Abstract—
The evolution of stress–strain state (SSS) of multilayer shell mold (SM) has been simulated upon variation of properties between the layers during cooling of casted steel. A mathematical model has been developed and the stress state of SM has been theoretically investigated in the case of absence of interrelation between the layers in multilayer composite material. The complex three-component system (liquid metal, solid metal, ceramic shell mold) has been analyzed. The solid metal and the SM are considered as isotropic. In order to solve the formulated problem, the theory of small elastic deformations and the equations of heat conductance have been applied as well as verified numerical methods. The SSS evolution in shell molds can be traced by time steps. The thickness of solidified metal is determined by the equation of interphase transition. Heating of axisymmetric SM during pouring of liquid metal is analyzed. The stress state has been estimated by stresses and displacements occurring in SM. During cooling of liquid metal at the contact between the shell mold and supporting filler (SF), the surface between them can be detached. In this case, the contact problem is solved. The calculations for the case of complete sliding of layers have been carried out with consideration of the compiled algorithm for problem solving by using the developed numerical schemes and software. The obtained numerical results are presented in the form of diagrams and plots. The obtained results have been analyzed in detail. The inconsistency of the previously proposed concept about applicability of sliding between the layers in multilayer composite material in terms of its strain state has been demonstrated. The experimental results can be useful for analysis of other functional multilayer shell systems.
Similar content being viewed by others
REFERENCES
Odinokov, V.I., Dmitriev, E.A., Evstigneev, A.I., and Sviridov, A.V., Matematicheskoe modelirovanie protsessov polucheniya otlivok v keramicheskie obolochkovye formy (Mathematical Modeling of Castings Obtaining in Ceramic Shell Molds), Moscow: Innovatsionnoe Mshinostroenie, 2020.
Odinokov, V.I., Dmitriev, E.A., Evstigneev, A.I., Sviridov, A.V., and Ivankova, E.P., Modeling and optimizing the property choices of materials and structures of shell molds for investment casting, Steel Transl., 2020, vol. 50, pp. 684–695. https://doi.org/10.3103/S0967091220100071
Repyakh, S.I., Tekhnologicheskie osnovy lit’ya po vyplavlyaemym modelyam (Technological Basics of Casting by Investment Models). Dnepropetrovsk: Lira, 2006.
Evstigneev, A.I., Odinokov, V.I., Dmitriev, E.A., Sviridov, A.V., and Ivankova, E.P., Influence of external thermal action on stress state of shell molds by smelting molds, Math. Models Comput. Simul., 2021, vol. 13, no. 5, pp. 780–789. https://doi.org/10.1134/S2070048221050112
Kulikov, G.M., Influence of anisotropy on the stress state of multilayer reinforced shells, Soviet Appl. Mech., 1987, vol. 22, no. 12, pp. 1166–1170. https://doi.org/10.1007/BF01375815
Zveryaev, E.M., Berlinov, M.V., and Berlinova, M.N., The integral method of definition of basic tension condition anisotropic shell, Int. J. Appl. Eng. Res., 2016, vol. 11, no. 8, pp. 5811–5816.
Maximyuk, V.A., Storozhuk, E.A., and Chernyshenko, I.S., Stress state of flexible composite shells with reinforced holes, Int. Appl. Mech., 2014, vol. 50, no. 5, pp. 558–565. https://doi.org/10.1007/s10778-014-0654-6
Vetrov, O.S. and Shevchenko, V.P., Study of the stress-strain state of orthotropic shells under the action of dynamical impulse loads, J. Math. Sci., 2012, vol. 183, no. 2, pp. 231–240. https://doi.org/10.1007/s10958-012-0809-0
Vasilenko, A.T. and Urusova, G.P., The stress state of anisotropic conic shells with thickness varying in two directions, Int. Appl. Mech., 2000, vol. 35, no. 5, pp. 631–638. https://doi.org/10.1007/BF02682077
Tovstik, P.E. and Tovstik, T.P., Two-dimensional linear model of elastic shell accounting for general anisotropy of material, Acta Mech., 2014, vol. 225, no. 3, pp. 647–661. https://doi.org/10.1007/s00707-013-0986-z
Grigorenko, Y.M., Vasilenko, A.T., and Pankratova, N.D., Stress state and deformability of composite shells in the three-dimensional statement, Mech. Compos. Mater., 1985, vol. 20, no. 4, pp. 468–474. https://doi.org/10.1007/BF00609648
Vasilenko, A.T. and Sudavtsova, G.K., The stress state of stiffened shallow orthotropic shells, Int. Appl. Mech., 2001, vol. 37, no. 2, pp. 251–262. https://doi.org/10.1023/A:1011393724113
Nemish, Yu.N., Zirka, A.I., and Chernopiskii, D.I., Theoretical and experimental investigations of the stress-strain state of nonthin cylindrical shells with rectangular openings, Int. Appl. Mech., 2000, vol. 36, pp. 1620–1625. https://doi.org/10.1023/A:1011344031264
Rogacheva, N.N., The effect of surface stresses on the stress-strain state of shells, J. Appl. Math. Mech., 2016, vol. 80, no. 2, pp. 173–181. https://doi.org/10.1016/j.jappmathmech.2016.06.011
Banichuk, N.V., Ivanova, S.Yu., and Makeev, E.V., On the stress state of shells penetrating into a deformable solid, Mech. Solids, 2015, vol. 50, no. 6, pp. 698–703. https://doi.org/10.3103/S0025654415060102
Krasovsky, V.L., Lykhachova, O.V., and Bessmertnyi Ya.O., Deformation and stability of thin-walled shallow shells in the case of periodically non-uniform stress-strain state, Proc. 11th Int. Conf. Shell Structures: Theory and Applications, 2018, vol. 4, pp. 251–254. https://doi.org/10.1201/9781315166605-55.
Storozhuk, E.A., Chernyshenko, I.S., and Kharenko, S.B., Elastoplastic deformation of conical shells with two circular holes, Int. Appl. Mech., 2012, vol. 48, no. 3, pp. 343–348. https://doi.org/10.1007/s10778-012-0525-y
Ivanov, V.N., Imomnazarov, T.S., Farhan, I.T.F., and Tiekolo, D., Analysis of stress-strain state of multi-wave shell on parabolic trapezoidal plan, Adv. Struct. Mater., 2020, vol. 113, pp. 257–262. https://doi.org/10.1007/978-3-030-20801-1_19
Gerasimenko, P.V. and Khodakovskiy, V.A., Numerical algorithm for investigating the stress-strain state of cylindrical shells of railway tanks, Vestn. St. Petersburg Univ.: Math., 2019, vol. 52, no. 2, pp. 207–213. https://doi.org/10.1134/S1063454119020067
Meish, V.F. and Maiborodina, N.V., Stress state of discretely stiffened ellipsoidal shells under a nonstationary normal load, Int. Appl. Mech., 2018, vol. 54, no. 6, pp. 675–686. https://doi.org/10.1007/s10778-018-0922-y
Marchuk, A.V. and Gnidash, S.V., Analysis of the effect of local loads on thick-walled cylindrical shells with different boundary conditions, Int. Appl. Mech., 2016, vol. 52, no. 4, pp. 368–377. https://doi.org/10.1007/s10778-016-0761-7
Maksimyuk, V.A., Mulyar, V.P., and Chernyshenko, I.S., Stress state of thin spherical shells with an off-center elliptic hole, Int. Appl. Mech., 2003, vol. 39, no. 5, pp. 595–598. https://doi.org/10.1023/A:1025147927708
Grigorenko, Ya.M., Grigorenko, A.Ya., and Zakhariichenko, L.I., Analysis of influence of the geometrical parameters of elliptic cylindrical shells with variable thickness on their stress-strain state, Int. Appl. Mech., 2018, vol. 54, no. 2, pp. 155–162. https://doi.org/10.1007/s10778-018-0867-1
Odinokov, V.I., Kaplunov, B.G., Peskov, A.V., and Bakov, A.V., Matematicheskoe modelirovanie slozhnykh tekhnologicheskikh protsessov (Mathematic Modeling of Complex Technological Processes), Moscow: Nauka, 2008.
Odinokov, V.I., Prokudin, A.N., Sergeeva, A.M., and Sevast’yanov, G.M., Certificate of State Registration of the Computer Program 2012661389, 2012.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by I. Moshkin
About this article
Cite this article
Odinokov, V.I., Evstigneev, A.I., Dmitriev, E.A. et al. The Influence of Internal Factor on Crack Resistance of Shell Mold for Investment Models. Steel Transl. 52, 159–164 (2022). https://doi.org/10.3103/S0967091222020152
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0967091222020152