Study of bending of plate steel with a through-the-thickness gradient of strength properties

The paper considers the studies of bending of a plate made of A32 ship steel with a through-the-thickness gradient of strength properties. The grading was produced by accelerated one-sided cooling of the plate from the austenitic area. As a result, a spectrum of microstructures was formed over the thickness of the plate: from ferrite-bainite on the cooled surface to ferrite-perlite on the other. During elastic-plastic bending of a steel plate with a homogeneous microstructure, the neutral surface shifts towards the compressed fibers, which is explained by the greater resistance of the material to compression than to tension. The purpose of this work was to develop a finite plastic deformation model of bending of a steel plate with tension/ compression (T/C) asymmetry and a strength gradient to confirm the expediency of one-sided thermal reinforcement of rolled sheets. It is confirmed that the displacement of the neutral surface caused by T/C asymmetry depends on the asymmetry ratio and does not depend on the steel microstructure, and is directed towards the compressed fibers. The displacement caused by the strength gradient depends on the absolute value of this gradient and is directed towards it. Calculations revealed that the critical bending moment for a plate made of A32 steel with a strength gradient is not less than that for the normalized and thermally hardened (by quenching and tempering ) states, at any direction of the strength gradient with respect to the bending direction. It is concluded that the proposed technology of thermal reinforcement of heavy-plate rolled products made of carbon and low-alloy steels using accelerated one-sided cooling provides mechanical properties not worse than for the thermally hardened state. This saves up to 40 % of cooling water.

1. Podgaiskii M.S., Maksimov A.B., Nalivaichenko T.M. Plastic deformation during cyclic alternating bending. Fiziko-khimicheskaya mekhanika materialov. 1983, no. 1, pp. 115–116. (In Russ.).

2. Hill R. The Mathematical Theory of Plasticity. Oxford: Clarendom Press, 1950, 368 p.

3. Kulawinski D., Nagel K., Henkel S., Hubner P., Kuna M., Biermann H. Characterization of stress-strain behavior of a cast TRIP steel under different biaxial planar load rations. Engineering Fracture Mechanics. 2011, vol. 78, no. 8, pp. 1684–1695. https://doi.org/10.1016/j.engfracmech.2011.02.021

4. N’souglo K.E., Rodríguez-Martínez J.A., Vaz-Romero A., Cazacu O. The combined effect of plastic orthotropy and tension-compression asymmetry on the development of necking instabilities in flat tensile specimens subjected to dynamic loading. International Journal of Solids and Structures. 2019, vol. 159, pp. 272–288. https://doi.org/10.1016/j.ijsolstr.2018.10.006

5. Pavilainen G.V. Mathematical model of the bending task of a plastically anisotropic beam. Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya. 2015, vol. 2(60), no. 4, pp. 633–638. (In Russ.).

6. Alexandrov S., Hwang Y.-M. The bending moment and springback in pure bending of anisotropic sheets. International Journal of Solids and Structures. 2009, vol. 46, no. 25–26, pp. 4361–4368. https://doi.org/10.1016/j.ijsolstr.2009.08.023

7. Ahn K. Plastic bending of sheet metal with tension/compression asymmetry. International Journal of Solids and Structures. 2020, vol. 204–205, pp. 65–80. https://doi.org/10.1016/j.ijsolstr.2020.05.022

8. Maksimov A.B., Shevchenko I.P., Erokhina I.S. Sheet metal with variable mechanical properties over its thickness. Izvestiya. Ferrous Metallurgy. 2019, no. 8, vol. 62, pp. 587–593. (In Russ.). https://doi.org/10.17073/0368-0797-2019-8-587-593

9. Maksimov A.B., Erokhina I.S. Properties of rolled plate with strength gradient across thickness. Inorganic Materials: Applied Research. 2021, vol. 12, no. 1, pp. 172–176. http://doi.org/10.1134/s2075113321010251

10. Verguts H., Sorwerby R. The pure plastic bending of laminated sheet metals. International Journal of Mechanical Sciences. 1975, vol. 17, no. 1, pp. 31–51. https://doi.org/10.1016/0020-7403(75)90061-2

11. Majlessi S.A., Dadras P. Pure plastic bending of sheet laminates under plane strain condition. International Journal of Mechanical Sciences. 1983, vol. 25, no. 1, pp. 1–14. https://doi.org/10.1016/0020-7403(83)90082-6

12. Yartsev B.A. Introduction to the Mechanics of Monoclinic Composites. St. Petersburg: Krylovskii gosudarstvennyi nauchnyi tsentr, 2020, 224 p. (In Russ.).

13. Srividhya S., Raghu P., Rajagopal A., Reddy J.N. Nonlocal nonlinear analysis of functionally graded plates using third-order shear deformation theory. International Journal of Engineering Science. 2018, vol. 125, pp. 1–22. https://doi.org/10.1016/j.ijengsci.2017.12.006

14. Ghayesh M.H., Farajpour A. A review on the mechanics of functionally graded nanoscale and microscale structures. International Journal of Engineering Science. 2019, vol. 137, pp. 8–36. https://doi.org/10.1016/j.ijengsci.2018.12.001

15. Gholipour A., Ghayesh M.H. Nonlinear coupled mechanics of functionally graded nanobeams. International Journal of Engineering Science. 2020, vol. 150, article 103221. https://doi.org/10.1016/j.ijengsci.2020.103221

16. Chen W., Yan Z., Wang L. On mechanics of functionally graded hard-magnetic soft beams. International Journal of Engineering Science. 2020, vol. 157, article 103391. https://doi.org/10.1016/j.ijengsci.2020.103391

17. Zaides S.A., Vu Van H., Doan Thanh V. Developing installation to increase cylindrical part surface hardness. iPolytech Journal. 2020, vol. 24, no. 2, pp. 262–274. https://doi.org/10.21285/1814-3520-2020-2-262-274

18. Chukin M.V., Paletskov P.P., Gushchina M.S., Berezhnaya G.A. Determination of mechanical properties of high-strength and superstrength steels by hardness. Proizvodstva prokata. 2016, no. 12, pp. 37–42. (In Russ.).

19. Falope F.O., Lanzonia L., Tarantino A.M. The bending of fully nonlinear beams. Theoretical, numerical and experimental analyses. International Journal of Engineering Science. 2019, vol. 145, article 103167. https://doi.org/10.1016/j.ijengsci.2019.103167

20. Pinnola F.P., Faghidian S.A., Barretta R., Marotti de Sciarra F. Variationally consistent dynamics of nonlocal gradient elastic beams. International Journal of Engineering Science. 2020, vol. 149, article 103220. https://doi.org/10.1016/j.ijengsci.2020.103220

21. Eismondt K.Yu. Development and introduction into production of devices for thermal hardening of rolled products by controlled cooling based on the analysis of heat exchange processes: Extended Abstract of Cand. Sci. Diss. Yekaterinburg, 2011. (In Russ.).

22. Gulyaev A.P. Metal Science. Moscow: Metallurgiya, 1977, 600 p. (In Russ.).

23. Pronina Y., Maksimov A., Kachanov M. Crack approaching a domain having the same elastic properties but different fracture toughness: Crack deflection vs penetration. International Journal of Engineering Science. 2020, vol. 156, article 103374. https://doi.org/10.1016/j.ijengsci.2020.103374