On determining the elastic limit of an adhesive layer in the opening mode of loading

V. E. Bogacheva   ; V. V. Glagolev   ; L. V. Glagolev   ; A. A. Markin

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 83 (2023), pp. 59-73

Résumé

In this paper, the problem of determining the limit of elastic strain of an extremely thin adhesive layer in the opening mode of loading (mode I) is considered. The presence of a nonzero component of the stress tensor along the layer axis is taken into account. The Tresca – Saint-Venant criterion is used as a condition for the transition to a plastic strain state. On the basis of the general variational problem formulation with account for restrictions on the displacement field, the problem is formulated in a differential form. A simplified problem formulation is solved analytically. According to the solution, the stress state in the layer does not depend on its thickness and is specified by the plane problem type. In the plane strain state, the cleavage stress significantly exceeds that in the plane stress state. In this case, Poisson's ratio of the adhesive significantly affects the ratio of cleavage stresses. For a certain value of Poisson's ratio, the Irwin empirical correction is obtained. It is shown that for the transition to a plastic state in the case of plane strain, larger external load is required in contrast to the plane stress state. Due to the finiteness of the stress state in the adhesive layer, as the relative thickness of the layer tends to zero, the plasticity occurs in the layer at an arbitrary small external load.

Détail

Keywords: elasticity, extremely thin layer, opening mode of loading.
Mots-clés : Tresca–Saint-Venant criterion

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