Insights into Temperature and Strain Rate Dependent Deformation Behaviors of BCC Fe from Discrete Dislocation Dynamics Simulations

doi:10.1007/s40195-025-01930-1

Abstract

Abstract:

Despite the promising prospects of body-centered cubic iron (BCC Fe) in aerospace, energy transportation, and nuclear applications, the effects of extreme environments on its mechanical behaviors and deformation mechanisms remain elusive to date. In this work, the mechanical responses and deformation behaviors of BCC Fe single crystals under extreme loading conditions are investigated by performing the three-dimensional discrete dislocation dynamics simulations. It turns out that the yield strength (σ_y) of BCC Fe can be enhanced by increasing the strain rate ($\dot{{\boldsymbol{\varepsilon}}}$) and/or decreasing the deformation temperature (T). With the strain rate increasing from $\dot{{\boldsymbol{\varepsilon}}}$= 10² s⁻¹ to 10⁶ s⁻¹, the yield strength at 300 K rises from σ_y = 51.14 MPa to 1114.57 MPa. When the strain rate exceeds 10³ s⁻¹, an elastic overshoot phenomenon appears because the applied stress and the low initial dislocation density at the early tensile stage cannot drive the plastic deformation immediately. With the temperature increasing from T = 100 K to 800 K, the yield strength at $\dot{{\boldsymbol{\varepsilon}}}$= 10³ s⁻¹ decreases from σ_y = 64.97 MPa to 59.50 MPa. Such temperature and strain rate sensitivity of deformation behaviors are clarified from variations in the configurations of dislocation evolution and dislocation density fluxes. It is demonstrated that at low strain rate ($\dot{{\boldsymbol{\varepsilon}}}$≤ 10³ s⁻¹) conditions, the deformation behaviors of BCC Fe are dominated by the dislocation multi-slip mechanism. With increasing strain rate to e.g., $\dot{{\boldsymbol{\varepsilon}}}$> 10³ s⁻¹, the deformation behaviors are governed by the dislocation single-slip. Our investigation on the temperature and strain rate sensitivity of deformation behaviors provides insightful guidance for optimizing the mechanical performances of BCC Fe based ferritic steels.

Key words: Body-centered cubic iron (BCC Fe), Deformation behaviors, Dislocation evolution, Temperature and strain rate sensitivity, Discrete dislocation dynamics

Yu Liu, Jinglian Du, Jianwei Xiao, Haotian Xue, Kexing Song, Feng Liu. Insights into Temperature and Strain Rate Dependent Deformation Behaviors of BCC Fe from Discrete Dislocation Dynamics Simulations[J]. Acta Metallurgica Sinica (English Letters), 2025, 38(12): 2279-2288.

Figures/Tables 8

Table 1 Initial conditions for the 3D DDD simulations on the uniaxial tensile of the BCC Fe single crystal, including the tensile directions < uvw >, the initial dislocation densities (m−2), the deformation temperature (K), and the strain rate (s−1)

Simulation series	Fixed parameters	Variable parameter	Reference
Tensile directions, < uvw >	ρ₀ = 1.73 × 10¹² m⁻² T = 300 K $\dot{\varepsilon }$= 10³ s⁻¹	< 100 > < 110 > < 111 > < 112 >	[4, 12, 22, 25]
Initial dislocation densities, ρ₀ (m⁻²)	T = 300 K $\dot{\varepsilon }$= 10³ s⁻¹ < uvw > = < 100 >	6.10 × 10¹² 1.73 × 10¹² 8.74 × 10¹²	[4, 22]
Temperature, T (K)	ρ₀ = 1.73 × 10¹² m⁻² $\dot{\varepsilon }$= 10³ s⁻¹ < uvw > = < 100 >	100 300 600 800	[12, 22]
Strain rate, $\dot{\varepsilon }$ (s⁻¹)	ρ₀ = 1.73 × 10¹² m⁻² T = 300 K < 100 > -oriented	10² 10³ 10⁴ 10⁵ 10⁶	[12, 22]

Table 2 Fundamental materials’ parameters for the 3D DDD simulations of the BCC Fe single crystal, including the Poisson’s ratio (v), the Young’s Modulus (E), the Burgers vector (b), and the dislocation radius (r0)

Input parameters	Value	Reference
v	0.291	[4]
E (GPa)	222.052	[49]
b (nm)	0.48	[32]
r₀ (b)	2.9	[49]

Table 3 Temperature-dependent coefficients of the BCC Fe single crystal, including the shear modulus (µ), along with the drag coefficient of screw dislocations (Bs) and edge dislocations (Be)

T (K)	100	300	600	800	Reference
µ (GPa)	86	80	68	60	[31]
B_s (× 10^-4 Pa·s)	2.7	2.6	1.88	2.5	[31, 32]
B_e (× 10^-4 Pa·s)	1.7	0.94	1.88	2.5	[31, 33]

Fig. 1 Stress-strain curves of the BCC Fe single crystal under different loading conditions: a tensile curves along < 100 >, < 112 >, < 110 >, and < 111 > orientations; b tensile curves at the initial dislocation densities of ρ0 = 6.10 × 1012 m−2, 1.73 × 1012 m−2, and 8.74 × 1011 m−2, respectively

Fig. 2 Stress–strain curves and the dislocation density evolution curves of the BCC Fe single crystal under different temperature and strain rate conditions: a1 tensile curves and a2 dislocation density evolution curves at deformation temperatures of T = 100 K, 300 K, 600 K, and 800 K, respectively; b1 tensile curves and b2 dislocation density evolution curves at low strain rates of $\dot{\varepsilon }$= 102 s−1 and 103 s−1, respectively; c1 tensile curves and c2 dislocation density evolution curves at high strain rates of $\dot{\varepsilon }$= 104 s−1, 105 s−1, and 106 s−1, respectively

Fig. 3 Snapshots for dislocation configurations and dislocation distributions in the BCC Fe single crystal at different magnitudes of strain under different loading temperatures T and strain rates $\dot{\varepsilon }$: a(i)–a(iii) T = 100 K and $\dot{\varepsilon }$= 103 s−1; b(i)-b(iii) T = 800 K $\dot{\varepsilon }$= 103 s−1; c(i)-c(iii) T = 300 K and $\dot{\varepsilon }$= 103 s−1; d(i)-d(iii) T = 300 K $\dot{\varepsilon }$= 106 s−1

Fig. 4 Dislocation density fluxes of BCC Fe for each type of dislocation, characterized by different Burgers vectors (including b1 = 1/2[111], b2 = 1/2[${\bar{1}}11$], b3 = 1/2[$1{\bar{1}}1$], b4 = 1/2[$11{\bar{1}}$]) under different loading temperatures T and strain rates $\dot{\varepsilon }$: a T = 100 K and $\dot{\varepsilon }$= 103 s−1; b T = 800 K and $\dot{\varepsilon }$= 103 s−1; c T = 300 K and $\dot{\varepsilon }$= 103 s−1; d T = 300 K $\dot{\varepsilon }$= 106 s−1, respectively

Fig. 5 Variations in the yield strength and flow stress of the BCC Fe single crystal with respect to deformation temperature and strain rate: a yield strength of the BCC Fe single crystal at the strain rate of 103 s−1 under different deformation temperatures, T = 100 K, 300 K, 600 K, and 800 K; b yield strength and flow stress at deformation temperature of 300 K under different strain rates, including $\dot{\varepsilon }$= 102 s−1, 103 s−1, 104 s−1, 105 s−1, and 106 s−1, respectively; The inset in b presents the double logarithmic plot of yield strength as a function of strain rate for determining the strain rate sensitivity m of BCC Fe single crystal at 300 K

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