Title | An edge crack with cohesive zone |
Publication Type | Journal Article |
Year of Publication | 2019 |
Authors | Selivanov, MF |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2019.03.046 |
Issue | 3 |
Section | Mechanics |
Pagination | 46-54 |
Date Published | 03/2019 |
Language | Ukrainian |
Abstract | 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. |
Keywords | cohesive zone model, condition of smooth crack closure, edge crack, integral equation with generalized Cauchy kernel |
1. 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
2. Petroski, H. (1979). Dugdale plastic zone sizes for edge cracks. Int. J. Fract,15,pp. 217-230.
3. 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
4. Tada, H., Paris, P. C. & Irwin, G. (1973). The Stress Analysis of Cracks Handbook. Hellertown, Pennsylvania: Del Research Corporation.
5. 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
6. 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
7. 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).
8. 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
9. Broberg, K. B.(1999). Cracks and fracture. London: Academic Press.
10. 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
11. 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
12. 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