# Sohesive zone length influence on the critical load for a body with mode I crack

 1Kaminsky, AA1Selivanov, MF1Chornoivan, Yu.O1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv Dopov. Nac. akad. nauk Ukr. 2018, 8:36-44 https://doi.org/10.15407/dopovidi2018.08.036 Section: Mechanics Language: Ukrainian Abstract:  The limiting state of an elastic infinite body with mode I crack is studied, by using the fracture process zone model. A numerical method is proposed to solve fracture mechanics problems for various traction—separation laws. The validity of the proposed method application is proven by a comparison of the results for a simple linear softening relationship with the results by other researchers, which were obtained within different methods. The influence of the cohesive length on the critical load is investigated. An error of the neglect of the stress finiteness condition is determined for the statements, which are common for FEM solutions. Keywords: fracture, process zone, shape factors, stress finiteness condition, traction—separation law
References:
1. Barenblatt, G. I. (1962).The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech., 7, pp. 55-129. doi: https://doi.org/10.1016/S0065-2156(08)70121-2
2. Dugdale, D. S. (1960). Yielding of steel sheets containing slits. J. Mech. Phys. Solids., 8, pp. 100-108. doi: https://doi.org/10.1016/0022-5096(60)90013-2
3. Erdogan, F., Gupta, G.D. & Cook, T. S. (1973). Solution of singular integral equations. 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
4. Hillerborg, A., Modeer, M. & Petersson, P. E. (1 973). Analysis of crack formation and crack growth in con- crete by means of fracture mechanics and finite elements. Cem. Concr. Res., 6, pp. 773-781. doi: https://doi.org/10.1016/0008-8846(76)90007-7
5. Leonov, M. Ya. & Panasyuk, V. V. (1959). Growth of smallest cracks in solids. Prikl. Mekh., 5, pp. 391-401.
6. Stang, H., Olesen, J. F., Poulsen, P. N. & Dick-Nielsen, L. (2007). On the application of cohesive crack mo- deling in cementitious materials. Mater. Struct., 40, pp. 365-374. doi: https://doi.org/10.1617/s11527-006-9179-8
7. Turon, A., Davila, C. G., Camanho, P. P. & Costa , J. (2007). An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models. Eng. Fract. Mech., 74, pp. 1665-1682. doi: https://doi.org/10.1016/j.engfracmech.2006.08.025
8. Selivanov, M. F. (2014). Determination of the sa fe crack length and cohesive traction distribution using the model of a crack with prefacture zone. Dopov. Nac. akad. nauk Ukr., No. 11, pp. 58-64. doi: https://doi.org/10.15407/dopovidi2014.11.058 (in Ukrainian).
9. Selivanov, M. F. & Chornoivan, Yu. O. (2017). Comparison of the crack opening displacement determination algorithms for a cohesive crack. Dopov. Nac. akad. nauk Ukr., No. 7, pp. 29-36. (in Ukrainian) doi: https://doi.org/10.15407/dopovidi2017.07.029