Contact of the faces of the interfacial crack outcoming from angular point of the broken interface
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 2
Abstract
The model of the interfacial crack outcoming from the angular point of the broken interface of two different homogeneous isotropic materials has been developed. The model assumes the existence of a near the tip of the crack small-scale contact region of the faces interacting according to the law of dry friction. Owing to the small sizes of the contact zone the condition on the infinity as a demand of the possibility of sewing together the sought solution with the asymptotic solution near the crack tip of the analogous problem about an interfacial crack without contact of faces was formulated. The solution of the suitable static boundary-value problem of the theory of elasticity under the conditions of plane deformation is found by using the Wiener – Hopf method. The equations for the determination of the length of the contact zone and stress singularity index near the crack tip and an expression for the contact stress were obtained. The numerical analysis of the dependence of the contact zone length and stress singularity index on the external load configuration, friction and elastic characteristics of the joined materials was made. The fact that the length of the contact zone decreases impetuously under the normal component of the load increases or the moduli of elasticity of the joined materials become closer was discovered. At the same time, its dependence on the friction coefficient is less pronounced: with the enhancement of the friction of the faces, the faces eliminates the physically uncorrected spatial oscillation of the displacements predicted by the classic theory of the interfacial cracks with the exception of a narrow enough interval of the interfacial angle.
Authors and Affiliations
M. V. Dudyk, Yu. V. Reshitnyk, V. M. Fen’kiv
Keywords
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