3D-corner effects in crack propagation

Full text: Crack propagation in real 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' (the crack termination point on a free surface for instance), where the elastic fields are of three-dimensional nature. In this case, the solution can be expanded near the comer in an asymptotical series u {sigma}{sub i} K{sub i} r{sup {lambda}}{sup {}sub i} f{sub i}({theta}, {phi}), where r, {theta}, {phi} are the spherical coordinates and {lambda}{sub i} are the corner singularity exponents. According to the concept of weak and strong singularities, it is possible to obtain the asymptotics for the stress intensity factor (SIF) and for the energy release rate (ERR) in the neighborhood of a corner depending on its singularity exponents. The convenient single parameter description of fracture can be extended therefore to problems with corners within a generalized Griffith theory. In the present work the surface breaking crack is considered. First, the singularity exponents for this problem are calculated by the method for arbitrary inclined crack geometries. A Galerkin-Petrov finite-element approximation is used to obtain a quadratic eigenvalue problem, which is solved iteratively by the Arnoldi method. The corresponding eigenvalues are FE-approximations of {lambda}{sub i}. Furthermore, detailed numerical results for the ERR distribution along the crack front of a SEN-specimen under a different kind of loading are presented and compared with the theoretical expectations. These calculations are performed by the modified virtual crack closure integral method (MVCCIM). And finally, related fracture experiments are discussed under the special consideration of the point, where the crack intersects the free surface. It is shown that all 3D-effects predicted by the asymptotical theory are in good agreement with the numerical and experimental findings. Refs. 5 (author)