Funct. Mater. 2021; 28 (4): 652-661
Effects of grain-size and specimen thickness on dislocation kinetics in uniaxially strained thin Al sheets with one grain in thickness
V.Karazin Kharkiv National University, 4 Svobody Sq., 61022 Kharkiv, Ukraine
This study expands the well-known Kocks-Mecking strain hardening model by describing the effects of grain size and sample thickness, as well as the kinetics of dislocations during uniaxial deformation of thin aluminum sheets with one grain in thickness. In the kinetic equation for the dislocation density, the coefficients are determined for the case of flat samples with a "pancake" grain structure. The kinetic equation was transformed using Taylor's law of strain hardening in a standard way; and the solution to this equation was obtained to calculate the stress - strain curve of Al specimens with average grain sizes and thicknesses in the range of 0.2 <ds <20 mm and 0.05 <t <1 mm, respectively. An approximate Hall-Petch type relation is obtained. Based on the kinetic consideration of the processes of storage and recovery of dislocations, the effect of the grain size and specimen thickness on the flow stress and the strain-hardening rate is studied. The calculation results are in good agreement with obtained experimental data.
| 1. H.-J.Leea, P.Zhang, J.C.Bravman, J. Appl. Phys., 93, 1443 (2003). https://doi.org/10.1063/1.1532933 |
||||
| 2. P.J.Janssen, T.H.de Keijser, M.G.Geers, Mater. Sci. Eng., A 419, 238 (2006). https://doi.org/10.1016/j.msea.2005.12.029 |
||||
| 3. C.Keller, E.Hug, R.Retoux, X.Feaugas, Mechan. Mater., 42, 44 (2010). https://doi.org/10.1016/j.mechmat.2009.09.002 |
||||
| 4. G.A.Malygin, Phys. Solid State, 54, 559 (2012). https://doi.org/10.1134/S1063783412030171 |
||||
| 5. K.M.Davoudi, J.J.Vlassak, J. Appl. Phys., 123, 085302 (2018). https://doi.org/10.1063/1.5013213 |
||||
| 6. T.R.Bielera, R.Alizadeh, M.Pena-Ortega, J.Llorca, Intern. J. Plasticity, 118, 269 (2019). https://doi.org/10.1016/j.ijplas.2019.02.014 |
||||
| 7. E.O.Hall, Proc. Phys. Soc. B., 64, 747 (1951). https://doi.org/10.1088/0370-1301/64/9/303 |
||||
| 8. N.J.Petch, J. Iron Steel Inst., 174, 25 (1953). | ||||
| 9. S.Miyazaki, K.Shibata, H.Fujita, Acta Metall., 27, 855 (1978). https://doi.org/10.1016/0001-6160(79)90120-2 |
||||
| 10. U.F.Kocks, H.Mecking, Acta Metall., 29, 1865 (1981). https://doi.org/10.1016/0001-6160(81)90112-7 |
||||
| 11. Y.Estrin, H.Mecking, Acta Metall., 32, 57 (1984). https://doi.org/10.1016/0001-6160(84)90202-5 |
||||
| 12. U.F.Kocks, H.Mecking, Progr. Mater. Sci., 48, 171 (2003). https://doi.org/10.1016/S0079-6425(02)00003-8 |
||||
| 13. E.E.Badiyan, A.G.Tonkopryad, Ye.V.Ftomov, O.V.Shekhovtsov, Functional Materials, 26, 484 (2019). https://doi.org/10.15407/fm26.01.88 |
||||
| 14. N.Hansen, X.Huang, Acta Mater., 46, 1827 (1998). https://doi.org/10.1016/S1359-6454(97)00365-0 |
||||
| 15. E.E.Badiyan, A.G.Tonkopryad, O.V.Shekhovtsov et al., Functional Materials, 22, 396 (2015). https://doi.org/10.15407/fm22.03.396 |
||||
| 16. Ye.V.Ftomov, J. V.Karazin Kharkiv National University, Ser. "Physics", 34, 25 (2021). | ||||
| 17. G.I.Taylor, Proc. Roy. Soc. A., 145, 362 (1934). https://doi.org/10.1098/rspa.1934.0106 |
||||
| 18. G.A.Malygin, Phys. Solid State, 52, 49 (2010). https://doi.org/10.1134/S1063783410010099 |
||||
| 19. G.I.Taylor, J. Inst. Metals, 62, 307 (1938). | ||||
| 20. X.Huang, A.Borrego, W.Pantleon, Mater. Sci. Engin. A, 319-321, 237 (2001). https://doi.org/10.1016/S0921-5093(01)01019-X |
||||
| 21. G.A.Malygin, Phys. Solid State, 49, 1013 (2007). https://doi.org/10.1134/S1063783407060017 |
||||
| 22. J.C.M.Li, T.Chou, Metal. Trans., 1, 1145 (1970). https://doi.org/10.1007/BF02900225 |
||||
| 23. E.S.Venkatesh, L.E.Murr, Mater. Sci. Eng., 33, 69 (1978). https://doi.org/10.1016/0025-5416(78)90155-6 |
||||
| 24. E.V.Esquivel, L.E.Murr, Mater. Sci. Eng. A, 409, 13 (2005). https://doi.org/10.1016/j.msea.2005.04.063 |
||||
| 25. Z.C.Cordero, B.E.Knight, C.A.Schuh, Intern. Mater. Rev., 61, 495 (2016). https://doi.org/10.1080/09506608.2016.1191808 |
||||