Solving a problem on an edge crack with cohesive zone by the regularization of a singular integral equation

1Selivanov, MF
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 5:34-43
Section: Mechanics
Language: Ukrainian

An edge mode I crack in a semiinfinite plane is considered. The fracture zone at the front of the crack is modeled with the use of the cohesive zone model, which is based on the non-uniform traction-separation law. The singular integral equation with a generalized Cauchy kernel is solved by the collocation method after the regularization, using the method allowing us to consider the coupling of traction and separation. The constructed algorithm for solving the problem also includes the condition of smooth crack closure. The numeric example is built, by meeting the limiting equilibrium condition for the power traction–separation law with a hardening segment. It is established that the regularization in solving the problem has no effect on the value of critical loading.

Keywords: cohesive zone model, condition of smooth crack closure, edge crack, integral equation with a generalized Cauchy kernel

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