Assessment of the strength of a material using deformable discs with a variable type of stress state

The paper considers a technique for assessing the strength of a material in a complex stress-strain state. For this purpose, the strength of disk-shaped material samples with stress concentrators is being investigated. Stress-strain state modeling was implemented in this work using the finite element method, taking into account the nonlinear nature of the processes under consideration. The reliability of the obtained numerical simulation results was evaluated on the basis of a sequence of FE approximations. The experimental destruction of the proposed samples was carried out on a typical Instron 5989 machine and confirmed the possibility of creating in the tested samples a given level of the ratio of the main stresses arising under biaxial tension conditions. Using the example of steel 45, it is shown that the use of the samples under consideration makes it possible both to evaluate the structural strength of materials and to carry out a local approximation of the corresponding marginal surface. A modified version of the Pisarenko – Lebedev criterion was used as the theoretical basis for its local approximation. It is shown that the proposed disk samples have a relatively simple shape and have a high variability in the type of stress state. This circumstance allows us to transfer the assessment of the structural strength of materials to the stage of its laboratory studies.

1. Makhutov N. A., Makarenko I. V., Makarenko L. V. Computational and experimental analysis of the stress-strain state for inclined semi-elliptical surface cracks / Industr. Lab. Mater. Diagn. 2016. Vol. 82. No. 3. P. 49 – 53 [in Russian].

2. Aniskovich E. V., Lepikhin A. M., Moskvichev V. V. Assessment of static crack resistance of thin-walled pressure vessels / Industr. Lab. Mater. Diagn. 2018. Vol. 84. No. 9. P. 55 – 63 [in Russian]. DOI: 10.26896/1028-6861-2018-84-9-55-63

3. Tsvik L. B. A sample for mechanical testing of structural steels under cyclic loading conditions / Proc. of the Int. Conf. Transport infrastructure of the Siberian region. 2017. Vol. 2. P. 834 – 839 [in Russian].

4. Tsvik L. B., Zenkov E. V., Elovenko D. A., Malomigev D. O. Deformation of laboratory truncated disc samples with stress concentrators / Engineering Solid Mechanics. 2025. Vol. 13. P. 15 – 26. DOI: 10.5267/j.esm.2024.10.002

5. Savkin A. N., Gorobtsov A. S., Andronik A. V., Sedov A. A. Forecasting the durability of car structural elements under accidental loading / Sovr. Mashinostr. Nauka Obraz. 2012. No. 2. P. 651 – 660 [in Russian].

6. Birger I. A., Shorr B. F., Iosilevich G. B. Strength calculations of machine parts: Handbook — Moscow: Mashinostroenie, 1993. — 640 p. [in Russian].

7. Karatushin S. I., Khramova D. A., Bokuchava P. N. Modeling of the stress-strain state of bolt joints in the ANSYS environment / Izv. Vuzov. Mashinostr. 2018. No. 8. P. 11 – 18 [in Russian]. DOI: 10.18698/0536-1044-2018-8-11-18

8. Lobytsin I. O., Dulskiy E. Yu., Milovanova E. A., Pykhalov A. A. Evaluation of the stress-strain state of gear transmission casings of the Ermak series electric locomotive / Modern Technol. Syst. Anal. Modeling. 2019. Vol. 63. No. 3. P. 119 – 126 [in Russian]. DOI: 10.26731/1813-9108.2019.3(63).119-126

9. Tsvik L. B., Zapolsky D. V., Zenkov E. V., Eremeev V. K. Comparative analysis of deformation of the disc part of solid-tank railway wheels of various structural designs / Russ. Railway Sci. J. 2013. No. 5. P. 29 – 36 [in Russian].

10. Belsky A. O. Design analysis of cast and welded side frames of three-element racks of freight wagons / Izv. Transsiba. 2013. No. 2. P. 6 – 11 [in Russian].

11. Tsvik L. B., Shapova M. V., Khramenok M. A. Stress state and fatigue strength of axisymmetric pipe zones of high-pressure vessels / Vestn. Mashinostr. 2010. No. 2. P. 18 – 24 [in Russian].

12. Tsvik L. B., Khramenok M. A., Shapova M. V. Investigation of the level and rigidity of the stress state of the branch pipe zones of convex bottoms of vessels during their deformation by internal pressure / Tyazh. Mashinostr. 2009. No. 4. P. 24 – 26 [in Russian].

13. Serensen S. V. Quasi-static and permanent destruction of materials and structural elements. Vol. 3. — Kiev: Naukova dumka, 1985. — 232 p. [in Russian].

14. Makhutov N. A. Structural strength, resource and technogenic safety. Criteria of strength and resource. — Novosibirsk: Nauka, 2005. — 494 p. [in Russian].

15. Poroshin V. B. Structural strength: textbook. — Chelyabinsk: YuUrGU, 2019. — 335 p. [in Russian].

16. Tsvik L. B., Khramenok M. A., Shapova M. V. On the influence of the parameters of strengthening the openings of the branch pipe zones of pressure vessels on the type of their stress state / Izv. Vuzov. Mashinostr. 2008. No. 1. P. 18 – 24 [in Russian].

17. Kogaev V. P., Makhutov N. A., Gusenkov A. P. Calculations of machine parts and structures for strength and durability: Handbook. — Moscow: Mashinostroenie, 1985. — 224 p. [in Russian].

18. Kolmogorov V. L. Plasticity and destruction. — Moscow: Metallurgiya, 1977. — 336 p. [in Russian].

19. Kogaev V. P. Calculations for strength under stresses of variables over time. — Moscow: Mashinostroenie, 1977. — 232 p. [in Russian].

20. Lebedev A. A., Lamashevsky V. P. The influence of the type of stress state on the deformation and strength of heat-resistant steels / Nauch. Zametki. 2011. No. 32. P. 210 – 218 [in Russian].

21. Zorin E. E., Efimov V. M., Zorin N. E. The influence of a complex stress-strain state on the mechanical characteristics of metal pipelines / Estestv. Tekhn. Nauki. 2019. No. 11. P. 288 – 292 [in Russian]. DOI: 10.25633/etn.2019.11.40

22. Pisarenko G. S., Lebedev A. A. Deformation and strength of materials under complex stress. — Kiev: Naukova Dumka, 1976. — 416 p. [in Russian].

23. Pisarenko G. S., Yakovlev A. P., Matveev V. V. Handbook of material resistance. — Kiev: Naukova Dumka, 1988. — 736 p. [in Russian].

24. Smirnov-Alyaev G. A., Chikidovsky V. P. Experimental research in metal processing by pressure. — Moscow – Leningrad: Mashinostroenie, 1972. — 324 p. [in Russian].

25. Alexandrov A. V. Resistance of materials. — Moscow: Vysshaya shkola, 2003. — 560 p. [in Russian].

26. Lebedev A. A. The development of strength theories in the mechanics of materials / Probl. Prochn. 2010. No. 5. P. 127 – 146 [in Russian].

27. Zenkov E. V., Tsvik L. B. Formation of multidirectional test forces and experimental assessment of material strength under biaxial tensile conditions / Vestn. PNIPU. Mekhanika. 2015. No. 4. P. 110 – 120 [in Russian]. DOI: 10.15593/perm.mech/2015.4.07

28. RF Pat. No. 2839724, IPC G 01 N 1/28, G 01 N 3/02, G 01 N 3/08. A sample for testing the structural strength of a material / Malomyzhev D. O., Malomyzhev O. L., Tsvik L. B.; applicant and patent holder of the FSBEI HE IrGUPS. — No. 2024115056; announced on 12.05.25. Byull. No. 14 [in Russian].

29. Zhilkin V. A. ABC of engineering calculations in MSC Patran-Nastran-Marc. — St. Petersburg: Prospekt nauki, 2024. — 576 p. [in Russian].