Abstract
The singular plastic field at the tip of a notch, in anti-plane shear, is analyzed within the framework of small strain plasticity. The faces of the notch are either both free or one free and one clamped. Material behaviour is governed by the deformation theory of plasticity with a pure power hardening characteristic. Explicit relations are given for the level of stress singularity, and a detailed numerical study is presented for the circumferential profile of the plastic zone. The results indicate a stronger singularity for the clamped-free notch, with a shift of the singular area in the direction of the clamped face.
Résumé
Dans le cadre d'une étude de la plasticité à faible échelle, on analyse le champ plastique singulier règnant à la pointe d'une entaille soumise à cisaillement anti-planaire. Les faces de l'entaille sont soit toutes deux libres, soit l'une libre et l'autre fixée. Le comportement du matériau est régi par la théorie de la déformation en plasticité, avec une caractéristique d'écrouissage selon loi quadratique simple. On fournit des relations explicites quant au niveau de singularité des contraintes, et on présente une étude numérique détaillée relative au profil circonférentiel de la zone de plastification. Les résultats indiquent une singularité plus sévère pour une entaille à faces libres, et un glissement de la zone de singularitié de la face fixée.
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References
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This paper is based in part on the first author's M.Sc. research thesis [1].
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Ore, E., Durban, D. Boundary effects at a notch tip in anti-plane shear. Int J Fract 38, 15–24 (1988). https://doi.org/10.1007/BF00034273
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DOI: https://doi.org/10.1007/BF00034273