Integrated optimization of mechanical alloying parameters for nanostructured Ti-Mg-Zr alloy using desirability function, educational competition, and grey wolf algorithms

• Synthesized a Ti-Mg-Zr nanostructured alloy via mechanical alloying for biomedical use. • XRD, SEM, and TEM analyses confirmed nano-grain boundaries in the morphology. • Integrated DFA-ECO-GWO optimization reduce CS by 28.6 nm and increase LS by 0.812 %. • Empirical equations predicted outcomes with 3.88 % deviation for CS and 3.34 % for LS. • An inverse correlation showed CS decreases by ∼142.3 nm for each 1 % increase in LS. The present study aims to develop a novel nanostructured ternary Ti-Mg-Zr alloy using a mechanical alloying (MA) process designed for biomedical applications. The Ti-Mg-Zr alloy was designed with the desirable characteristics of Titanium offering the highest biocompatibility (among all metallic materials), Magnesium (Mg) possessing lightweight characteristics with improved strength and elastic compatibility with bone, Zirconium (Zr) minimizes the magnetic resonance imaging (MRI) artefacts and improved corrosion resistance. Synthesizing and retaining nanostructure in alloy development requires appropriate control of MA parameters such as milling speed (MS), milling time (MT), and ball-to-powder-weight ratio (BPR). Experiments are designed with simultaneously varying parameters and levels to collect the developed alloy's overall performance (crystallite size, CS, and lattice strain, LS). MS showed a dominant effect, followed by MT and BPR towards CS and LS. The model produced a better coefficient of determination (0.9908 for CS and 0.9803 for LS), resulting in the average absolute percent deviation in predicting ten random experimental cases equal to 3.88 % for CS and 3.34 % for LS. The best-fit curve drawn with 1000 data points resulted in the CS establishing a strong linear inverse relationship (correlation coefficient of 0.9821) with LS. The complex interplay (BPR exhibited non-linear behaviour, while MS and MT demonstrated linear relationships with both CS and LS) among MA parameters require solving conflicting responses (simultaneously minimizing CS and maximizing LS). Educational competition optimizer (ECO) and grey wolf optimizer (GWO) integrated with desirability function approach (DFA) determined single optimal conditions (MS: 400 rpm; MT: 30 h, and BPR: 10) resulted in the highest composite desirability value (say 1) with reduced CS of 26.73 nm, and higher LS of 0.816 %. The experimental value of CS and LS corresponding to optimal conditions is found to be equal to 28.6 nm and 0.812 %, respectively. GWO converges marginally faster than ECO in locating the highest composite desirability value. Morphological analysis of powdered samples was carried out using XRD, SEM and TEM. The minimum CS and maximum LS ensure nanostructure in synthesized Ti-Mg-Zr alloy and are treated as promising alloys for permanent implants that require frequent MRI assessments.