Abstract
A conic-section simulation analysis to determine the stress intensity factors for fracture mechanics problems of practical interest using the finite element method is presented. The method makes use of elliptic displacement functions which are satisfied by the introduction of an “equivalent ellipse” obtained through first simulating the actual crack surface displacements as a part of a parabola or a hyperbola. Unlike other finite element approaches that incorporate no special crack-tip treatment, the present approach requires neither extremely small finite elements in the vicinity of the crack tip nor the computation of several strain energies. The cases examined include not only problems of the opening mode (I) or the edge-sliding mode (II), but also the combined modes of crack deformation.
Résumé
On présente une analyse par simulation permettant de déterminer les facteurs d'intensité de contraintes pour des problèmes de mécanique de rupture d'intérêt pratique, en utilisant la méthode des éléments finis. On recourt à des fonctions de déplacement elliptique, qui sont satisfaites par l'introduction d'une ellipse équivalente, obtenue en assimilant les déplacements réels en surface de la rupture à une portion de parabole ou d'hyperbole. Au contraire des autres approches par éléments finis qui ne prévoient pas un traitement particulier de l'extrémité de la fissure, la méthode proposée ne requiert ni de mailles extrêmement fines au voisinage de cette extrémité, ni de nombreux calculs d'énergies de déformation. Les cas examinés ne se limitent pas aux problèmes d'ouverture de mode I ou de mode II, mais couvrent aussi des modes combinés déformation de la fissure.
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Chow, C.L., Lau, K.J. A conic-section simulation analysis of two-dimensional fracture problems using the finite element method. Int J Fract 12, 669–684 (1976). https://doi.org/10.1007/BF00037914
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DOI: https://doi.org/10.1007/BF00037914