Abstract
The stress singularity at the tip of a crack, either lying along or perpendicular to the interface of the two materials, is first investigated by the complex variable method. The order of the singularity is shown to be dependent on both the crack geometry and two parameters α, β which are related to the four elastic constants of the two materials. A hybrid crack element is constructed to properly account for the crack tip singularity. The stress intensity factors and energy release rate for cracks in different bi-material continua are then calculated using the finite element method. The results show that the present finite element analysis makes possible a highly accurate and efficient numerical solution of fracture mechanics problems.
Résumé
On étudie la singularité de la contrainte à l'extrémité d'une fissure située le long de ou perpendiculairement à l'interface de deux matériaux, en recourant d'abord à la méthode des variables complexes. On montre que l'ordre de la singularité dépend à la fois de la géométrie de la fissure et de deux paramètres α et β, en relation avec les quatre constantes élastiques des deux matériaux. On construit un élément de fissure hybride propre à tenir compte de la singularité d'extrémité de fissure, et on calcule par éléments finis les facteurs d'intensité des contraintes et le taux de relaxation de l'énergie, pour des fissures dans différents continuum à deux matériaux. Les résultats montrent que les techniques actuelles d'analyse aux éléments finis permettent de trouver une solution numérique efficace et de haute précision aux problèmes de mécanique de la rupture.
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Lin, K.Y., Mar, J.W. Finite element analysis of stress intensity factors for cracks at a bi-material interface. Int J Fract 12, 521–531 (1976). https://doi.org/10.1007/BF00034638
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DOI: https://doi.org/10.1007/BF00034638