Modelling of cracking in circular disk loaded by concentrated forces

V. M. Mirsalimov ; N. M. Kalantarly

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 1, pp. 90-97.

Résumé

An isotropic disk of radius $R$, loaded on the contour by two concentrated forces $P$, apllied to the points $z_1=R$ and $z_2=-R$, is considered. A model of cracking in a circular disk, based on consideration of fracture process zone, is proposed. It is assumed that the fracture process zone is a finite length layer, containing material with partially broken bonds between individual structural elements. Equations for determination of the external load critical value at which the crack is observed are obtained.

Bibliographie

[1] Bolotin V. V., “Mechanics of the initiation and initial development of fatigue cracks”, Soviet materials science, 22:1 (1986), 14–19 | DOI

[2] Mirsalimov V. M., “Initiation of defects such as a crack in the bush of contact pair”, Matem. Mod., 17:2 (2005), 35–45 (in Russian)

[3] Mirsalimov V. M., “The solution of a problem in contact fracture mechanics on the nucleation and development of a bridged crack in the hub of a friction pair”, J. Appl. Math. Mech., 71:1 (2007), 132–151 | DOI

[4] Mir-Salimzade M. V., “Generation of Cracks in a Perforated Reinforced Plate”, J. Applied Mechanics and Technical Physics, 49:6 (2008), 1030–1039

[5] Vagari A. P., Mirsalimov V. M., “Nucleation of Cracks in a Perforated Heat-Releasing Material with Temperature-Dependent Elastic Properties”, J. Applied Mechanics and Technical Physics, 2012, no. 4, 138–148

[6] Zolgharnein E., Mirsalimov V. M., “Nucleation of a Crack under Inner Compression of Cylindrical Bodies”, Acta Polytechnica Hungarica, 9:2 (2012), 169–183

[7] Akhmedova M. V., “Cracks nucleation in thin plate, weakened by the periodic system of the curvilinear holes”, Vestnik chuvashskogo gosudarstvennogo pedagogicheskogo universiteta im. I. Ia. Iakovleva. Ser. Mekhanika predel'nogo sostoianiia, 2013, no. 4(18), 3–14

[8] Iskenderov R. A., “The crack nucleation in the isotropic plate, weakened by a periodical system of circular holes under transverse bending”, Structural Mechanics of Enginiring Constructions and Buildings, 2013, no. 3, 18–28

[9] Mirsalimov V. M., Hasanov Sh. G., “Modeling of crack nucleation in covering on an elastic base”, Intern. J. Damage Mech., 23:3 (2014), 430–450 | DOI

[10] Fundamental and applied problems of engineering and technology, 2014, no. 1(303), 24–30 (in Russian)

[11] Mohammed I., Liechti K. M., “Cohesive zone modeling of crack nucleation at bimaterial corners”, J. Mech. Phys. Solids, 48:4 (2000), 735–764 | DOI

[12] Yang B., “Examination of free-edge crack nucleation around an open hole in composite laminates”, Intern. J. Fracture, 115:2 (2002), 173–191 | DOI

[13] Yang Q., Cox B., “Cohesive models for damage evolution in laminated composites”, Intern. J. Fracture, 133:2 (2005), 107–137 | DOI

[14] Lipperman F., Ryvkin M., Fuchs M. B., “Nucleation of cracks in two-dimensional periodic cellular materials”, Computational Mechanics, 39:2 (2007), 127–139 | DOI

[15] Gutkin M. Yu., Ovid'ko I. A., Skiba N. V., “Effect of inclusions on heterogeneous crack nucleation in nanocomposites”, Physics of the Solid State, 49:2 (2007), 261–266 | DOI

[16] Chen Z., Butcher C., “Estimation of the Stress State Within Particles and Inclusions and a Nucleation Model for Particle Cracking”, Micromechanics Modelling of Ductile Fracture: Solid Mechanics and Its Applications, 195 (2013), 223–243 | DOI

[17] Hasanov F. F., “Nucleation of cracks in isotropic medium with periodic system of the circular holes filled with rigid inclusions, at longitudinal shear”, Structural Mechanics of Enginiring Constructions and Buildings, 2014, no. 3, 44–50 (in Russian)

[18] Hasanov F. F., “Nucleation of the crack in a composite, reinforced unidirectional orthotropous fibres at longitudinal shear”, Mechanics of machines, mechanisms and materials, 2014, no. 2(27), 45–50 (in Russian)

[19] Muskhelishvili N. I., Some Basic Problems of Mathematical Theory of Elasticity, Nauka, M., 1966, 707 pp. (in Russian)

[20] Mirsalimov V. M., Multidimensional elasto-plastic problems, Nauka, M., 1987, 256 pp. (in Russian)

[21] Il'yushin A. A., Plasticity, GITTL, M.–L., 1948, 376 pp. (in Russian)