Kinetics and Evolution Modeling of Hydrogen-Induced Cracking in Low-Carbon Steel
Abstract
1. Introduction
2. Materials and Methods
2.1. Cathodic Charging Procedure
2.2. Fractographic Examination
2.3. A Theoretical Model of HIC Kinetics
3. Results
3.1. HIC Growth Morphology
3.2. HIC Kinetics
- (a)
- Cracks of near-circular shape nucleated within the first 24 h of cathodic charging.
- (b)
- Cracks growing individually or with interconnection only at the moment of inspection.
- (c)
- Irregularly shaped cracks or very elongated cracks were not considered.
3.3. Fractographic Examination
3.4. Computational Modeling of HIC Kinetics
- If the point distribution is random, the K curve deviates little from πr2, and the K curve remains close to the reference value, , for all radii, .
- If the point distribution is regular, < . Because the points are repulsive, they have fewer neighbors on average in a radius than they would have based on the assumption of a random distribution of points.
- In the case of an aggregated distribution, there are more points in a radius around the points than the expected number under a random distribution: consequently, the points attract each other and > .
- Poisson Process: The process of generating initial points is based on a Poisson distribution to simulate the location of the initially formed HIC cracks in a completely random distribution of individual cracks that grow independently of each other, using a two dimensional rectangular domain of 110 × 180 arbitrary units, corresponding to 11 cm × 18 cm in physical dimensions. This domain represents the exposed section of the steel in contact with the electrochemical solution; the nuclei were randomly distributed within this domain, and open boundary conditions were assumed to allow cracks to evolve naturally without artificially constraining their growth near the domain edges. Throughout the simulation, no significant clustering or accumulation of cracks near the boundaries was observed. This is attributed to the use of a homogeneous Poisson spatial distribution of nucleation sites and the statistical nature of crack growth and coalescence, which together promote a uniform evolution of damage across the domain. Crack growth was too confined within the domain limits, and cracks reaching the edges were not allowed to propagate beyond them. The Poisson distribution is defined as follows [43]:Where P (X = x) is the probability of x events occurring, x is a non-negative integer, X is a discrete random variable, λ is a positive constant, and x! is the factorial of x.
- Ellipsoidal Geometry: These cracks are modeled as ellipses in the plane and are mathematically defined by the following equation:
- Interconnection: The interconnection is modeled as the overlap area among multiple ellipses by using the Monte Carlo technique [44] to simulate random points within the domain and count how many fall inside any ellipse, providing a statistical estimate of the overlap area. The Monte Carlo method introduces a degree of statistical uncertainty that depends on the number of sampled points; larger sample sizes reduce variability in the estimation of the overlapped area.
- Time Tracking: The code iterates in time increments to simulate the temporal evolution of the total crack area by HIC.
4. Discussion
5. Conclusions
- The model proposed in this study successfully simulated the kinetics and morphology of hydrogen-induced cracking (HIC) nucleation and growth in a low-carbon steel plate under static loading conditions. It does not currently account for cyclic stresses or temperature fluctuations. The model incorporates key factors, such as the spatial distribution of HIC nucleation sites, the hydrogen influx represented by the applied current density, and experimentally observed features, like the delayed onset of HIC. This framework offers a valuable tool for understanding HIC evolution by varying input parameters and analyzing the resulting total cracked area and the final morphology of HIC-damaged regions in low-carbon steel plates. It is considered an important first step toward developing a predictive algorithm for estimating the remaining service life of process piping and equipment made of low-carbon steel exposed to hydrogen-charging environments. Future improvements to the model will aim to incorporate microstructural parameters, such as grain size and phase distributions, local stress fields, cyclic loading conditions, and steel samples with different fracture toughness levels, in order to evaluate how these variables affect HIC kinetics.
- The results of investigations into the kinetics and morphology of hydrogen-induced cracking (HIC) in low-carbon steel, determined after the cathodic charging of steel plates, indicate that the number of nucleated cracks and the kinetics of HIC are proportional to the applied current density, primarily because it determines the hydrogen influx. Furthermore, it was observed that the activation of HIC nuclei sites is also proportional to the applied current density in the cathodic charging experiment. It was found that HIC initiates at only a small fraction of NMIs that have favorable characteristics to act as hydrogen traps and start the HIC process, and their spatial distribution is a key factor in the overall kinetics and morphology of HIC.
- It was observed that the HIC process is divided into two stages: Stage I, nucleation and growth of individual cracks, and Stage II, interconnection of cracks. The growth rate is not constant in each stage, being higher in Stage I and very low in Stage II. This behavior was explained by the combined effects of the fracture mechanism (quasi-cleavage) and the pressure mechanism, which suggest that the nucleation and growth of HIC depend on reaching the internal pressure in the crack that is sufficient to overcome the cohesive strength of the crack plane. This strength is constant and dependent on the microstructure and the hydrogen concentration in the lattice for each particular steel composition and microstructure.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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C 0.106 | Si 0.184 | Mn 0.844 | P 0.006 | S 0.026 | Cu 0.270 | Al 0.025 | Cr 0.041 |
Mo 0.0007 | Ni 0.019 | V 0.010 | Ti 0.004 | Nb 0.030 | W 0.013 | B 0.001 | Fe 98.4 |
Sample Direction | Area Inclusions % | ASTM Inclusion Type | Ferrite % | Pearlite % |
---|---|---|---|---|
LS | 0.38 | A | 93.77 | 6.23 |
TS | 0.39 | A | 92.78 | 7.22 |
Current/Time | 24 h | 48 h | >144 h | Total |
---|---|---|---|---|
1 mA/cm2 | 3 | 6 | 32 | 56 |
4 mA/cm2 | 13 | 26 | 1 | 50 |
5.5 mA/cm2 | 43 | 1 | 0 | 44 |
Subtotal | 59 | 33 | 34 | 150 |
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Mortera-Bravo, I.; González-Velázquez, J.L.; Rívas-López, D.I.; Beltrán-Zuñiga, M.A. Kinetics and Evolution Modeling of Hydrogen-Induced Cracking in Low-Carbon Steel. Materials 2025, 18, 3813. https://doi.org/10.3390/ma18163813
Mortera-Bravo I, González-Velázquez JL, Rívas-López DI, Beltrán-Zuñiga MA. Kinetics and Evolution Modeling of Hydrogen-Induced Cracking in Low-Carbon Steel. Materials. 2025; 18(16):3813. https://doi.org/10.3390/ma18163813
Chicago/Turabian StyleMortera-Bravo, Iván, Jorge Luis González-Velázquez, Diego Israel Rívas-López, and Manuel Alejandro Beltrán-Zuñiga. 2025. "Kinetics and Evolution Modeling of Hydrogen-Induced Cracking in Low-Carbon Steel" Materials 18, no. 16: 3813. https://doi.org/10.3390/ma18163813
APA StyleMortera-Bravo, I., González-Velázquez, J. L., Rívas-López, D. I., & Beltrán-Zuñiga, M. A. (2025). Kinetics and Evolution Modeling of Hydrogen-Induced Cracking in Low-Carbon Steel. Materials, 18(16), 3813. https://doi.org/10.3390/ma18163813