Effect of Hydrogen Diffusion Model on Hydrogen Concentration Calculation Around a Crack Tip in Hydrogen-exposed Structures

doi:10.11902/1005.4537.2024.320

Journal of Chinese Society for Corrosion and protection

2025, Vol. 45

Issue (4): 1070-1080 DOI: 10.11902/1005.4537.2024.320

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Effect of Hydrogen Diffusion Model on Hydrogen Concentration Calculation Around a Crack Tip in Hydrogen-exposed Structures

ZHU Tao¹, SUN Haoxiang¹, ZHOU Yahong¹, ZHAO Yuhang², WANG Yanfei²(

)

1 Special Equipment Safety Supervision Inspection Institute of Jiangsu Province, Nanjing 210036, China
2 School of Chemical Engineering & Technology, China University of Mining and Technology, Xuzhou 221116, China

Cite this article:

ZHU Tao, SUN Haoxiang, ZHOU Yahong, ZHAO Yuhang, WANG Yanfei. Effect of Hydrogen Diffusion Model on Hydrogen Concentration Calculation Around a Crack Tip in Hydrogen-exposed Structures. Journal of Chinese Society for Corrosion and protection, 2025, 45(4): 1070-1080.

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Abstract

Hydrogen vessels and pipelines with cracks are at risk of hydrogen-induced cracking (HIC) failure. Predicting or assessing HIC requires accurate knowledge of hydrogen concentration at the crack tip. Due to the difficulty related with directly detecting hydrogen atoms, numerical methods are commonly used to acquire the hydrogen diffusion and concentration distribution. However, the chosen diffusion constitutive model can significantly influence the calculation results of hydrogen concentration. Herein, for two selected hydrogen diffusion models, namely a model of hydrogen diffusion coupled with hydrogen trapping and another model of considering only the hydrostatic stress-induced hydrogen diffusion, an Abaqus subroutine was proposed to calculate the hydrogen diffusion around a mode I crack tip during loading and load-holding periods. The differences in hydrogen concentration evolution between the two models were evaluated under various conditions. The results showed that differences in diffusible hydrogen concentration evolution between the two models during loading became more pronounced when the diffusion rate was slower or the material had lower strength. If only the diffusible concentration is needed and the diffusion rate is fast, both diffusion models are applicable. The steady-state hydrogen concentration distribution in low-strength steels was strongly influenced by hydrogen trapping, whereas in high-strength steels, stress effects gradually dominated as the initial hydrogen concentration increased. Therefore, for low-strength steels, the hydrogen trapping effect must be considered, whereas for high-strength steels, it can be neglected. The effect of hydrogen trapping on steady-state hydrogen concentration distribution increased significantly with higher trap binding energy. When the trap binding energy was relatively low, the two models produced comparable results, allowing the use of the trapping-free diffusion model. However, the model with hydrogen trapping was more appropriate when hydrogen-induced softening was also considered. These results provide a valuable reference for selecting a diffusion model when analyzing the HIC behavior of metals.

Key words: hydrogen diffusion hydrogen-induced cracking hydrogen embrittlement hydrogen trapping hydrostatic stress hydrogen-induced softening

Received: 02 October 2024 32134.14.1005.4537.2024.320

ZTFLH:

TG142

Fund: National Natural Science Foundation of China(22208369);Key Project of the Higher Education Scientific Research Planning(23SYS0201);Innovation Project of the Safety Discipline Group "Double First Class" Provincial Supplementary Fund(AQQ-SYLSB2003-0X);Scientific and Technological Projects of Jiangsu Provincial Special Equipment Safety Supervision and Inspection Research Institute(KJ(Y)2023049);Scientific and Technological Projects of Jiangsu Provincial Special Equipment Safety Supervision and Inspection Research Institute(KJ(Y)2023012)

Corresponding Authors: WANG Yanfei, E-mail: wyf_hg@cumt.edu.cn

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	ZHU Tao
	SUN Haoxiang
	ZHOU Yahong
	ZHAO Yuhang
	WANG Yanfei

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https://www.jcscp.org/EN/10.11902/1005.4537.2024.320 OR https://www.jcscp.org/EN/Y2025/V45/I4/1070

Heat conduction		Diffusion
Governing equation	$ρ ∂ U ∂ t = ∇ ⋅ k ∇ T$	Governing equation	$∂ C ∂ t = ∇ ⋅ D ∇ C L$
Internal energy	$U = c p T$	Total concentration	$C = C L + C T$
Heat flux	$q = - k ∇ T$	Mass flux	$J = - D ∇ C L$
Temperature	T	Lattice concentration	C_L
Heat conductivity	k	Lattice diffusion coefficient	D_L
Heat capacity	c_p	-	D_L/D_app
Density	ρ	-	1

Table 1 Analogy between heat conduction and mass diffusion

Fig.1 Relationship diagram of hydrogen diffusion user subroutines implemented in Abaqus

Fig.2 Initial condition and boundary condition of the model (a) and the mesh (b)

Table 2 Main material properties

Fig.3 Hydrostatic stress, plastic strain and hydrogen concentration near crack tip varying with loading time of low strength steel. (a) hydrostatic stress and plastic strain; (b) normalized hydrogen concentration in trap sites and occupancy in trapping sites of slow diffusion case; (c) and (e) normalized NILS hydrogen concentration corresponding to fast and slow diffusion without hydrogen trapping, respectively; (d) and (f) normalized NILS concentration corresponding to fast and slow diffusion with hydrogen trapping, respectively

Fig.4 Hydrostatic stress and normalized NILS hydrogen concentration distribution near crack tip at time of 130 s of high strength steel

Fig.5 Total hydrogen concentration and hydrogen cov-erage distribution near crack tip: (a) low strength steel, (b) high strength steel

Fig.6 Total hydrogen concentration and the occupancy of the trapping sites near crack tip (a) low strength steel, (b) high strength steel

Fig.7 Relationship between yield stress of pure iron and total hydrogen concentration

Fig.8 Dislocation densities of pure iron as a function of equivalent plastic strain

Fig.9 Hydrogen induced dilatation (a) and hydrostatic stress and hydrogen softening ratio (b) distribution near crack tip

Fig.10 Hydrogen distribution near crack tip (a) and comparison of crack opening displacement and plastic strain in different analysis type (b). T—trapping, S—softening

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