Phase Field and Crystal Plasticity Simulation of Irradiation-Induced He Bubbles Evolution and Mechanical Behavior in 316H Steel and Weld Metal

doi:10.11900/0412.1961.2025.00239

Acta Metall Sin

2026, Vol. 62

Issue (1): 173-190 DOI: 10.11900/0412.1961.2025.00239

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Phase Field and Crystal Plasticity Simulation of Irradiation-Induced He Bubbles Evolution and Mechanical Behavior in 316H Steel and Weld Metal

WANG Dong¹^,²^,³, XU Lianyong¹^,²^,³(

), ZHAO Lei¹^,²^,³(

), HAN Yongdian¹^,²^,³, SONG Kai¹^,²^,³

1 School of Materials Science and Engineering, Tianjin University, Tianjin 300350, China
2 Tianjin Key Laboratory of Advanced Joining Technology, Tianjin 300350, China
3 State Key Laboratory of High Performance Roll Materials and Composite Forming, Tianjin 300350, China

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WANG Dong, XU Lianyong, ZHAO Lei, HAN Yongdian, SONG Kai. Phase Field and Crystal Plasticity Simulation of Irradiation-Induced He Bubbles Evolution and Mechanical Behavior in 316H Steel and Weld Metal. Acta Metall Sin, 2026, 62(1): 173-190.

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Abstract

316H steel is an important structural material candidate for Generation-IV advanced nuclear reactors. During service, the material operates under conditions of high temperature, irradiation, and complex stress for extended durations, and the working environment is extremely harsh. In particular, He bubbles, generated through nuclear transmutation under irradiation, can cause severe irradiation embrittlement and accelerate the failure of the material. To clarify the role of He bubbles in the degradation of 316H steel and weld metal, this study proposes a coupled computational framework that integrates the phase field model and crystal plasticity. Within this framework, the nucleation, growth, and coalescence of He bubbles in 316H steel and weld metal were simulated, and their mechanical responses were systematically analyzed. The research shows that He bubbles nucleate and grow by absorbing supersaturated vacancies and He atoms. In the later stage, they grow through coalescence and Ostwald ripening processes. As the He bubble size increases, the internal pressure gradually decreases until reaching an equilibrium state. The high density of dislocations in the weld metal, which preferentially absorb interstitial atoms, results in an increased vacancy concentration. Meanwhile, dislocations act as rapid diffusion channels. These two factors together contribute to the rapid growth of He bubbles. An increase in diffusion capacity does not change the final proportion of He bubbles; instead, it accelerates the nucleation and growth processes, thereby promoting the kinetic evolution of He bubbles in the weld metal. At small strains, the stress-strain response is governed by the effects of external strain and the internal pressure of He bubbles, with the macroscopic stress value being negative. As the external strain increases, the stress-strain response becomes influenced by the external strain. During tensile deformation, significant stress concentration arises at the He bubble-matrix interface, leading to considerable plastic deformation in these regions. At 4% applied strain, distinct plastic deformation bands form in both 316H steel and the weld metal. However, due to strain localization in the weld metal, the degree of plastic deformation is greater than that observed in 316H steel.

Key words: 316H steel weld metal irradiation He bubble phase field simulation

Received: 20 August 2025

ZTFLH:

TG47

Fund: National Funds for Distinguished Young Scholars(52025052)

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	WANG Dong
	XU Lianyong
	ZHAO Lei
	HAN Yongdian
	SONG Kai

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https://www.ams.org.cn/EN/10.11900/0412.1961.2025.00239 OR https://www.ams.org.cn/EN/Y2026/V62/I1/173

Table 1 Chemical compositions of the 316H base metal and welding wuire

Fig.1 Microstructures of 316H base metal and weld metal (WM)
(a, b) EBSD inverse pole figures (IPFs) of 316H steel (a) and 316H WM (b) (c, d) TEM images of dislocations in 316H steel (c) and in 316H WM (d) (e) TEM image of δ-ferrites in 316H WM

Fig.2 Equilibrium concentration of He atoms in the bubble vs bubble radius of 316H steel at the temperature (T) of 550 ^oC

Parameter	Value	Unit
V_a^[32]	7.06	cm³·mol^-1
$E v f$ ^[12]	3.2 × 10^-19	J
$E g f$ ^[12]	6.4 × 10^-19	J
Ω^[32]	1.17 × 10^-29	m³
b_v^[33]	0.039	nm³·atom^-1
a^[33]	0.0034	J·m³·mol^-2
γ_s^[34]	1.82	J·m^-2

Table 2 Thermodynamic parameters used in phase field simulation^[12,32-34]

Fig.3 Free energy densities of matrix (a) and He bubble (b) at 550 ^oC in the phase field model of He bubble evolution

Fig.4 Flow chart of phase field and crystal plasticity simulation of He bubbles

Parameter	Value	Unit
K_HP^[39]	1.1	MPa· $m$
d_grain	50 (base), 100 (weld)	μm
ρ	1 × 10¹² (base), 6 × 10¹³ (weld)	m^-2
$γ ˙ 0$ ^[24]	1 × 10^-3	s^-1
n^[53]	5	-
k_mul	0.03 (base), 0.02 (weld)	-
R_cp	2 × 10^-9	nm
β_p	0.015 (base), 0.01 (weld)	–
k_recov	200	–
C₁₁, C₁₂, C₄₄	157, 114, 99	GPa
μ^[39]	88 - 3 × 10^-5T² - 5.6 × 10^-3T	GPa

Table 3 Parameters used in crystal plasticity model

Fig.5 Evolution of a single bubble in the supersaturated matrix (The color bar implies the values of He concentration (c_g) and vancay concentration (c_v), the same in Fig.6; Δx^*—dimexsionless length scale)
(a-c) He concentration fields under t^* = 0 (a), t^* = 10 (b), and t^* = 80 (c) (t^*—dimensionless time) (d-f) vacancy concentration fields under t^* = 0 (d), t^* = 10 (e), and t^* = 80 (f) (g-i) profiles of He and vacancy concentrations across the He bubble under t^* = 0 (g), t^* = 10 (h), and t^* = 80 (i)

Fig.6 Evolutions of multiple He bubbles under irradiation
(a-d) He concentration fields under He concentrations of 0.007 (a), 0.01 (b), 0.015 (c), and 0.04 (d) (e-h) vacancy concentration fields under He concentrations of 0.007 (e), 0.01 (f), 0.015 (g), and 0.04 (h) (The circular area B in Fig.6g implies the Ostwald ripening and the elliptical area A in Fig.6h implies the coalescence)

Fig.7 Evolution of porosity and number of He bubbles under irradiation (The area Ⅰ is nucleation incubation stage, area Ⅱ is nucleation and growth stage, and Ⅲ is coarsening stage. JMAK—Johnson-Mehl-Avrami-Kolmogorov)

Fig.8 Pressure evolution (a) and He concentration evoution (b) inside the He bubble during the growth of He bubble (EOS—equation of state)

Fig.9 Comparison of He bubble microstructures between experiment (a-d) and phase field simulation (a1-d1)
(a, a1, b, b1) He bubble in 316H steel under the He concentrations of 0.01 (a, a1) and 0.04 (b, b1)
(c, c1, d, d1) He bubble in 316H WM under the He concentrations of 0.01 (c, c1) and 0.04 (d, d1)

Fig.10 Quantitative statistical comparisons of diameter evolution (a, c) and diameter distribution (He concentration is 0.04) (b, d) of He bubbles in 316H steel (a, b) and 316H WM (c, d)

Fig.11 He bubble under different ratios of vacancy to He concentration and diffusion conditions ((M_v,g)_base and (M_v,g)_weld are the chemical mobilities of vacancy and He atom in 316H steel and 316H WM, respecyively; $g v 0$ and $g g 0$ are the production rates of vacancy and He atom during irradiation, respectively)
(a-d) He bubble evolutions under the values of

g v 0

g g 0

are 6 (a), 9 (b), 12 (c), and 15 (d) with (M_v,g)_weld = 6(M_v,g)_base (e-h) He bubble evolutions under the values of

g v 0

g g 0

are 6 (e), 9 (f), 12 (g), and 15 (h) with (M_v,g)_weld = (M_v,g)_base (i, j) porosity (i) and diameter (j) under different conditions

Fig.12 Microstructures of system with the He bubble porosities of 0.6% (a), 5% (b), and 10% (c) and system with the He bubble diameters of 1.1 nm (d), 1.4 nm (e), and 2 nm (h)

Fig.13 Effects of He bubble porosity (a, c) and size (b, d) in 316H steel (a, b) and 316H WM (c, d) on stress-strain curves unde 550 ^oC (The circular areas in Figs.13a and c imply the applied strain begins to dominate the mechanical response)

Fig.14 Stress (S₂₂, GPa) (a, b, e, f) and plastic strain ( $ε 22 p l$ ) (c, d, g, h) distributions during the deformation process of 316H steel (a-d) and 316H WM (e-h) (The elliptical areas A and B in Figs.14d and h imply the bands of plastic deformation)
(a, c, e, g) 0.04% strain (b, d, f, h) 4% strain

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