Unraveling the Discontinuous Dynamic Recrystallization of the TC17 Titanium Alloy during Hot Deformation by Crystal Plasticity Modeling

doi:10.1007/s40195-025-01927-w

Abstract

Abstract:

A dislocation density-based crystal plasticity finite element (CPFE) model is developed to reveal the mechanism of discontinuous dynamic recrystallization (DDRX) of the TC17 dual-phase titanium alloy during hot deformation. The model incorporates the temperature and strain rate dependence of nucleation, growth and evolution during DDRX. The evolution of the dislocation densities in the matrix grains (MGs) and the recrystallized grains (RGs) is considered individually. The mechanical response and underlying microstructural evolution are systematically investigated by comparing the CPFE model predictions with experimental tests. The results indicate that at lower temperatures (700 °C and 800 °C), TC17 titanium alloy exhibits a higher volume fraction of recrystallization and a notable drop in flow stress. As the temperature increases (900 °C and 1000 °C), the volume fraction of recrystallization decreases, resulting in a weakened flow stress softening. The nucleation rate of DDRX increases with decreasing deformation temperature and increasing strain rate, while the size of RGs increases with higher temperature and lower strain rate. DDRX nuclei primarily occur at grain boundaries with high dislocation density. Furthermore, DDRX consumes a large number of dislocations and thus reduces the stress concentration and dislocation density at grain boundaries. This study provides a robust model that enhances the understanding of hot deformation mechanisms and informs the design of high-performance titanium alloys for future applications.

Key words: Crystal plasticity, Dual-phase titanium alloy, Discontinuous dynamic recrystallization, Dislocation density

Xiangru Guo, Jian Zhang, Tieqiang Kong, Junjie Shen, Qingjian Liu, Chaoyang Sun, Peipei Li. Unraveling the Discontinuous Dynamic Recrystallization of the TC17 Titanium Alloy during Hot Deformation by Crystal Plasticity Modeling[J]. Acta Metallurgica Sinica (English Letters), 2025, 38(12): 2243-2264.

Figures/Tables 21

Table 1 Chemical composition of TC17 titanium alloy

Al	Mo	Cr	Sn	Zr	Ti
5.0	4.0	3.9	2.1	2.2	Bal.

Fig. 1 Hot compression experiments of TC17 titanium alloy under different loading conditions: a schematic of hot deformation procedure, b experimental setup

Fig. 2 IPF maps, phase diagrams and grain size charts for: a1, b1, c1 initial samples, a2, b2, c2 samples held at 700 °C for 5 min, a3, b3, c3 samples held at 1000 °C for 5 min

Fig. 3 Pole figure obtained in the samples after 5-min holding at a 700 °C and b 1000 °C

Fig. 4 Schematic diagram of DDRX mechanisms in TC17 titanium alloy during hot deformation. The black lines represent grain boundaries, light gray areas indicate the α phase, dark gray areas represent the β phase, and yellow grains symbolize RGs

Table 2 Model constants with physical meanings

Physical meaning	Symbol	Value		References
Elastic constants (α-Ti) (GPa)	C₁₁, C₁₂, C₁₃, C₃₃, C₄₄	160, 86, 55, 183, 54		[60]
Elastic constants (β-Ti) (GPa)	C₁₁, C₁₂, C₄₄	130.2, 70.6, 45.8		[60]
Reference shear strain rate (s⁻¹)	$\dot{\gamma }_{0}$	0.001		[61]
Strain rate sensitivity exponent	m	0.08		[61]
Number of slip systems	N_s	3 (α), 12 (β)		[11]
Magnitude of Burgers vector (nm)	b	0.295 (α)		[11]
Magnitude of Burgers vector (nm)	b	0.286 (β)
Diffusion activation energy (J mol⁻¹)	Q_diffu	150 × 10³		[13]
Ideal gas constant (J K⁻¹ mol⁻¹)	R	8.314		[13]
Boltzmann constant (J K⁻¹)	K_B	1.38 × 10^-23		[66]
Activated energy for deformation (J mol⁻¹)	Q_deform	150 × 10³		[11]
Poisson’s ratio	ν	0.3		[64]
Critical temperature for phase transition (°C)	T_β	890		[40]
Interaction coefficients for slip	A_αα´		I: 0.122, II: 0.122, III: 0.625, IV: 0.07, V: 0.137, VI: 0.122	[63]
Activated energy for nucleation (J mol⁻¹)	Q_act	140 × 10³		[11]
Melting point temperature (°C)	T_m	1640		[67]
Product of boundary thickness and diffusion coefficient (m³ s⁻¹)	δD_0b	2.0 × 10^-13		[11]
Initial dislocation density (m⁻²)	ρ₀	9.0 × 10¹³ (700 °C), 1.7 × 10¹³ (800 °C), 1.0 × 10¹³ (900 °C), 1.5 × 10¹² (1000 °C)
Initial grain size (µm)	r₀	2.5 ( 700 °C), 6 (800 °C), 20 (900 °C), 55 (1000 °C)
Dynamic recovery coefficient	$k_{{\text{M}}}^{\alpha }$, $k_{{\text{R}}}^{\alpha }$	2.0 × 10^-5, 1.0 × 10^-4

Table 3 Parameters determined by fitting experimental data

Symbol	Value	Symbol	Value
c₀	0.15	c₉	0.1
c₁	1 × 10³	c₁₀	2.0 × 10^-6
c₂	0.5 [12]	c₁₁	2.2
c₃	1.2 × 10⁴	ω	0.24
c₄	1.1	$k_{1}^{\alpha }$	0.025
c₅	5 × 10^-5	θ	− 3 × 10^-4
c₆	8.5 × 10³	n^α	2
c₇	0.16	$k_{{\text{M}}}^{\alpha }$	2.0 × 10^-5
c₈	10	$k_{{\text{R}}}^{\alpha }$	1.0 × 10^-4

Fig. 5 a Initial grain size after 5 min of holding, b initial volume fraction of α phase under different temperatures, c dislocation density after 5-min holding

Fig. 6 a Schematic of dual-phase polycrystalline model, b boundary conditions applied in the hot compression simulation of TC17 titanium alloy

Fig. 7 IPFs and microstructure angles under different temperature and strain rate loading conditions: a T = 700 °C, strain rate = 0.01 s−1; b T = 700 °C, strain rate = 1 s−1; c T = 800 °C, strain rate = 0.01 s−1; d T = 800 °C, strain rate = 1 s−1; e T = 900 °C, strain rate = 0.01 s−1; f T = 900 °C, strain rate = 1 s−1; g microstructure angle curves at different temperatures; h T = 1000 °C, strain rate = 1 s−1

Fig. 8 KAM maps under different temperature conditions with a strain rate of 1 s−1: a1 at 700 °C in the MG, a2 at 700 °C in the RG, b1 at 1000 °C in the MG, b2 at 700 °C in the RG, a3 IQ + GOS map under the condition of 700 °C, b3 a magnified view of a3 and the corresponding phase diagram

Fig. 9 Mechanical responses of TC17 titanium alloy under different temperatures and strain rates loading conditions: a 700 °C, b 800 °C, c 900 °C, d 1000 °C

Fig. 10 Evolution of the dislocation density in the MGs, RGs and the critical dislocation density (ρc) in TC17 titanium alloy under different temperatures and strain rates: a 700 °C, b 800 °C, c 900 °C, d 1000 °C

Fig. 11 Nuclei generated in unit surface area (1 µm2) of TC17 titanium alloy under different temperatures and strain rates: a 700 °C, b 800 °C, c 900 °C, d 1000 °C

Fig. 12 Comparison between the simulated (Sim) and experimentally (Exp) measured recrystallization volume fractions

Fig. 13 a RG size (Exp), b MG size (Exp), c RG size (Sim), d MG size (Sim) in hot compressed TC17 titanium alloy at different temperatures and strain rates

Fig. 14 Stress distribution under different temperature conditions: a 700 °C, b 800 °C, c 900 °C, d 1000 °C. The calculation conditions are performed under a constant strain of 0.8 and a strain rate of 1 s−1

Fig. 15 Recrystallization distribution under different temperatures and strain: a1 at a strain of 0.4 and temperature of 700 °C; a2 at a strain of 0.8 and temperature of 700 °C; b1 at a strain of 0.4 and temperature of 1000 °C; b2 at a strain of 0.8 and temperature of 1000 °C

Fig. 16 Evolution of recrystallization fraction and Mises stress in the MN region during DDRX

Fig. 17 Dislocation density distribution in the RGs under various temperature conditions: a 700 °C, b 800 °C, c 900 °C, d 1000 °C. The calculations are performed under a constant strain of 0.8 and a strain rate of 1 s−1

Fig. 18 Dislocation density distribution in the MGs under various temperature conditions: a 700 °C, b 800 °C, c 900 °C, d 1000 °C. The calculations are performed under a constant strain of 0.8 and a strain rate of 1 s−1

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