Influence of support filler and structure of shell mold on its crack resistance

Recently, researchers have been paying more and more attention to the influence of internal and external factors on stress state of shell mold (SM). Internal factors should include morphological structure of SM, its types and connections between the contacting layers. External factors should include all types of force and temperature effects on SM external surface. The purpose of this work was to establish the sliding effect of SM internal layers in contact with each other on the level of SM stress state. The mathematical model for determining the stress-strain state (SSS) in the multilayer SM when it is filled with a liquid metal is presented. Moreover, the SM is made in such a way that its layers can slide relative to each other with the presence of friction. This work is a continuation of the recent works of the authors, where the influence of the temperature factor on the studied SM was estimated. At the same time, SM layers have the same physical and mechanical properties. The problem was solved in the same formulation as in the previous works of the authors. The task was set to determine the influence of the support filler (SF) and the clamp in the upper part of SM on SSS in its sections. The influence of SF was estimated by the amount of friction between the outer surfaces of SM and SF. Just as in the previous works of the authors, the linear theory of elasticity, heat conduction equations, and numerical methods were used to solve the problem. On the contact of  SM outer surface with SF surface, the contact problem was solved. Solid phase in the liquid metal during cooling was determined from the equation of interphase transition. Results of the calculations are presented in the form of graphs and plots. It is shown that the absence of friction between the layers reduces the crack resistance of SM multilayer.

1. Odinokov V.I., Dmitriev E.A., Evstigneev A.I., Sviridov A.V. Mathe­matical Modeling of Processes of Castings Production into Cera­mic Shell Molds. Moscow: Innovatsionnoe mashinostroenie, 2020, 224 p. (In Russ.).

2. Odinokov V.I., Dmitriev E.A., Evstigneev A.I., Sviridov A.V., Ivankova E.P. Choice of materials properties and structure of shell molds by investment models. Izvestiya. Ferrous Metallurgy. 2020, vol. 63, no. 9, pp. 742–754. (In Russ.) https://doi.org/10.17073/0368-0797-2020-9-742-754

3. Odinokov V.I., Evstigneev A.I., Dmitriev E.A., Chernyshova D.V., Evstigneeva A.A. Influence of internal factor on crack resistance of shell mold by investment models. Izvestiya. Ferrous Metallurgy. 2022, vol. 65, no. 2, pp. 137–144. (In Russ.). https://doi.org/10.17073/0368-0797-2022-2-137-144

4. Kulikov G.M. Influence of anisotropy on the stress state of multi­layer reinforced shells. Soviet Applied Mechanics. 1987, vol. 22, no.  12, pp. 1166–1170.

5. Zveryaev E.M., Berlinov M.V., Berlinova M.N. The integral method of definition of basic tension condition anisotropic shell. International Journal of Applied Engineering Research. 2016, vol. 11, no.  8, pp. 5811–5816.

6. Maximyuk V.A., Storozhuk E.A., Chernyshenko I.S. Stress state of flexible composite shells with reinforced holes. International App­lied Mechanics. 2014, vol. 50, no. 5, pp. 558–565. https://doi.org/10.1007/s10778-014-0654-6

7. Vetrov O.S., Shevchenko V.P. Study of the stress-strain state of orthotropic shells under the action of dynamical impulse loads. Journal of Mathematical Sciences. 2012, vol. 183, no. 2, pp. 231–240. https://doi.org/10.1007/s10958-012-0809-0

8. Vasilenko A.T., Urusova G.P. The stress state of anisotropic conic shells with thickness varying in two directions. International Applied Mechanics. 2000, vol. 35, no. 5, pp. 631–638. https://doi.org/10.1007/BF02682077

9. Tovstik P.E., Tovstik T.P. Two-dimensional linear model of elastic shell accounting for general anisotropy of material. Acta Mechanica. 2014, vol. 225, no. 3, pp. 647–661. https://doi.org/10.1007/s00707-013-0986-z

10. Grigorenko Y.M., Vasilenko A.T, Pankratova N.D. Stress state and deformability of composite shells in the three-dimensional statement. Mechanics of Composite Materials. 1985, vol. 20, no. 4, pp.  468–474. https://doi.org/10.1007/BF00609648

11. Vasilenko A.T., Sudavtsova G.K. The stress state of stiffened shallow orthotropic shells. International Applied Mechanics. 2001, vol.  37, no. 2, pp. 251–262. https://doi.org/10.1023/A:1011393724113

12. Nemish Yu.N., Zirka A.I., Chernopiskii D.I. Theoretical and experimental investigations of the stress-strain state of nonthin cylindrical shells with rectangular holes. International Applied Mechanics. 2000, vol. 36, no. 12, pp. 1620–1625.

13. Rogacheva N.N. The effect of surface stresses on the stress-strain state of shells. Journal of Applied Mathematics and Mechanics. 2016, vol. 80, no. 2, pp. 173–181. https://doi.org/10.1016/j.jappmathmech.2016.06.011

14. Banichuk N.V., Ivanova S.Yu., Makeev E.V. On the stress state of shells penetrating into a deformable solid. Mechanics of Solids. 2015, vol. 50, no. 6, pp. 698–703. https://doi.org/10.3103/S0025654415060102

15. Krasovsky V.L., Lykhachova O.V., Bessmertnyi Ya.O. Deformation and stability of thin-walled shallow shells in the case of periodically non-uniform stress-strain state. In: Proc. of the 11th Int. Conference “Shell Structures: Theory and Applications”. 2018, vol. 4, pp. 251–254.

16. Storozhuk E.A., Chernyshenko I.S., Kharenko S.B. Elastoplastic deformation of conical shells with two circular holes. International Applied Mechanics. 2012, vol. 48, no. 3, pp. 343–348. https://doi.org/10.1007/s10778-012-0525-y

17. Ivanov V.N., Imomnazarov T.S., Farhan I.T.F., Tiekolo D. Analysis of stress-strain state of multi-wave shell on parabolic trapezoidal plan. Advanced Structured Materials. 2020, vol. 113, pp. 257–262. https://doi.org/10.1007/978-3-030-20801-1_19

18. Gerasimenko P.V., Khodakovskiy V.A. Numerical algorithm for investigating the stress-strain state of cylindrical shells of railway tanks. Vestnik of the St. Petersburg University: Mathematics. 2019, vol. 52, no. 2, pp. 207–213.

19. Meish V.F., Maiborodina N.V. Stress state of discretely stiffened ellipsoidal shells under a nonstationary normal load. International Applied Mechanics. 2018, vol. 54, no. 6, pp. 675–686. https://doi.org/10.1007/s10778-018-0922-y

20. Marchuk A.V., Gnidash S.V. Analysis of the effect of local loads on thick-walled cylindrical shells with different boundary conditions. International Applied Mechanics. 2016, vol. 52, no. 4, pp. 368–377. https://doi.org/10.1007/s10778-016-0761-7

21. Grigorenko Ya.M., Grigorenko A.Ya., Zakhariichenko L.I. Analysis of influence of the geometrical parameters of elliptic cylindrical shells with variable thickness on their stress-strain state. International Applied Mechanics. 2018, vol. 54, no. 2, pp. 155–162. https://doi.org/10.1007/s10778-018-0867-1

22. Repyakh S.I. Technological Basics of Casting by Investment Mo­dels. Dnepropetrovsk: Lira, 2008, 1056 p.

23. Odinokov V.I., Kaplunov B.G., Peskov A.V., Bakov A.V. Mathema­tic Modeling of Complex Technological Processes. Moscow: Nauka, 2008, 176 p. (In Russ.).

24. Odinokov V.I., Prokudin A.N., Sergeeva A.M., Sevast’yanov G.M. ODYSSEUS. Certificate of state registration of the computer prog­ram no. 2012661389. Registered in the Register of Computer Prog­rams on 13.12.2012. (In Russ.).