Modeling of elastic-plastic deformation of the ring parts as applied to the analysis of the results of testing the material of the fuel-element cladding

An analytical formula for a smooth description of the tension diagram of EK-181 steel and a method for rearranging the diagram when changing the direction of deformation are proposed for the first time. The process of straightening a quarter of an annular sample and further stretching is numerically modeled. It is shown that the conditional yield strength of the material of the straightened sample is 7.5% less than the actual conditional yield strength of steel. It is shown that the test for pure bending of a cantilever sample in the form of a semicircle with the processing of the bending diagram (by analogy with GOST 3565–80 for torsion) provides an estimate of the conditional yield strength which is 32% higher than the actual yield strength. The possibility of numerical reconstruction of the tension diagram from the diagram of pure bending of a cantilevered semi-ring sample is proved. It is shown that this procedure really gives the value of the conditional yield strength of steel EK-181 with a tolerance for the residual deformation of 0.2%. The analysis of the test procedure for the rings of fuel element cladding and the proposed algorithm for determination of the conditional yield stress of the ring material is carried out. Attention is drawn to the arbitrariness of the choice of the designed load on the two-stage diagram of the diametrical tension of the ring and to the lack of scientific substantiation of the possibility of determining the yield stress on the second part of the diagram. It is shown that this method in the current form contradicts GOST for tensile testing due to the absence of a base with a uniform stress state on the ring. Therefore, the considered method is not recommended for determining the values of the conditional yield strength suitable for strength calculations.

1. Kiparisov A. G., Mironov A. A., Mikheev N. N., Zhukov A. E. Mechanica tests of materials. — Nizhny Novgorod: Nizhegorodskii Gos. Tekhn. Univ., 2004. — 81 p. [in Russian].

2. Goltsev V. Yu. Methods of mechanical tests and mechanical properties of materials. — Moscow: NIYaU MIFI. 2012. — 228 p. [in Russian].

3. Krylov V. D. Determination of the bending yield strength / Vestn. TGU. 2013. Vol. 18. N 4. P. 937 – 1938 [in Russian].

4. Matyunin V. M., Marchenkov A. Yu. Determination of the conditional yield stress from the kinetic diagram of indentation of a spherical indenter / Zavod. Lab. Diagn. Mater. 2007. Vol. 83. N 6. P. 57 – 61 [in Russian].

5. Markochev V. M., Olfer’eva M. A. Elastoplastic states and strength of structures. — Moscow: NIYaU MIFI, 2001. — 140 p. [in Russian].

6. Markochev V. M., Tarasov N. I. Modeling of processes of elastoplastic deformation of protective covers of equipment / Atom. Énergiya. 2016. Vol. 121. N 2. P. 85 – 90 [in Russian].

7. Markochev V. M. Non-stationary fields of temperatures and stresses in multilayer plates. — Moscow: Izd. fonda «Stalingrad», 2020. — 180 p. [in Russian].

8. Kazantsev A. G., Markochev V. M., Sugirbekov B. A. Statistical evaluation of the determination of the critical temperature of the brittleness of the metal of the VVER-1000 reactor vessel according to the impact bending test data / Zavod. Lab. Diagn. Mater. 2018. Vol. 83. N 3. P. 47 – 54 [in Russian]. DOI: 10.26896/1028-6861-2018-84-3-47-54

9. Markochev V. M. Mathematical model of the transition of a material from an elastic state to an elastoplastic one / Zavod. Lab. Diagn. Mater. 2018. Vol. 84. N 8. P. 55 – 58 [in Russian]. DOI: 10.26896/1028-6861-2018-84-8-55-58

10. Panin A. V., Leont’eva-Smirnova M. V., Tsernov V. M., et al. Improving the strength characteristics of EK-181 steel based on a multilevel approach of physical mesomechanics / Fiz. Mezomekh. 2007. Vol. 10. N 4. P. 73 – 86 [in Russian].

11. Leont’eva-Smirnova M. V., Ismalkov I. N., Valitov I. R., et al. Determination of the yield point of EK-181 steel during tensile tests of ring specimens / Zavod. Lab. Diagn. Mater. 2016. Vol. 82. N 10. P. 56 – 61 [in Russian].

12. Feodos’ev V. I. Resistance of materials. — Moscow: Izd. MGTU im. N. É. Baumana, 2000. — 592 p. [in Russian].

13. Nadai A. Theory of flow and fracture of solids. Vol. 1. — New York: McGraw-Hill Book Company, 1950. — 647 p.

14. Makarichev Yu. A., Ivannikov Yu. N. Methods of experiment planning and data processing. — Samara: Samar. Gos. Tehn. Univ., 2016. — 131 p. [in Russian].

15. Syzrantsev V. M., Syzrantseva K. V., Chernaya L. A. Evaluation of the error of data processing of fatigue tests by linear regression analysis / Zavod. Lab. Diagn. Mater. 2017. Vol. 83. N 5. P. 50 – 55 [in Russian].