Fig. 1 FSAM experiment and the schematic diagrams: a experiment of FSAM, b first-pass FSAM, c second-pass FSAM, d third-pass FSAM, e fourth-pass FSAM

Fig. 2 Dimension of the tensile specimen

Fig. 3 Finite element model of friction stir additive manufacturing

Fig. 4 Flowchart of the numerical model: a temperature distribution, b temperature history, c precipitate evolution model, d particle number density, e grain morphology of first layer

Fig. 5 Temperature distribution during FSAM: a temperature measured by IRT system, b comparison of numerical and experimental results, c temperature distribution calculated by finite element model

Fig. 6 Validation of precipitates evolution model: a comparison of hardness between experimental and numerical results, b comparison of stress-strain curves between experimental and numerical results

Fig. 7 Comparison of grain morphologies in SEM b, d, f, h and numerical model a, c, e, g in different additive layers a, b 4th layer, c, d 3rd layer, e, f 2nd layer, g, h 1st layer

Fig. 8 Variations of precipitate hardening and particle number density a, particle number density and mean radius b in 4th additive layer

Fig. 9 Effect of magnesium content on hardness a and constitutive relation b-e in different layers (the first additive layer—b, the second additive layer—c, the third additive layer—d, the fourth additive layer—e)

Fig. 10 Particle number density distribution of different additive layers: a the first additive layer, b the second additive layer, c the third additive layer, d the fourth additive layer

Fig. 11 Effect of magnesium content on volume fraction and average grain size: a the first additive layer, b the second additive layer, c the third additive layer, d the fourth additive layer

Fig. 12 Variation of precipitate hardening and solute hardening a, particle number density and mean radius b

Fig. 13 Effect of silicon content on hardness a and constitutive relation b-e in different layers (the first additive layer—b, the second additive layer—c, the third additive layer—d, the fourth additive layer—e)

Fig. 14 Precipitate number density distribution of different additive layers: a the first additive layer, b the second additive layer, c the third additive layer, d the fourth additive layer

Fig. 15 Effect of silicon content on volume fraction and average grain size: a the first additive layer, b the second additive layer, c the third additive layer, d the fourth additive layer

Fig. 16 Effect of magnesium a and silicon b contents change on mechanical properties of different additive layers