Fig. 1. (a) Components of an artificial neuron; (b) Schematic diagram of machine learning. The calculated fractions of phases/structures and the measured mechanical properties were set as the input dataset, and the UTS, YS, and EL were the output data.

Fig. 2. Ternary Al-Mg-Sr system. (a) Calculated vertical section from Al35Mg65 to Al7Mg13Mg80 (in wt.%), compared with the experimental data by DSC measurement in Refs. [35,36]. (b) Calculated vertical section along 10 wt.% Sr, compared with the experimental data by DSC measurement in Refs. [35,36]. (c) Calculated isothermal section at 400 °C, compared with the EPMA data at 400 °C from Refs. [35], [36], [37], [38]. All the points represent the solubility of the third element in the boundary binary phases. (d) Comparison between the model-predicted phase transition temperatures due to the thermodynamic database and the experimental data in Refs. [35,36,38]. Along the diagonal line, the model-predicted and the experimental values are exactly equal.

Fig. 3. Quaternary Al-Si-Mg-Sr system. (a) Calculated vertical section of A356-xSr (i.e., 92.6-x)Al-7.0Si-0.4Mg-xSr, in wt.%), compared with the experimental data from the DSC heating curves in the present work. (b) Constructed Scheil-Gulliver solidification diagram of A356-xSr (i.e., (92.6-x)Al-7.0Si-0.4Mg-xSr, in wt.%), compared with the experimental data from the DSC cooling curves in the present work.

Fig. 4. Volume fraction of different phase/structures of as-cast microstructure in A356 alloy with different Sr contents. (a) A1 alloy, (b) A2 alloy, (c) A3 alloy, and (d) A4 alloy. In each sub-figure, the model-predicted volume fractions of (Al), (Si), Mg2Si and Al2Si2Sr phases of the as-cast microstructure are compared with the presently measured data.

Fig. 5. Strategic workflow for presently efficient alloy design approach by combing CT and ML techniques. The fraction of phases/structures calculated from the thermodynamic database and the measured mechanical properties were used as the input data for the machine learning model to establish the relation of “composition-process-microstructure-property”, from which the optimal alloy composition with the best comprehensive mechanical properties was designed. Moreover, the strengthening and toughening mechanisms of Sr-modified A356 alloy were analyzed.

Fig. 6. Alloy design of Sr-modified A356 alloys. (a) Fractions of different phases/structures (i.e., primary (Al), Eutectic (Al), Eutectic (Si), and Al2Si2Sr) in Sr-modified A356 alloy obtained by CT; (b) Mechanical properties of Sr modified A356 alloys. The open symbols represent the measured mechanical properties for machine learning, while the solid lines represent the mechanical properties predicted by machine learning; (c) Quality index of Sr-modified A356 alloys computed from the predicted and the experimental data. The inserted microstructures of A356 alloys without and with 0.005 wt.% Sr show that 0.005 wt.% Sr almost modifies all Si particles from needle-like to finer fibrous morphology; (d) Experimental verification of the predicted optimal Sr additional content (i.e., 0.005 wt.%) and corresponding best mechanical properties. The solid red symbols represent the experimental mechanical properties at the designed optimal alloy composition for validation.

Fig. 7. OM images of A356 alloys with different Sr contents: (a) Basic A356 alloy; (b) 15 ppm Sr; (c) 35 ppm Sr; (d) 50 ppm Sr; (e) 75 ppm Sr; (f) 100 ppm Sr; (g) 140 ppm Sr; (h) 650 ppm Sr; (i) 1000 pm Sr; (j) 2200 ppm Sr; (k) 2400 ppm Sr (l) 2700 ppm Sr. The morphology of Si changes dramatically after the addition of Sr. When the amount of Sr is lower (e.g., 15 ppm), partial Si particles in the alloy transform from needle-like to finer fibrous morphology. As the Sr content increases to e.g., 50 ppm, almost all the Si particles change into finer fibrous morphology; When the content of Sr increases further to 1000 ppm, the coarse plate-like Al2Si2Sr phase appears, while Si particles still own finer fibrous morphology.

Fig. 8. BSE images of A356 alloys with different Sr contents: (a) Basic A356 alloy; (b) 40 ppm Sr; (c) 650 ppm Sr; (d) 1000 ppm Sr; (e) 2200 ppm Sr; (f) 2400 ppm Sr; (g) 2700 ppm Sr; (h) 3600 ppm Sr.

Fig. 9. Relations between different mechanical properties and volume fractions of different phases/structures after standardization. (a) primary α-(Al); (b) eutectic (Al); (c) eutectic (Si); (d) Al2Si2Sr.

Fig. 10. Analysis of strengthening and toughing mechanisms according to CT. (a) Calculated growth restriction factor Q in quaternary alloys A356-xSr; (b) Solidification diagram for Sr-modified A356 alloy constructed from a series of Scheil-Gulliver simulations; (c) Calculated fractions of different phases/structures in A356 alloys with different Sr additional contents; (d) Summary of the bulk modulus of pure Al, pure Si, and Al2Si2Sr due to the first-principles calculations [61].