Abstract
Plane stress mode I crack-tip fields for perfectly plastic orthotropic materials are studied. Plastic orthotropy is described by Hill's quadratic yield function. The construction of crack-tip fields is based on the general crack-tip field analysis for elastic perfectly plastic materials given by Rice [1] and guided by the corresponding low-hardening power-law solutions. Two very different types of plane-stress crack-tip fields emerge as plastic orthotropy is varied. The first one consists of a centered fan sector in front of the crack tip and two neighboring constant stress sectors. The second one consists of a constant stress sector in front of the crack tip, a constant stress sector bordering the crack face, and a centered fan sector between the two constant stress sectors. All the perfectly plastic crack-tip solutons are verified by the corresponding low-hardening power-law solutions. General trends of crack-tip stress solutions as functions of plastic orthotropy and implications of these solutions to the design of ductile composite materials are discussed.
Résumé
On étudie les champs de contraintes planes de mode I à l'extrémité d'une fissure, dans les matériaux orthotropiques parfaitement plastique. L'orthotropie plastique est décrite par la fonction quadratique de plasticité de Hill. On base les constructions des champs de constraintes sur l'analyse générale des constraintes à l'extrémité d'une fissure fournie par Rice pour les matériaux élastiques parfaitement plastiques, que l'on règle par les lois paraboliques caractérisant un faible écrouissage. Lorsque l'on modifie l'orthotropie plastique, il apparaît deux types de champs de contraintes à l'extrémité de la fissure très différents. Le premier comporte un secteur en éventail centré sur le front de fissure, et deux secteurs voisins à contraintes constantes. Le second consiste en une secteur à contrainte au bord de la surface de la fissure, et un secteur en éventail centré sur les deux secteurs à contraintes constantes. Toutes les solutions relatives à une extrémité de fissures parfaitement plastique sont vérifiées par les fonctions paraboliques d'écrouissage faible correspondantes. On discute des tendances générales que suivent les solutions pour les contraintes en extrémité de fissure selon l'orthrotropie plastique, et des implications que comportent ces solutions dans la conception de matériaux composites ductiles.
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Pan, J. Plane-stress crack-tip fields for perfectly plastic orthotropic materials. Int J Fract 38, 103–122 (1988). https://doi.org/10.1007/BF00033001
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DOI: https://doi.org/10.1007/BF00033001