An edge crack with cohesive zone in the orthotropic body

1Selivanov, MF
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 6:25-34
https://doi.org/10.15407/dopovidi2019.06.025
Section: Mechanics
Language: Ukrainian
Abstract: 

The integral equations for the problem on displacements of an edge crack in the orthotropic body and a technique of their solving are presented. The technique is exemplified by finding the stress intensity factor, which is compared with the results known from the literature. Fit rational functions are built for the obtained dependence of the stress intensity factor on the parameter of orthotropy. The problem on an edge crack in an orthotropic half-plane is also solved in the frame of a cohesive zone model with non-uniform traction—separation law.

Keywords: cohesive zone model, crack in the orthotropic body, edge crack, influence of orthotropy, stress intensity factor
References: 

1. Sweeney, J. (1988). The stress intensity for an edge crack in a semi-infinite orthotropic body. Int. J. Fract., 37, pp. 233-241. doi: https://doi.org/10.1007/BF00045865
2. Suo, Z. (1990). Delamination specimens for orthotopic materials. J. Appl. Mech., 57, pp. 627-634. doi: https://doi.org/10.1115/1.2897068
3. Broberg, K. B. (1999). Cracks and fracture, London: Academic Press.
4. Kaminsky, A. A., Selivanov, M. F. & Chornoivan, Yu. O. (2018). Cohesive zone length influence on the critical load for a body with mode I crack. Dopov. Nac. akad. nauk Ukr., No. 8, pp. 36-44 (in Ukrainian). doi: https://doi.org/10.15407/dopovidi2018.08.036
5. Selivanov, M. F. (2019). An edge crack with cohesive zone. Dopov. Nac. akad. nauk Ukr., No. 3, pp. 46-54 (in Ukrainian). doi: https://doi.org/10.15407/dopovidi2019.03.046
6. Selivanov, M.F. & Chornoivan, Yu. O. (2018). The cohesive zone model with a non-uniform traction-se paration law for a system of several collinear cracks Dopov. Nac. akad. nauk Ukr., No. 9, pp. 35-41 (in Ukrainian). doi: https://doi.org/10.15407/dopovidi2018.09.035
7. Erdogan, F., Gupta, G.D. & Cook, T. S. (1973). Solution of singular integral equations. In: Sih, G.C. (ed.), Methods of analysis and solutions of crack problems. Mechanics of Fracture, 1, pp. 368-425. doi: https://doi.org/10.1007/978-94-017-2260-5_7
8. Savruk, M. P., Madenci, E. & Shkarayev, S. (1999). Singular integral equations of the second kind with ge neralized Cauchy-type kernels and variable coefficients. Int. J. Numer. Meth. Engng., 1999, 45, pp. 1457-470. doi: https://doi.org/10.1002/(SICI)1097-0207(19990810)45:10<1457::AID-NME639>3.0.CO;2-P
9. Selivanov, M. F. Quasi-static problems of fracture mechanics for elastic and viscoelastic bodies in the framework of cohesive zone models: dr. sci. in physics and mathematics. Kyiv, 2017. 322 p. (in Ukrainian)
10. Gerstle, F. P. (1991). Composites. In: Encyclopedia of Polymer Science and Engineering, Wiley, New York.
11. Zweben, C. (2015). Composite materials. In: Kutz M. (ed.), Mechanical Engineers’ Handbook, Fourth Edition, John Wiley & Sons, Inc. doi: https://doi.org/10.1002/9781118985960.meh110