Abstract
This paper deals with stress-strain fields and strain energy density distribution in single and mixed mode crack configurations.
To avoid stress singularity in the neighbourhood of the crack tip a proper physical-mathematical model has been devised, where plasticization effects are taken into account. Following the Dugdale model, a “continuous fictitious crack extension” is realized. In this way the original nonlinear boundary-value problem is reduced to a linear one that is of elastic-perfectly plastic type.
The governing equations are derived within the mathematical framework of “free boundary problems”, and the solution is evaluated by a numerical procedure based on the incremental loading method and the Williams' stress function.
Experimental investigations, by using the optical method of caustics have been carried out, evaluating the SED distributions and the fracture angles for several crack configurations.
Résumé
L'étude est relative aux champs de contraintes-dilatations et à la distribution de la densité de déformation dans des configurations de fissures de modes simple et mixte. En vue d'éviter une singularité de contraintes au voisinage de l'extrémité de la fissure, on a conçu un modèle physico-mathématique adéquat, où l'on prend en compte les effects de la plastification. En suivant le modèle de Dugdale, on arrive au concept d'extension continue d'une fissure fictive”. De la sorte, le problème initial des valeurs aux limites non linéaires est ramené à un problème linéaire de type élastique-parfaitement plastique.
Les équations directrices sont établies dans le cadre mathématique des problèmes aux limites non définies, et la solution est évaluée par une procédure numérique basée sur une méthode de mise en charge par incréments et par la fonction de contraintes de Williams.
On effectue également des travaux expérimentaux en utilisant la méthode optique de la caustique, pour évaluer les distributions de densité d'énergie de déformation et les angles, pour diverses configurations de fissures.
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La Barbera, A., Marchetti, M. & Tizzi, S. Elasto-plasto overall response in single and mixed mode crack configurations. Int J Fract 43, 25–45 (1990). https://doi.org/10.1007/BF00018125
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DOI: https://doi.org/10.1007/BF00018125