Abstract
Since the theoretical stresses and strains at the tip of a V-notched crack in an elastic continuum are infinite, the question arises as to the accuracy of strain energy as calculated from finite element computer programs for systems containing such a crack. Two geometries for which analytical solutions are available were analyzed using a plane stress finite element computer program. Results show that accuracy in both cases depended upon proper selection of a grid network. Several methods of calculating stress intensity factors are discussed. Application of the finite element computer program in the analysis of fracture in solid propellant rocket motor cartridge or grain is included.
Résumé
Dans un continuum élastique, les contraintes et les déformations à l'extrémité d'une fissure en Vé sont théoriquement infinies. La question se pose donc de savoir quel est le degré de précision que l'on peut attendre du calcul à l'ordinateur par éléments finis de l'énergie de déformation correspondant à des systèmes où se rencontrent de telles fissures.
On a analysé deux types de géométries différentes, pour lesquelles existent des solutions analytiques, en utilisant un programme d'ordinateur pour l'étude par éléments finis de l'état plan de tension.
Les résultats montrent que, daps les deux cas, la précision dépend du choix du réseau le plus adéquat.
Diverses méthodes de calcul des facteurs d'intensité des contraintes sont discutées. On traite de l'application des programmes de calcul par ordinateur des élements finis à l'analyse des conditions de rupture dans les cartouches ou éléments de combustible solide pour fusées.
Zusammenfassung
Die theoretischen Spannungen und Dehnungen an der Spitze eines V-förmigen Risses in einem elastischen Kontinuum sind unendlich groß. Es stellt sich die Frage der Genauigkeit der, für Systeme mit solchen Rissen, nach dem Verfahren der endlichen Elementen errechneten Dehnungsenergie.
Zwei geometrische Formen, für welche analytische Ergebnisse vorlagen, wurden an Hand eines Rechenprogramms für die Ermittlung des planen Spannungszustandes durch endliche Elemente untersucht.
Die Ergebnisse zeigen, daß in beiden Fällen die Genauigkeit von der Wahl eines passenden Netzes abhängt.
Es werden verschiedene Verfahren zur Bestimmung der Spannungsintensitätsfaktoren besprochen; die Anwendung des Rechenprogramms zur Ermittlung der Bruchbedingungen in Festbrennstoffelementen für Raketen wird behandelt.
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Anderson, G.P., Ruggles, V.L. & Stibor, G.S. Use of finite element computer programs in fracture mechanics. Int J Fract 7, 63–76 (1971). https://doi.org/10.1007/BF00236483
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DOI: https://doi.org/10.1007/BF00236483