Abstract
Utilizing the form of a general 3D solution, the author investigates analytically the stress field in the neighborhood of the intersection of a cylindrical inclusion and a free surface. The inclusion is assumed to be of a homogeneous and isotropic material and is to be embedded in an isotropic plate of an arbitrary thickness. The stress field is induced by a uniform tension applied on the plate at points far remote from the inclusion (see Fig. 1).
The displacement and stress fields are derived explicitly and a stress singularity is shown to exist for the case when the inclusion is stiffer than the plate material. Moreover, the stress singularity is shown to be a function of the respective ratios of the shear moduli and Poisson's.
The special case of G 2→0, G 2=G 1 and G 2→∞ are also investigated.
Résumé
En utilisant la forme d'une solution générale à trois dimensions, l'auteur analyse le champ de contraintes au voisinage de l'intersection d'une inclusion cylindrique et d'une surface libre. On suppose que l'inclusion est constituée d'une matériau homogène et isotrope, et qu'elle est insérée dans une plaque isotrope d'épaisseur arbitraire. Le champ de contraintes et dû à une tension uniforme appliquée en des points suffisamment éloignés de l'inclusion.
On exprime de manière explicite les champs de déplacements et de contraintes, et on montre qu'il existe une singularité de la contrainte dans le cas où l'inclusion est dans un matériau plus rigide que celui de la plaque. En outre, on montre que la singularité de la contrainte est fonction des rapport respectifs des modules de cisaillement et de Poisson.
On étudie également les cas spéciaux G 2→0, G 2=G 1 et G 1→∞.
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Folias, E.S. On the stress singularities at the intersection of a cylindrical inclusion with the free surface of a plate. Int J Fract 39, 25–34 (1989). https://doi.org/10.1007/BF00047437
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DOI: https://doi.org/10.1007/BF00047437