An edge crack with cohesive zone
DOI:
https://doi.org/10.15407/dopovidi2019.03.046Keywords:
cohesive zone model, condition of smooth crack closure, edge crack, integral equation with generalized Cauchy kernelAbstract
The present paper is focused on an edge crack in a halfinfinite plane under tension by uniform remote stresses normal to the crack plane. An iterative procedure is built to solve the problem in the frame of the cohesive zone model with a nonuniform traction–separation law. The procedure allows one to account for the condition of smooth crack closure. At each iteration, the singular integral equation with generalized Cauchy kernel is solved by the collocation method without regularization. The numerical example is built meeting the limiting equilibrium condition for the power traction–separation law with a hardening segment.
Downloads
References
Ferdjani, H. & Abdelmoula, R. (2017). Propagation of a Dugdale crack at the edge of a half plane.Continuum Mech. Thermodyn. doi: https://doi.org/10.1007/s0016101705946
Petroski, H. (1979). Dugdale plastic zone sizes for edge cracks. Int. J. Fract,15,pp. 217-230.
Bowie, O. & Tracy, P. (1978). On the solution of the Dugdale model. Eng. Fract. Mech., 10, pp. 249-256. doi: https://doi.org/10.1016/0013-7944(78)90008-5
Tada, H., Paris, P. C. & Irwin, G. (1973). The Stress Analysis of Cracks Handbook. Hellertown, Pennsylvania: Del Research Corporation.
Howar, I. & Otter, N. J. (1975). On the elastic–plastic deformation of a sheet containing an edge crack. J. Mec. Phys. Solids, 23, pp. 139-149. doi: https://doi.org/10.1016/0022-5096(75)90023-X
Wang, S. & Dempsey, J. P. (2011). A cohesive edge crack. Eng. Fract. Mech., 78, pp. 1353-1373. doi: https://doi.org/10.1016/j.engfracmech.2011.02.018
Selivanov, M. F. (2014). Determination of the safe crack length and cohesive tractiondistribution using the model of a crack with prefacture zone. Dopov. Nac. acad.nauk Ukr., No. 11, pp. 58-65 (in Ukrainian).
Selivanov, M. F. & Chornoivan, Yu. A.(2018). A semianalytical solution method for problems of cohesive fracture and some of its applications. Int. J. Fract., 212, pp. 113–121. doi: https://doi.org/10.1007/s10704-018-0295-6
Broberg, K. B.(1999). Cracks and fracture. London: Academic Press.
Erdogan, F., Gupta, G. D. & Cook, T. S. (1973). Numerical solution of singular integral equations. In Sih, G.C. (Ed.). Methods of analysis and solutions of crack problems (pp. 368-425). Mechanics of Fracture, Vol. 1. Dordrecht: Springer. doi: https://doi.org/10.1007/978-94-017-2260-5_7
Savruk, M. P., Madenci, E. & Shkarayev, S. (1999). Singular integral equations of the second kind with generalized Cauchytype kernels and variable coefficients. 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, Yu. A. (2017). Comparison of the crack opening displacement determination algorithms for a cohesive crack.Dopov. Nac. acad.nauk Ukr., No. 7, pp. 29-36 (in Ukrainian). doi: https://doi.org/10.15407/dopovidi2017.07.029
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
