Optimizing of micro-hardness of nanostructured Cu–Cr solid solution produced by mechanical alloying using ANN and genetic algorithm

Abstract

In this study, a feed-forward back-propagation artificial neural network (ANN) was designed for the predicting of the micro-hardness of nano-sized Cu-Cr solid solution. The network with 10 and 18 neurons in the first and second hidden layers, respectively, was created based on the 36 extracted data (7 variables and 36 datasets) from a similar study. Then, the genetic algorithm of the effective parameters of mechanical alloying was developed to specify the maximum hardness of Cu-Cr alloys. Consequently, the milling process was performed to validate the created network according to the obtained factors in the genetic algorithm. For this purpose, mechanical alloying was carried out by ball milling of the Cu-Cr powders at 3 and 4.5 weight percentages, respectively. The ball-to-powder weight ratio was kept at 15:1 in the Ar atmosphere and the milling times for Cu-3wt%Cr and Cu-4.5wt%Cr were 48 and 63 h, respectively. Produced powders were studied by scanning electron microscope (SEM) and X-ray diffraction (XRD). Lattice strain, crystallite size, and internal strain were calculated by Rietveld refinement, using the Maud software. Next, the produced powders compressed via a cold press and annealed at 601 °C. The micro-hardness for the Cu-3wt%Cr and Cu-4.5wt%Cr were 228 and 255 Vickers, respectively, while the predicted micro-hardness by the artificial neural network and genetic algorithm were 237 and 243 Vickers, respectively. The root mean square error was 4.25% in the regression of 0.99063 at the proposed sintering temperature. Finally, the result of the sensitivity analysis shows that the milling time, percentage of Cr, and annealing temperature had the highest impact on the micro-hardness of the products.