Fig. 1. Related thermodynamic data of Ti-V alloys. (a) Chemical-free energy curves of the α and β phases for Ti-V alloys at different temperatures with constant average composition. (b) Values of c0 at various temperatures for Ti-V alloys with constant average composition.

Fig. 2. SEM observation and related mechanical properties of Ti1023 after aging at different temperatures. (a-c) Microstructures after aging at (a) 650 °C, (b) 600 °C, (c) 550 °C. (d) Related stress-strain curves of Ti1023 alloys after aging at 650, 600, 550, 450, 350 °C, respectively. (e) Ultimate tensile strength vs. elongation for Ti1023 after aging at different temperatures (650, 600, 550, 450, 350 °C).

Fig. 3. Calculated microstructures of α precipitates and statistical results under different two-step aging simulations. (a-c) Microstructure evolution of the composition field at 650 °C for t* = 100 and followed by aging at 550 °C for t* = 100 and t* = 1000. (d-f) Microstructure evolution of the composition field at 650 °C for t* = 200 and followed by aging at 550 °C for t* = 100 and t* = 1000. (g-i) Microstructure evolution of the composition field at 650 °C for t* = 300 and followed by aging at 550 °C for t* = 100 and t* = 1000. (j) Schematic drawing of the two-step aging simulation processes. (k, l) The related length distribution of α precipitates for two-step aging simulations with different simulation time.

Fig. 4. CPFEM calculation of the true strain-true stress curves of Ti-V alloy for different heat treatments at room temperature along with different directions (x = [101] and y = [$1\bar{2}\bar{1}$]), and “+” represents tension and “-” represents compression. Homogeneous microstructure (i.e., Fig. 2(f)) is defined as conventional aging, and heterogeneous microstructure (i.e., Fig. 3(i)) is defined as two-step aging.

Fig. 5. Typical experimental results of model materials Ti-1023 samples after different heat treatments. (a) Ultimate tensile strength versus elongation of Ti1023 alloys under different heat treatments. (b) SEM micrograph for the whole microstructure with a mixture of fine α precipitates and coarse α precipitates after two-step aging. (c) Enlarged SEM micrograph for the coarse α precipitates. (d) Enlarged SEM micrograph for the fine α precipitates. (e) Stress-strain curves for different heat treatments (black, red and blue curves represent the conventional single temperature aging at 550 °C/500 °C, two-step aging at 650 °C for 10 min and at 550 °C for 3 h, two-step aging at 650 °C for 10 min and at 500 °C for 3 h, respectively).

Fig. 6. SEM observations of Ti1023 after two-step aging with different heat treatment conditions. (a-c) SEM observations of Ti1023 after two-step aging with different second-step temperatures. (d-f) SEM observations of Ti1023 alloys after two-step aging with different first-step temperatures. (g-i) SEM observations of Ti1023 alloys after two-step aging with different first-step time.

Fig. 7. Dependence of yield strength and total elongation of Ti1023 on the volume fraction of α phase and the size of α phase after single-step aging and two-step aging. (a) Yield strength vs. the volume fraction of α phase and the average size of α phase after single-step aging at different temperatures (650-550 °C). The insert shows the volume fraction of α phase at different temperatures. (b) Yield strength vs. the volume fraction and size of coarse and fine α phase after different two-step aging processes. The insert shows the volume fraction of coarse and fine α phase after different two-step aging processes. (c) Total elongation vs. the volume fraction of α phase and the average size of α phase after single-step aging at different temperatures. The insert shows the average size of α phase at different temperatures. (d) Total elongation vs. the volume fraction and size of the coarse and fine α phase after different two-step aging processes. The insert shows the average size of coarse and fine α phase after different two-step aging processes.

Fig. 8. Tensile fracture surface morphology for heterogeneous microstructure after two-step aging. (a) Low magnification of fracture surface morphology, and enlarged fracture surface morphology for the region (b) and region (c) in (a).

Fig. 9. TEM observations of the microstructure and dislocation distribution for heterogeneous microstructure after two-step aging. (a) Bright field image of deformation twinning in coarse α precipitates. (b) Diffraction pattern of SAED1 region for deformation twin in coarse α precipitates. (c) Corresponding dark field image of deformation twinning from diffraction spot (white circle) in (b). (d) Dislocation distribution in coarse α precipitates. (e) Dislocation distribution in fine α precipitates.

Fig. 10. Chemical-free energy curves of two phases (α and β) at two aging temperatures in two-step aging simulation and the statistical distribution of concentration after first-step aging. (a) A close-up of the free energy curves of the α phase and β phase at T1 = 650 °C and T2 = 550 °C with the value of C0 5.2% and 7.2%, respectively. The black dotted line marks the initial average concentration Ca = 7.5%. The insert figure shows the linear relationship between C0 and temperature. (b) Statistical distribution of concentration after aging at 650 °C with different simulation time steps (t* = 0, 10, 100, 200, 300, 1000). The purple dotted line marks the value of C0 at the second-step temperature (550 °C). (c) Statistical distribution of concentration after aging at 550 °C with different simulation time step (t* = 0, 1, 2, 3, 4, 5, 10, 1000). (d) Statistical distribution of concentration after aging at different temperatures (650, 640, 630, 620, 610, 600 °C) with constant simulation time step (t* = 100) in the first stage. The purple dotted line marks the value of C0 at the second-step temperature (550 °C).

Fig. 11. Calculated α precipitate morphology under different two-step aging simulations. (a, b) The two-step aging process with 650 °C/t* = 1000 plus 550 °C/t* = 100. (c-n) The two-step aging process with T = 650 °C to 600 °C/t* = 100 plus 550 °C/t* = 100.

Fig. 12. Von Mises stress and true strain of Ti-V system for homogeneous and heterogeneous microstructures after room temperature tensile deformation along x-direction ([101]) 10% elongation by using of CPFEM method. (a1, d1) Von Mise stress and true strain of the whole homogeneous microstructures with coarse α precipitates from Fig. 2(b’), respectively. (b1, e1) Mises stress and true strain of the whole homogeneous microstructures with fine α precipitates from Fig. 2(f’), respectively. (c1, f1) Mises stress and true strain of the whole heterogeneous microstructures from Fig. 3(i’), respectively. (a2) (b2) (c2) (d2) (e2) (f2) show the stress or strain distribution of α phase part corresponding to (a1) (b1) (c1) (d1) (e1) (f1).

Fig. 13. Von Mise stress and true strain of Ti-V system for homogeneous and heterogeneous microstructures after tensile deformation along x-direction ([101]) 0.5%, 5% and 10% elongation by using of CPFEM method. (a-c) Von Mise stress and (g-i) true strain of the whole homogeneous microstructures after 0.5%, 5% and 10% deformation. (d-f) Von Mise stress and (j-l) true strain of the whole heterogeneous microstructures after 0.5%, 5% and 10% deformation.