Abstract
A numerical stress analysis of an elastic three-dimensional specimen similar to the compact tension specimen used in fracture investigations is presented. The numerical results are achieved using singular integral equations which are analogous to Green's boundary formula in potential theory. The analysis yields details of the stresses near the crack tip and clearly shows their three-dimensional character. Some results are also given to indicate the influence of thickness and Poisson's ratio on the stresses.
Résumé
On présente une analyse numérique des contraintes dans une éprouvette à trois dimensions en sollicitation dans le domaine élastique, éprouvette similaire à l'éprouvette de traction utilisée dans les études de mécanique de rupture.
Les résultats numériques sont obtenus en recourant à des équations à intégrales singulières, qui sont analogues à l'équation aux limites de Green dans la théorie du potentiel.
L'analyse conduit à fournir la distribution complète des contraintes au voisinage de l'éxtremité de la fissure et démontre clairement le caractère tridimensionnel de celle-ci.
L'influence de l'épaisseur et du module de Poisson sur les contraintes est également dégagée de certains résultats qui ont été obtenus.
Zusammenfassung
Es wird für eine dreidimensionale elastische Probe, ähnlich der kompakten Zugprobe für Bruchuntersuchungen, eine zahlenmässige Analyse der Spannungen dargelegt. Die numerischen Ergebnisse wurden über singulare Integralgleichungen analog den Greenschen Formeln in der Potentialtheorie ermittelt. Die Untersuchung ergibt Einzelheiten über die Spannungen in der Umgebung der Rißspitze und zeigt klar deren dreidimensionalen Charakter. Es werden auch einige Resultate mitgeteilt die den Einfluß der Dicke und des Poissonschen Moduls auf die Spannungen herausstellen.
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Cruse, T.A., Vanburen, W. Three-dimensional elastic stress analysis of a fracture specimen with an edge crack. Int J Fract 7, 1–15 (1971). https://doi.org/10.1007/BF00236479
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DOI: https://doi.org/10.1007/BF00236479