Optimization of micro hardness of nanostructure Cu-Cr-Zr alloys prepared by the mechanical alloying using artificial neural networks and genetic algorithm

Document Type: Research Paper


Department of Materials Science and Engineering, Shahid Bahonar University of Kerman, Kerman, Iran.


Cu–Cr-Zr alloys had wide applications in engineering applications such as electrical and welding industrial especially for their high strength, high electrical as well as acceptable thermal conductivities and melting points. It was possible to prepare the nano-structure of these age hardenable alloys using mechanical alloying method as a cheap and mass production technique to prepare the non-equilibrium materials such as solid solution structures. In this study, artificial neural networks (ANNs) program was developed to establish the relationship between the practical parameters of mechanical alloying, i.e., weight percentages of Cr and Zr as alloying element, milling times, milling speed, sintering time and temperature, on the micro hardness of prepared Cu-Cr-Zr nanostructure alloys. The results of sensitivity analysis showed that the alloying elements and sintering temperature had the highest and lowest effect on the micro hardness of products, respectively. Also, the optimum milling speed and sintering temperature proposed as 255-291 rpm and 530-590°C, respectively. The established models of ANN introduced to genetic algorithm (GA) for determination of the optimal condition. The results were evaluated using the confirmation experiments. Moreover, the optimal condition of nanostructures alloy preparation with the highest micro hardness had been proposed as 310 Hv with the root mean square error (RMSE) of lower than 3.4%.


  1. Wright RN, Anderson IE. Age-hardening behavior of dynamically consolidated rapidly solidified Cu-2%Zr powder. Materials Science and Engineering: A. 1989;114:167-72.
  2. Wang W, Li R, Zou C, Chen Z, Wen W, Wang T, et al. Effect of direct current pulses on mechanical and electrical properties of aged Cu–Cr–Zr alloys. Materials & Design. 2016;92:135-42.
  3. Holzwarth U, Stamm H. The precipitation behaviour of ITER-grade Cu–Cr–Zr alloy after simulating the thermal cycle of hot isostatic pressing. Journal of Nuclear Materials. 2000;279(1):31-45.
  4. Wang N, Li C, Du Z, Wang F, Zhang W. The thermodynamic re-assessment of the Cu–Zr system. Calphad. 2006;30(4):461-9.
  5. Holzwarth U, Stamm H, Pisoni M, Volcan A, Scholz R. The recovery of tensile properties of CuCrZr alloy after hot isostatic pressing. Fusion Engineering and Design. 2000;51-52:111-6.
  6. Abib K, Larbi FH, Rabahi L, Alili B, Bradai D. DSC analysis of commercial Cu–Cr–Zr alloy processed by equal channel angular pressing. Transactions of Nonferrous Metals Society of China. 2015;25(3):838-43.
  7. Fuxiang H, Jusheng M, Honglong N, Zhiting G, Chao L, Shumei G, et al. Analysis of phases in a Cu–Cr–Zr alloy. Scripta Materialia. 2003;48(1):97-102.
  8. Wang Z-q, Zhong Y-b, Rao X-j, Wang C, Wang J, Zhang Z-g, et al. Electrical and mechanical properties of Cu–Cr–Zr alloy aged under imposed direct continuous current. Transactions of Nonferrous Metals Society of China. 2012;22(5):1106-11.
  9. León KV, Muñoz-Morris MA, Morris DG. Optimisation of strength and ductility of Cu–Cr–Zr by combining severe plastic deformation and precipitation. Materials Science and Engineering: A. 2012;536:181-9.
  10. Mughrabi H. On the Grain-Size Dependence of Metal Fatigue: Outlook on the Fatigue of Ultrafine-Grained Metals. Investigations and Applications of Severe Plastic Deformation: Springer Netherlands; 2000. p. 241-53.
  11. Xia C, Jia Y, Zhang W, Zhang K, Dong Q, Xu G, et al. Study of deformation and aging behaviors of a hot rolled–quenched Cu–Cr–Zr–Mg–Si alloy during thermomechanical treatments. Materials & Design. 2012;39:404-9.
  12. Datta S, Chattopadhyay PP. Soft computing techniques in advancement of structural metals. International Materials Reviews. 2013;58(8):475-504.
  13. Dashtbayazi MR. Characterization of Al/SiC Nanocomposite Prepared by Mechanical Alloying Process Using Artificial Neural Network Model. Materials and Manufacturing Processes. 2007;23(1):37-45.
  14. Zhu X, He R, Lu X, Ling X, Zhu L, Liu B. A optimization technique for the composite strut using genetic algorithms. Materials & Design (1980-2015). 2015;65:482-8.
  15. Jenab A, Sari Sarraf I, Green DE, Rahmaan T, Worswick MJ. The Use of genetic algorithm and neural network to predict rate-dependent tensile flow behaviour of AA5182-O sheets. Materials & Design. 2016;94:262-73.
  16. Mozaffari S, Li W, Thompson C, Ivanov S, Seifert S, Lee B, et al. Colloidal nanoparticle size control: experimental and kinetic modeling investigation of the ligand–metal binding role in controlling the nucleation and growth kinetics. Nanoscale. 2017;9(36):13772-85.
  17. Varol T, Canakci A, Ozsahin S. Artificial neural network modeling to effect of reinforcement properties on the physical and mechanical properties of Al2024–B4C composites produced by powder metallurgy. Composites Part B: Engineering. 2013;54:224-33.
  18. Rashidi AM, Hayati M, Rezaei A. Application of artificial neural network for prediction of the oxidation behavior of aluminized nano-crystalline nickel. Materials & Design. 2012;42:308-16.
  19. Vettivel SC, Selvakumar N, Leema N. Experimental and prediction of sintered Cu–W composite by using artificial neural networks. Materials & Design. 2013;45:323-35.
  20. Ates H. Prediction of gas metal arc welding parameters based on artificial neural networks. Materials & Design. 2007;28(7):2015-23.
  21. Asadi P, Givi MKB, Rastgoo A, Akbari M, Zakeri V, Rasouli S. Predicting the grain size and hardness of AZ91/SiC nanocomposite by artificial neural networks. The International Journal of Advanced Manufacturing Technology. 2012;63(9-12):1095-107.
  22. Zare M, Vahdati Khaki J. Prediction of mechanical properties of a warm compacted molybdenum prealloy using artificial neural network and adaptive neuro-fuzzy models. Materials & Design. 2012;38:26-31.
  23. Muthukrishnan N, Davim JP. Optimization of machining parameters of Al/SiC-MMC with ANOVA and ANN analysis. Journal of Materials Processing Technology. 2009;209(1):225-32.
  24. Yang L, Wang B, Liu G, Zhao H, Xiao W. Behavior and modeling of flow softening and ductile damage evolution in hot forming of TA15 alloy sheets. Materials & Design. 2015;85:135-48.
  25. Jiang B, Zhang F, Sun Y, Zhou X, Dong J, Zhang L. Modeling and optimization for curing of polymer flooding using an artificial neural network and a genetic algorithm. Journal of the Taiwan Institute of Chemical Engineers. 2014;45(5):2217-24.
  26. Ghasemian N, Kalbasi M, Pazuki G. Experimental Study and Mathematical Modeling of Solubility of CO2in Water: Application of Artificial Neural Network and Genetic Algorithm. Journal of Dispersion Science and Technology. 2013;34(3):347-55.
  27. Anijdan SHM, Bahrami A, Hosseini HRM, Shafyei A. Using genetic algorithm and artificial neural network analyses to design an Al–Si casting alloy of minimum porosity. Materials & Design. 2006;27(7):605-9.
  28. Wong KP. Genetic and genetic/simulated-annealing approaches to economic dispatch. IEE Proceedings - Generation, Transmission and Distribution. 1994;141(5):507.
  29. Shojaeefard MH, Akbari M, Tahani M, Farhani F. Sensitivity Analysis of the Artificial Neural Network Outputs in Friction Stir Lap Joining of Aluminum to Brass. Advances in Materials Science and Engineering. 2013;2013:1-7.
  30. Liu G, Jia L, Kong B, Guan K, Zhang H. Artificial neural network application to study quantitative relationship between silicide and fracture toughness of Nb-Si alloys. Materials & Design. 2017;129:210-8.
  31. Inoue A. Amorphous, nanoquasicrystalline and nanocrystalline alloys in Al-based systems. Progress in Materials Science. 1998;43(5):365-520.
  32. McHenry ME, Willard MA, Laughlin DE. Amorphous and nanocrystalline materials for applications as soft magnets. Progress in Materials Science. 1999;44(4):291-433.
  33. Yoshizawa Y, Oguma S, Yamauchi K. New Fe‐based soft magnetic alloys composed of ultrafine grain structure. Journal of Applied Physics. 1988;64(10):6044-6.
  34. Clavaguera-Mora MT, Clavaguera N, Crespo D, Pradell T. Crystallisation kinetics and microstructure development in metallic systems. Progress in Materials Science. 2002;47(6):559-619.
  35. Bruna P, Crespo D, González-Cinca R, Pineda E. Effects of Soft-Impingement and Non-random Nucleation on the Kinetics and Microstructural Development of Primary Crystallization. Solid State Transformation and Heat Treatment: Wiley-VCH Verlag GmbH & Co. KGaA; 2005. p. 126-34.