abstract

Crack propagation in 3D-structures cannot be reduced (in general) to a series of plane problems along the crack front edge, due to the existence of some "corners'' on the crack front, where the elastic fields are of a real three-dimensional nature. The most important example for such a corner ist the point, where the crack front intersects a free surface of the body. According to the concept of weak and strong singularities, it is possible to obtain the asymptotics for the stress intensity factor (SIF) as well as the strain energy release rate (SERR) in the neighborhood of such a corner depending on its singular exponents, so that the convenient single parameter description on which fracture mechanics is based can be extended also to problems with corners.
Within the present work the surface-breaking crack is considered. First, the singular exponents and corresponding singular modes are calculated for arbitrarily-inclined crack geometries in order to obtain the asymptotics for the SERR from a theoretical point of view. Furthermore, detailed three-dimensional numerical results for the SERR distribution along the crack front of a single edge notched (SEN) specimen under different kind of loadings are presented in a number of case studies. And finally, related fracture experiments are discussed under special consideration of some 3D-effects near the point, where the crack front intersects the free surface.

### Keywords

Surface-breaking crack, corner singularity, weak and strong singularities, fracture parameter asymptotics, SEN specimen

Dimitrov, A., Buchholz, F., Schnack, E. (2006). On Three-dimensional Effects in Propagation of Surface-breaking Cracks. CMES-Computer Modeling in Engineering & Sciences, 12(1), 1–26.

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