Abstract
The bending of a rectangular, elastic plate containing a central, through crack is analyzed. Results are obtained numerically via a finite element analysis based on the assumptions of Mindlin sixth order plate theory. A special feature of the analysis is the modeling of crack face interference, or closure, at the compression surface of the plate. Results are presented for two cases, one that includes the effects of closure and one that does not, and comparisons are made with prior results based on Kirchhoff theory. It is shown that proper modeling of the boundary conditions is essential for obtaining accurate, credible results and that the effects of closure are significant and must be included when demanded by the actual physical situation.
Résumé
On analyse la flexion d'une plaque rectangulaire élastique comportant une fissure traversante centrale. Les résultats sont obtenus de façon numérique au moyen d'une analyse par élément fini basée sur les hypothèses de Mindlin dans la théorie du sixième ordre des plaques. Une caractéristique particulière de l'analyse est la formulation mathématique de l'interférence ou de la fermeture des faces de la fissure sur les surfaces en compression de la plaque. On présente les résultats pour deux cas, l'un comportant les effets de la fermeture et l'autre ne les comportant pas; des comparaisons sont établies avec les résultats antérieurs basés sur la théorie de Kirchhoff. On montre qu'une modélisation appropriée des conditions aux limites est essentielle pour obtenir des résultats fiables et crédibles, et que les effets de la fermeture sont significatifs; ces effets doivent être pris en considération lorsque l'exigent des situations physiques particulières.
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Heming, F.S. Sixth order analysis of crack closure in bending of an elastic plate. Int J Fract 16, 289–304 (1980). https://doi.org/10.1007/BF00018233
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DOI: https://doi.org/10.1007/BF00018233