The cohesive zone model with a non-uniform traction-separation law for a system of several collinear cracks

1Selivanov, MF
1Chornoivan, Yu.O
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 9:35-41
Section: Mechanics
Language: Ukrainian

The cohesive zone models are widely used for assessments of the critical loading level on structures. Here, an infinite plate with mode I collinear cracks is studied under a uniform tension applied at infinity. A proposed technique is applied to solve the problem basing on the cohesive crack model. The solution for the crack opening is found for a non-uniform traction-separation law with regard for the condition of smooth closure of the crack lips. Numerical results are presented for several values of the traction-separation law shape parameter. Some illustrations are given for the dependence of the crack opening on the external loading. It is found that its critical level is almost independent of the shape parameter.

Keywords: cohesive zone model, collinear cracks, finite stress condition, fracture, shape parameters, traction—separation law
  1. Stang, H., Olesen, J.F., Poulsen, P.N. & Dick–Nielsen, L. (2007). On the application of cohesive crack modeling in cementitious materials. Mater. Struct., 40, pp. 365-374. doi:
  2. Chang, D. & Kotousov, A. (2002). A strip yield model for two collinear cracks in plates of arbitrary thickness. Int. J. Fract., 176, pp. 39-47. doi:
  3. Feng, X. Q. & Gross, D. (2000). On the coalescence of collinear cracks in quasi-brittle materials. Eng. Fract. Mech., 65, pp. 511-524. doi:
  4. Kaminsky, A. A., Selivanov, M. F. & Chornoivan, Yu. O. (2011). Study of a displacement of crack edges for two collinear cracks of equal length. Dopov. Nac. akad. nauk Ukr., No. 11, pp. 51-60 (in Ukrainian).
  5. Bhargava, R. R. & Jangid, K. (2014). Strip-coalesced interior zone model for two unequal collinear cracks weakening piezoelectric media. Appl. Math Mech., 35 (10), pp. 1249-1260. doi:
  6. Theocaris, P. S. (1983). Dugdale models for two collinear unequal cracks. Eng. Fract. Mech., 18 (3), pp. 545-559. doi:
  7. Kaminsky, A. A., Selivanov, M. F. & Chornoivan, Yu. O. (2013). Determination of displacement of the faces of two collinear cracks of different lengths within the framework of the Leonov-Panasyuk model. J. Math. Sci., 190 (14), pp. 1-16. doi:
  8. Kaminsky, A. A., Selivanov, M. F. & Chornoivan, Y. O. (2013). Determining of three collinear cracks opening displacement using the process zone model. Int. J. Solids Struct., 50 (19), pp. 2929-2942. doi:
  9. Kaminsky, A. A., Selivanov, M. F. & Chornoivan, Yu. O. (2018). Cohesive zone length influence on the critical load for mode i crack. Dopov. Nac. akad. nauk Ukr., No. 8, pp. 36-44 (in Ukrainian). doi:
  10. Erdogan, F., Gupta, G. D. & Cook, T. S. (1973). Solution of singular integral equations. Methods of analysis and solutions of crack problems. Mechanics of Fracture, 1, pp. 368-425. doi:
  11. Gross, D. & Heimer, St. (1993). Crack closure and crack path prediction for curved cracks under thermal load. Eng. Fract. Mech., 46, pp. 633-640. doi:
  12. 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: