About the cohesive pre-fracture zone at the tip of a crack outcoming from the corner point of the broken interface of materials

1Kaminsky, AA
2Dudyk, MV
Reshitnyk, YV
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
2Pavlo Tychyna Uman State Pedagogical University
Dopov. Nac. akad. nauk Ukr. 2020, 4:34-42
https://doi.org/10.15407/dopovidi2020.04.034
Section: Mechanics
Language: Ukrainian
Abstract: 

Within the framework of the cohesion model, the solution of the problem of calculating the parameters of the pre-fracture zone in a joining material at the end of an interfacial crack propagating from the corner point of the broken interface of the two different homogeneous isotropic materials is obtained. The zone is modeled by the discontinuity line of displacements, on which the stresses meet the Mises—Hill strength criterion. By the Mellin integral transformation, the problem is reduced to the Wiener—Hopf vector equation. An approximate method of solution of the Wiener—Hopf vector equation is proposed. The method is based on the representation of the matrix coefficient of the equation in the form of a sum of two matrices, one of which allows for an exact factorization, while the other one is considered as a small perturbation to the first one. The solution of the equation is searched in the form of expansions by the degrees of a matrix-perturbation. From the found solution, the equations for calculating the pre-fracture zone length and the phase angle of stress in the zone, and the expression for the crack opening at the tip are obtained.

Keywords: cohesive model, interfacial crack, pre-fracture zone
References: 

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