Comparison of two potential-based cohesive models to predict the critical load of a finite orthotropic plate with oblique crack

1Selivanov, MF
Protsan, VV
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2020, 7:32-42
https://doi.org/10.15407/dopovidi2020.07.032
Section: Mechanics
Language: Ukrainian
Abstract: 

The boundary-value problem of the theory of elasticity for a finite orthotropic plate with an oblique edge crack is considered. A tensile load is applied to a cracked body, and the crack is located along the orthotropy axis, which is not aligned with the loading direction. A cohesive zone model for the mixed fracture mode is used to study crack growth mechanisms. The traction— separation laws are represented in the potential form. In this case, normal and tangential tractions are given by partial derivatives of the dissipation potential with respect to the corresponding separations. Two cohesive laws of different mixity forms are constructed basing on the pure-mode fracture models (normal separation and transverse shear) with no mode mixity parameters. An algorithm for the determination of critical state parameters of a crack using the finite-element method is constructed. An example of the calculation of critical load parameters and the corresponding stress field for the two cohesive laws of mixed-mode fracture is given. The impact of the mode-mixity form on the critical state parameters is studied. For the investigated range of orthotropic parameters, it is established that the mode-mixity of two cohesive laws well-known in the literature gives an error in determining the critical load to be less than five percent. This discrepancy decreases simultane ous ly with the cohesive length.

Keywords: crack in orthotropic body, mixed-mode fracture, potential-based traction—separation law, slanted edge crack
References: 

1. Dugdale, D. S. (1960). Yielding of steel sheets containing slits. J. Mech. Phys. Solids, 8, pp. 100-104, https://doi.org/10.1016/0022-5096(60)90013-2
2. Barenblatt, G. I. (1962). The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech., 7, pp. 55-129. https://doi.org/10.1016/S0065-2156(08)70121-2
3. Hillerborg, A., Modeer, M. & Petersson, P. E. (1976). Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res., 6, pp. 773-81, https://doi.org/10.1016/0008-8846(76)90007-7
4. Selivanov, M. F. & Chornoivan, Y. O. (2018). A semi-analytical solution method for problems of cohesive fracture and some of its applications. Int. J. Fract., 212, No. 1, pp. 113-121. https://doi.org/10.1007/s10704-018-0295-6
5. Needleman, A. (1987). A continuum model for void nucleation by inclusion debonding. J. Appl. Mech., 54, pp. 525-31. https://doi.org/10.1115/1.3173064
6. Selivanov, M. F. (2019). An edge crack with cohesive zone. Dopov. Nac. akad. nauk Ukr., No. 3, pp. 46-54 (in Ukrainian). https://doi.org/10.15407/dopovidi2019.05.046
7. Selivanov, M. F. (2019). Solving a problem on an edge crack with cohesive zone by the regularization of a singular integral equation. Dopov. Nac. akad. nauk Ukr., No. 5, pp. 34-43 (in Ukrainian). https://doi.org/10.15407/dopovidi2019.05.034
8. Selivanov, M. F. (2019). An edge crack with cohesive zone in orthotropic body. Dopov. Nac. akad. nauk Ukr., No. 6, pp. 25-34 (in Ukrainian). https://doi.org/10.15407/dopovidi2019.06.025
9. Selivanov, M. F. (2019). Subcritical and critical states of a crack with failure zones. Appl. Math. Model., 72, pp. 104-128. https://doi.org/10.1016/j.apm.2019.03.013
10. Selivanov, M. F. & Protsan, V. V. (2020). The impact of neglecting the smooth crack closure condition when determining the critical load. Dopov. Nac. akad. nauk Ukr., No. 3, pp. 28-35 (in Ukrainian). https://doi.org/10.15407/dopovidi2020.03.028
11. Park, K., Paulino, G. H. & Roesler, J. R. (2009). A unified potential-based cohesive model of mixed-mode fracture. J. Mech. Phys. Solids, 57, No. 6, pp. 891-908. https://doi.org/10.1016/j.jmps.2008.10.003
12. Park, K. & Paulino, G. H. (2013). Cohesive zone models: A critical review of traction-separation relationships across fracture surfaces. Appl. Mech. Reviews, 64, No. 6, 060802—060802—20. https://doi.org/10.1115/1.4023110
13. Selivanov, M. F. & Chornoivan, Y. O. (2019). Application of the complex cohesive zone model to the edge mixed-mode crack problem for orthotropic media. Dopov. Nac. akad. nauk Ukr., No. 11, pp. 31-40. https://doi.org/10.15407/dopovidi2019.11.031