Numerical study of the crack growth direction within a quasi-brittle material in a gradient temperature field

A. V. Zabolotskiy   ; A. I. Dmitriev

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 88 (2024), pp. 94-110

Résumé

The elliptical crack growth in a quasi-brittle material located in a gradient field of temperature next to the melting temperature for the thermodynamic phases of the material is studied. The elastic properties of the material are assumed to have an obvious dependence on temperature. This is typical for materials located close to the melting point. To determine the direction of crack growth, a gradient strain criterion is introduced, which assumes crack growth from the point of maximum elastic strain of the material toward its minimum. Depending on the orientation of the crack axis relative to the direction of the temperature gradient, the crack retardation, the change of the crack growth direction, or the appearance of secondary lateral cracks in the vicinity of the main crack tip are possible. The calculated results and the admissibility of applying the introduced criterion have been successfully validated by an experiment with thermal fracture of freshwater ice blocks. As a result, the phenomena predicted by finite element calculations have also been discovered experimentally.

Détail

Keywords: brittle fracture, melting temperature, crack trajectory calculation, premelting.

Bibliographie

[1] Sobolev R.N, “The temperature range of melting of crystalline material”, Doklady Earth Sciences, 473:1 (2017), 367–370 | DOI | DOI

[2] Gusarov V.V., Suvorov S.A., “Melting temperature of local-equilibrium surface phases in polycrystalline systems based on one phase”, Zhurnal prikladnoy khimii – Journal of Applied Chemistry of the USSR, 63:8 (1990), 1689–1694

[3] Rolov B.N., Yurkevich V.E., Physics of scouring phase transformations, Rostov State University, Rostov-on-Don, 1983

[4] Ubbelode A., Melting and a Crystal Structure, Clarendon Press, Oxford, 1965

[5] Stueckelschweiger M., Gruber D., Jin S., Harmuth H., “Creep testing of carbon containing refractories under reducing conditions”, Ceramics International, 45:8 (2019), 9776–9781 | DOI

[6] Bakunov V.S., Lukin E.S., Sysoev É.P., “Stress-rupture strength of polycrystalline oxide ceramic up to 1600$^\circ$C”, Refractories and Industrial Ceramics, 56:4 (2015), 375–382 | DOI

[7] Zabolotskii A.V., “Mathematical simulation of the thermal stability of magnesium oxide”, Refractories and Industrial Ceramics, 52:3 (2011), 170–177 | DOI

[8] Zabolotskiy A.V., Turchin M.Y., Khadyev V.T., Migashkin A.O., “Numerical investigation of refractory stress-strain condition under transient thermal load”, AIP Conference Proceedings, 2310 (2020), 020355 | DOI

[9] Dmitriev A.I., Nikonov A.Yu., Osterle W., “Molecular dynamics sliding simulations of amor phous Ni, Ni-P and nanocrystalline Ni films”, Computational Materials Science, 129 (2017), 231–238 | DOI

[10] Dmitriev A.I., Nikonov A.Y., Shugurov A.R., Panin A.V., “Numerical study of atomic scale deformation mechanisms of Ti grains with different crystallographic orientation subjected to scratch testing”, Applied Surface Science, 471 (2019), 318–327 | DOI

[11] Shugurov A.R., Panin A.V., Dmitriev A.I., “Multiscale Fracture of Ti-Al-N Coatings under Uniaxial Tension”, Physical Mesomechanics, 24 (2021), 185–195 | DOI

[12] Marchenko A.V., Karulin E.B., Chistyakov P.V., “Experimental studies of sea ice elastic behavior”, Vesti gazovoi nayki, 45:3 (2020), 129–140

[13] Voynov G.N., Tidal phenomena and methodology of their research in a shelf zone of the Arctic seas (using the example of the Kara and northeastern parts of the Barents Seas), Dissertation, Arctic and Antarctica Scientific Research Institute, Saint Petersburg, 2003

[14] Zubakin G.K., Dmitriev N.E., Voynov G.N., Nesterov A.V., Vinogradov R.A., “Dynamics of water and ice of the Pechora sea according to experimental data”, Trudy RAO-03 – Proceedings RAO-03 (Saint Petersburg, 2003), 2003, 300–303

[15] Stepanov I.V., Kubyshkin N.V., “Results of long-time expedition exploration of physical and mechanical properties of the Pechora sea ice”, Trudy RAO-03 – Proceedings RAO-03 (Saint Petersburg, 2003), 2003, 194–197

[16] Artyomov M.A., Baranovskiy E.S., Berdzenishvili G.G., Semka E.I., Fatkhudinov D.B., “On neutral loading of a disk under thermal and force influences”, Inzhenernyy Vestnik Dona – Engineering Journal of Don, 49:2 (2018), 1–11

[17] Konoplin N. A., “Temperature dependence of elasticity parameters of iron”, Prirodoobustroystvo – Enviromental Engineering, 2009, no. 4, 99–101

[18] Ershova A.Yu., Martirosov M.I., “Dispersion-reinforced composites experimental and theoretical studies as applied to the problems of the aerospace industry”, Trudy MAI, 2016, no. 89, 1–25

[19] Tokiy N.V., Tokiy V.V., Pilipenko A.N., Pismenova N.E., “Temperature dependence of the elastic modulus of submicrocrystalline copper”, Physics of Solid State, 56:5 (2014), 966–969 | DOI

[20] Grigoriev A.S., Danilchenko S.V., Zabolotsky A.V., Migashkin A.O., Turchin M.Y., Khadyev V.T., “Features of the fracture of refractory linings depending on the equipment size”, Refractories and Industrial Ceramics, 63:6 (2023), 585–592 | DOI

[21] Kuliev V.D., Morozov E.M., “The gradient deformation criterion for brittle fracture”, Doklady Physics, 61 (2016), 502–504 | DOI

[22] Gol'dsteyn R.V., Osipenko N.M., “The model of brittle fracture of porous materials under compression”, Matematicheskoe modelirovanie system i protsessov – PNRPU Mechanics Bulletin, 2009, no. 17, 47–58

[23] Zabolotsky A.V., Migashkin A.O., Grigor'ev A.S., Dmitriev A.I., Turchin M.Y., Khadyev V.T., Shil'ko E.V., “Simulation of crack nucleation in materials with regularly arranged spherical pores under multiaxial loading conditions”, Refractories and Industrial Ceramics, 64:2 (2023), 119–125 | DOI

[24] Voytkovskiy K.F., Mechanical properties of ice, Izdatel'stvo AN SSSR, M., 1960

[25] Bliznyak E.V., Engineering hydrology, Rechizdat, M., 1939

[26] Serikov M.I., “Determina tion of the modulus of elasticity of ice by the resonance method”, Problemy Arktiki, 1959, no. 6, 81–87

[27] Bogorodskiy V.V., Gavrilo V.P. Gusev A.V., On nonlinear effects during the ice destruction in a fluid, Transprint, M., 1970

[28] Ivanov B.D., “Thermal expansion of hexagonal ice”, Vestnik YaGU, 6:4 (2009), 35–39

[29] Chubik I.A., Maslov A.M., Handbook on the thermophysical characteristics of food products and semi-finished products, Pishchevaya promyshlennost', M., 1970

[30] Volkov A.I., Zharskiy I.M., Great chemical hand book, Sovetskaya shkola, M., 2005

[31] Results of water quality monitoring provided by the State Unitary Enterprise «Vodokanal of Saint Petersburg», https://www.vodokanal.spb.ru/vodosnabzhenie/kachestvo_vody

[32] Li L., Shkhinek K., “The ultimate bearing capacity of ice beams”, Magazine of Civil Engineering, 2013, no. 1(36), 65–74 | DOI

[33] Sodhi D.S., “Vertical penetration of floating ice sheets”, International Journal of Solid and Structures, 35:32 (1998), 4275–4294 | DOI