PSI - Issue 79

Mikhail Perelmuter et al. / Procedia Structural Integrity 79 (2026) 379–385

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corresponding to condition (7) simultaneously decreases. The smallest critical external stress is realized at E 1 / E 2 = 0 . 2 for a relatively soft materials. For relative crack length ℓ/ H = 1 and E 1 / E 2 = 0 . 2, we have σ cr /σ f = 0 . 356.With a 10-fold increase in crack length, the critical external stress decreases by approximately 3 times and this is true for all three dependencies in the Fig. 6.

5. Closing

The main features of the nonlocal fracture criterion (7) and (8) are the accounting of energy consumed by bonds during cracks growth and the analysis on this ground of non self-similar crack growth. This criterion implemented in the frames of the bridged crack model with assumption of singularity at the crack tip. The criterion consists of two conditions and the appropriate equations are defined by several physical-mechanical parameters or functions, in dependence on bonds deformation law which can be defined experimentally or obtained staring from the micromechanical modelling. In the case of linear-elastic bonds the criterion contents only two exper imentally defined parameters and can be regarded as the two-parametric fracture criterion. The nonlocal criterion of bridged cracks growth with energy and kinematic conditions of fracture allows to dedine the modes of subcritical and quasi-static cracks growth, as well as to estimate the limiting size of the crack bridged zone, the critical external load, and also fracture toughness of materials. Acknowledgements The work was done within the framework of Russian State Assignment, the project code FFGN-2024-0001. References Cherepanov, G.P., 1979. Mechanics of Brittle Fracture. McGraw Hill. Cox, B., Marshall, D., 1994. Concepts for bridged cracks in fracture and fatigue. Acta Metallurgica et Materialia 42, 341 – 363. doi: 10.1016/ 0956-7151(94)90492-8 . Goldstein, R., Perelmuter, M., 1999. Modeling of bonding at an interface crack. International Journal of Fracture 99, 53–79. doi: 10.1023/A: 1018382321949 . Grekov, M., Morozov, N., 2006. Equilibrium cracks in composites reinforced with unidirectional fibres. Journal of Applied Mathematics and Mechanics 70, 945–955. doi: 10.1016/j.jappmathmech.2007.01.011 . Hua, W., Li, J., Zhu, Z., Li, A., Huang, J., Gan, Z., Dong, S., 2023. A review of mixed mode I-II fracture criteria and their applications in brittle or quasi-brittle fracture analysis. Theoretical and Applied Fracture Mechanics 124, 103741. doi: 10.1016/j.tafmec.2022.103741 . Morozov, N., Paukshto, M., Ponikarov, N., 1997. On the problem of equilibrium length of a bridged crack. Journal of Applied Mechanics 64, 427–430. doi: 10.1115/1.2787327 . Perelmuter, M., 2007. A criterion for the growth of cracks with bonds in the end zone. Journal of Appl. Math. and Mech. (PMM) 71, 137 – 153. doi: 10.1016/j.jappmathmech.2007.03.002 . Perelmuter, M., 2011. An interface crack with non-linear bonds in a bridged zone. Journal of Applied Mathematics and Mechanics 75, 106 – 118. doi: 10.1016/j.jappmathmech.2011.04.016 . Perelmuter, M., 2013. Boundary element analysis of structures with bridged interfacial cracks. Computational Mechanics 51, 523–534. doi: 10. 1007/s00466-012-0817-4 . Perelmuter, M., 2015. Nonlocal criterion of bridged cracks growth: analytical analysis. Acta Mechanica 226, 397–418. doi: 10.1007/ s00707-014-1170-9 . Rose, L.R.F., 1987. Crack reinforcement by distributed springs. Journal of the Mechanics and Physics of Solids 35, 383 – 405. doi: 10.1016/ 0022-5096(87)90044-5 . Stang, H., Olesen, J.F., Poulsen, P.N., Dick-Nielsen, L., 2007. On the application of cohesive crack modeling in cementitious materials. Materials and Structures 40, 365–374. doi: 10.1617/s11527-006-9179-8 . Sun, C., Jin, Z.H., 2006. Modeling of composite fracture using cohesive zone and bridging models. Composites Science and Technology 66, 1297 – 1302. doi: 10.1016/j.compscitech.2005.10.013 . Yosibash, Z., 2004. Failure criteria for brittle elastic materials. International Journal of Fracture 125, 307 – 333. doi: 10.1023/B:FRAC. 0000022244.31825.3b .