Model of the structure of the near tip area of interface crack in a piece-homogeneous elastic-plastic body

Article type: Research Article

Authors: Dudyk, M.V.^a; | Kipnis, L.A.^a

Affiliations: [a] Department of Physics, Mathematics and Informatics, Uman State Pedagogical University, Uman, Ukraine

Correspondence: [*] Corresponding author: Tel.: +38 0474430775; Fax: +38 04744 34582; E-mail: dudik_m@hotmail.com

Abstract: The model of interface crack, which assumes the existence near its tip the area of the contact of faces interactive by the law of dry friction, and the plastic zone with the small scale destruction zone in the part adjoining the crack tip with the high level of tensile and shear deformations is extended in the article. Modelling a plastic zone under the plane strain conditions by the line of displacement rupture inclined to the interface and using the Wiener-Hopf method the equations for calculating the length and orientation of the plastic zone, the sizes of the contact faces area and of the destruction zone, the stress singularity indexes near the crack tip under the conditions of the prevailing shear or tensile loading were obtained. It is established that due to the formation of a lateral plastic zone near the crack tip at the prevailing tensile loading, the length of the contact area depends not only on the configuration but also on the module of loading. Herewith its value appears to be on a few more orders than if a plastic zone was absent. The change of the stress singularity index at approach to the crack tip is revealed.

Keywords: Interface crack, contact, friction, plastic zone, destruction zone, Wiener-Hopf method

DOI: 10.3233/SFC-180211

Journal: Strength, Fracture and Complexity, vol. 11, no. 1, pp. 31-50, 2018