Abstract
The paper considers a numerical study of the dynamic crack propagation in samples subjected to static loading. Experiments on dynamic crack propagation in samples of PMMA (polymethylmethacrylate) due to quasistatic stretching were simulated. The position of the crack tip and the current crack velocity were recorded in the experiments. The study showed that the ultimate crack velocity was significantly lower than the theoretically evaluated limiting value. An unstable behavior of the crack velocity was also found: the crack velocity oscillations were observed, with the amplitude of the oscillations increasing as the crack grows. In order to simulate the experiments, a numerical scheme was developed. The scheme is based on the finite element method and the structural-temporal fracture criterion. According to this criterion, the fracture scale level is set (namely, the minimum value of the crack advancement is introduced), and the characteristic fracture time is used – the incubation time parameter, which is considered to be a material parameter. This approach provides possibility to numerically obtain the discussed experimental results including considerable crack velocity oscillations.
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References
Sharon, E., Fineberg, J.: Confirming the continuum theory of dynamic brittle fracture for fast cracks. Nature 397, 333–335 (1999). https://doi.org/10.1038/16891
Zhuang, Z., O’Donoghue, P.E.: The recent development of analysis methodology for rapid crack propagation and arrest in gas pipelines. Int. J. Fract. 101, 269–290 (2000). https://doi.org/10.1023/A:10076143
Kanninen, M.F., O’Donoghue, P.: Research challenges arising from current and potential applications of dynamic fracture mechanics to the integrity of engineering structures. Int. J. Solids Struct. 32(17/18), 2423–2445 (1995). https://doi.org/10.1016/0020-7683(94)00275-2
Shen, W., Zhao, Y.-P.: Combined effect of pressure and shear stress on penny-shaped fluid-driven cracks. J. Appl. Mech. 85(3), 031003 (2017). https://doi.org/10.1115/1.4038719
Broberg, K.B.: On the speed of a Brittle Crack. J. Appl. Mech. 31, 546–547 (1964)
Kostrov, B.V.: Crack propagation at variable velocity. Int. J. Fract. 11(1), 47–56 (1975)
Freund, L.B.: Dynamic Fracture Mechanics. Cambridge University Press, Cambridge (1990). https://doi.org/10.1017/CBO9780511546761
Slepyan, L.I.: Principle of maximum energy dissipation rate in crack dynamics. J. Mech. Phys. Solids 41, 1019–1033 (1993). https://doi.org/10.1016/0022-5096(93)90053-I
Achenbach, J.D., Bazant, Z.P.: Elastodynamic near-tip stress and displacement fields for rapidly propagating crack in orthotropic media. J. Appl. Mech. 42, 183–189 (1975). https://doi.org/10.1115/1.3423513
Ravi-Chandar, K., Knauss, W.G.: An experimental investigation into dynamic fracture: III. On steady state crack propagation and crack brunching. Int. J. Fract. 26, 141–154 (1984). https://doi.org/10.1007/BF01157550
Fineberg, J., Gross, S.P., Marder, M., Swinney, H.L.: Instability in the propagation of fast cracks. Phys. Rev. B 45(10), 5146–5154 (1992). https://doi.org/10.1103/PhysRevB.45.5146
Kobayashi, T., Dally, J.W.: Relation between crack velocity and the stress intensity factor in birefringent polymers. Fast fracture and crack arrest. ASTM STP 627, 257–273 (1977). https://doi.org/10.1520/STP27392S
Kalthoff, J.F., Beinert, J., Winkler, S.: Measurements of dynamic stress intensity factors for fast running and arresting cracks in double-cantilever-beam specimens. ASTM STP 627, 161–176 (1977). https://doi.org/10.1520/STP27387S
Zehnder, A.T., Rosakis, A.J.: Dynamic fracture initiation and propagation in 4340 steel under impact loading. Int. J. Fract. 43, 271–285 (1990). https://doi.org/10.1007/BF00035087
Maigre, H., Rittel, D.: Dynamic fracture detection using the force-displacement reciprocity: application to the compact compression specimen. Int. J. Fract. 73, 67–79 (1995). https://doi.org/10.1007/BF00039852
Kalthoff, J.F., Shockey, D.A.: Instability of cracks under impulse loads. J. Appl. Phys. 48, 986–993 (1977). https://doi.org/10.1063/1.323720
Kalthoff, J.F.: Modes of dynamic shear failure in solids. Int. J. Fract. 101, 1–31 (2000). https://doi.org/10.1023/A:1007647800529
Dally, J.W., Fourney, W.L., Irwin, G.R.: On the uniqueness of the stress intensity factor – crack velocity relationship. Int. J. Fract. 27, 159–168 (1985). https://doi.org/10.1007/BF00017965
Kalthoff, J.F.: On Some Current Problems in Experimental Fracture Dynamics, Workshop on Dynamic Fracture. California Institute of Technology, pp. 11–25 (1983)
Irwin, G.: Analysis of stresses and strains near the end of a Crack traversing a plate. J. Appl. Mech. 24, 361–364 (1957)
Rosakis, A.J., Ravichandran, G.: Dynamic failure mechanics. J. Mech. Mater. Struct. 37, 331–348 (2000). https://doi.org/10.1016/S0020-7683(99)00097-9
Shockey, D.A., Erlich, D.C., Kathoff, J.F., Homma, H.: Short-pulse fracture mechanics. Eng. Fract. Mech. 23(1), 311–319 (1986). https://doi.org/10.1016/0013-7944(86)90195-5
Xu, X., Needleman, A.: Numerical simulations of dynamic crack growth along an interface. Int. J. Fract. 74, 289–324 (1995). https://doi.org/10.1007/BF00035845
Petrov, Y.V., Utkin, A.A.: Dependence of the dynamic strength on loading rate. Sov. Mater. Sci. 25(2), 153–156 (1989). https://doi.org/10.1007/BF00780499
Petrov, Y.V.: On “quantum” nature of dynamic failure of brittle media. Dokl. Akad. Nauk. SSSR 321(1), 66–68 (1991)
Bratov, V.: Incubation time fracture criterion for FEM simulations. Acta. Mech. Sin. 27(4), 541–549 (2011). https://doi.org/10.1007/s10409-011-0484-2
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This work was supported by the Russian Foundation for Basic Research (grants 19-31-60037 and 20-01-00291).
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Kazarinov, N., Petrov, Y., Benin, A. (2022). Modeling of Dynamic Crack Propagation Under Quasistatic Loading. In: Manakov, A., Edigarian, A. (eds) International Scientific Siberian Transport Forum TransSiberia - 2021. TransSiberia 2021. Lecture Notes in Networks and Systems, vol 402. Springer, Cham. https://doi.org/10.1007/978-3-030-96380-4_63
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