Modelling Dependency of the Steady-State Grain Size on the Stacking Fault Energy in Severely Plastic Deformed Materials

Subject Areas : Severe Plastic Defeormation

Maryam Bahmanpour ¹ ( Department of Mathematics, Islamic Azad University, Isfahan (khorasgan) Branch, Isfahan, Iran )
Majid Abdellahi ² ( Advanced Materials Research Center, Faculty of Materials Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran )

Received: 2021-04-24 Accepted : 2021-07-28 Published : 2021-08-01

Keywords: Severe Plastic Deformation (SPD), GEP-Modelling, stacking fault energy (SFE), Steady-state grain size,

Abstract :

In the present work, a computer-based method is proposed to investigate the relationship between the steady-state grain size (ds) and stacking fault energy (SFE) in severely plastic deformed (SPDed) materials. The stacking fault energy, γ, plays an important role in determining the mechanical properties of face-centered cubic (fcc) metals. A number of models have been proposed to show this role. These models have several shortcomings, including complex computational variables, data constraints and small computational range constraints. The present model compatible with experimental results does not employ hard calculable variables. Besides, it is applicable not only for pure metals but also for alloys. The squared regression (R2) and error sum of squares (SSE) for the training and testing data of the presented model are 0.93, 0.0006 and 0.98, 0.00018, respectively, which indicates the high accuracy of the proposed model. The slope of the versus is about 0.6453 which is comparable to all the models offered in this field.

References:

[1] S. Qu, X.H. An, H.J. Yang, C.X. Huang, G. Yang, Q.S. Zang, et al., Microstructural evolution and mechanical properties of Cu–Al alloys subjected to equalchannel angular pressing, Acta Mater. 57 (2009) 1586–1601.

[2] Mohamed FA. A dislocation model for the minimum grain size obtainable by milling. Acta Mater 2003;51:4107–19.

[3] Parvin H, Kazeminezhad M, Dependency Modeling of steady state grain size on the stacking fault energy through severe plastic deformation. Mater Let, http://dx.doi.org/10.1016/j.matlet.2015.07.041

[4] Mohamed FA. Correlation between the behavior of nanocrystalline HCP metals and the dislocation model for the minimum grain size obtainable by milling. Mater Sci Eng A 2010;527(9):2157-62.

[5] Edalati K, Akama D, Nishio A, Lee S, Yonenaga Y, Sesin JMC, Horita Z, Influence of dislocation–solute atom interactions and stacking fault energy on grain size of single-phase alloys after severe plastic deformation using high-pressure torsion. Acta Mater 2014;69:68-77.

[6] Lu S, Hu QM, Delczeg-Czirjak EK, Johansson B, Vitos L, Determining the minimum grain size in severe plastic deformation process via first-principles calculations. Acta Mater 2012;60:4506-13.

[7] Huang M, Rivera-Díaz-del-Castillo PEJ, Bouaziz O, Van Der Zwaag S. Irreversible thermodynamics modelling of plastic deformation of metals. Mater Sci Technol 2008;24:495-500.

[8] Cai B, Tao J, Wang W, Yang X, Gong Y, Cheng L, et al. The effect of stacking fault energy on equilibrium grain size and tensile properties of ultrafine-grained Cu-Al-Zn alloys processed by rolling. J Alloy Compd 2014;6:115-9.

[9] Zhao YH, Zhu YT, Liao XZ, Horita Z, Langdon TG. Influence of stacking fault energy on the minimum grain size achieved in severe plastic deformation. Mater Sci Eng A 2007;463(1):22-6

[10] Abdellahi M, A new predictive model for calculating the hardness of metal matrix nanocomposites produced by mechanical alloying. J Mater Res 2013;28:3270–78.

[11] Edalati K, Ito Y, Suehiro K, Horita Z. Softening of high purity aluminum and copper processed by high pressure torsion. Int J Mater Res 2009;100:1668-73.

[12] Edalati K, Yamamoto A, Horita Z, Ishihara T. High pressure torsion of pure magnesium. Scripta Mater 2011;64:880-3

[13] Edalati K, Horita Z, Yagi S, Matsubara E. Allotropic phase transformation of pure zirconium by high-pressure torsion. Mater Sci Eng A  2009;523:277.

[14] Edalati K, Horita Z. Significance of homologous temperature in softening behavior. Mater Sci Eng A 2011;528:7514-23.

[15] Edalati K, Fujioka T, Horita Z. Mater Trans. Evolution of Mechanical Properties and Microstructures with Equivalent Strain in Pure Fe Processed by High Pressure Torsion. 2009;50:44-50.

[16] Matsunaga H, Horita Z. Mater Trans. Softening and Microstructural Coarsening without Twin Formation in FCC Metals with Low Stacking Fault Energy after Processing by High-Pressure Torsion. 2009;50:1633-37.

[17] Edalati K, Toh S, Arita M, Watanabe M, Horita Z. Appl Phys Lett.  High-pressure torsion of pure cobalt: hcp-fcc phase transformations and twinning during severe plastic deformation.2013;102:181902.

[18] Ferreira C, Gene expression programming: a new adaptive algorithm for solving problems, Complex Syst. 2001;13:87–129