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

Authors

  • M.F. Selivanov S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kiev

DOI:

https://doi.org/10.15407/dopovidi2019.05.034

Keywords:

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

Abstract

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.

Downloads

Download data is not yet available.

References

Selivanov, M. F. (2019). An edge crack with cohesive zone. Dopov. Nac. acad. nauk Ukr., 2019, No. 3: рр. 46–54 (in Ukrainian). doi: https://doi.org/10.15407/dopovidi2019.03.046

Muskhelishvili, N. I. (1953). Some basic problems of the mathematical theory of elasticity. Groningen: Noordhoff.

Savruk, M. P., Madenci, E. & Shkarayev, S. (1999). Int. J. Numer. Meth. Engng., 45, pp. 1457-1470. doi: https://doi.org/10.1002/(SICI)1097-0207(19990810)45:10<1457::AID-NME639>3.0.CO;2-P

Selivanov, M. F. & Chornoivan, Y. O. (2018). A semi-analytical solution method for problems of cohesive fracture and some of its applications. Int. J. Fract., 212, 1, pp. 113-121. doi: https://doi.org/10.1007/s10704-018-0295-6

Selivanov, M. F., Chornoivan, Y. O. & Kononchuk, O. P. (2018). Determination of crack opening displacement and critical load parameter within a cohesive zone model. Continuum Mech. Thermodyn. doi: https://doi.org/10.1007/s00161-018-0712-0

Downloads

Published

21.04.2024

How to Cite

Selivanov, M. (2024). Solving a problem on an edge crack with cohesive zone by the regularization of a singular integral equation . Reports of the National Academy of Sciences of Ukraine, (5), 34–43. https://doi.org/10.15407/dopovidi2019.05.034

Issue

No. 5 (2019): Reports of the National Academy of Sciences of Ukraine

Section

Mechanics

License

Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Most read articles by the same author(s)

1 2 > >>