Advancing Reactor Safety: Direct FE2 Multiscale Modeling of Hydrogen-Induced Cracking in Pressure Vessels

Reactor pressure vessels, or RPVs, are vital to the operation of nuclear power plants. They hold the reactor core and are designed to withstand extreme conditions—high pressure, scorching temperatures, and relentless radiation. But these conditions take a toll on the RPV, creating challenges that are hard to ignore. One of the biggest threats is hydrogen-induced cracking (HIC) which happens when atomic hydrogen forms during coolant breakdown or interactions with the reactor’s cladding materials, and works its way into the steel walls of the RPV. Over time, this weakens the material, making it prone to cracks and potentially catastrophic failure. The risks are not just technical; they affect operational safety and have serious environmental consequences. HIC isn’t straightforward—it’s caused by a mix of interconnected factors. Hydrogen atoms diffuse through the steel, gathering in tiny voids and imperfections. Under pressure, these atoms combine to form molecular hydrogen, which causes the voids to expand and eventually coalesce into cracks. This whole process compromises the structural integrity of the vessel. Scientists have theories to explain parts of this, like the Hydrogen Pressure Theory, but predicting exactly how microscopic changes in the steel lead to large-scale failures remains a major challenge. The problem is that most modeling methods don’t tell the whole story. Traditional approaches either focus on the microscopic level—tracking how hydrogen moves and interacts with voids—or they zoom out to the macroscopic level to study the broader structural effects. What’s missing is a way to connect the dots between the two. On top of that, many existing techniques require significant computing power which makes them impractical for real-world use and therefore, a new approach is needed. This is exactly what a group of researchers set out to do. Led by Professor Vincent Beng Chye Tan and Dr. Kirk Ming Yeoh from the National University of Singapore, along with Professor Han Zhao from Chengdu Technological University and Professor Jie Zhi from Tongji University, the team developed new framework to tackle HIC. Their work, recently published in the International Journal of Mechanical Sciences, uses a method called Direct FE² multiscale modeling. This technique combines the detailed microscopic hydrogen behavior with the larger structural responses of the vessel in a single, unified approach. Unlike older methods, it avoids the need for separate analyses at different scales, making the process more efficient and accurate.

The researchers started by studying how hydrogen moves through the steel in RPVs. These vessels face extreme conditions in nuclear reactors, so the team simulated real-world environments to see what happens to hydrogen in the steel. They discovered that hydrogen doesn’t spread evenly—it tends to gather around tiny voids and defects. These areas, where chemical potential gradients are the weakest, act like magnets for hydrogen atoms. The more hydrogen collects, the more stress builds up in those spots, which makes it easier for cracks to form. They then looked at how these voids grow and how that affects the way hydrogen behaves. Using computer models called representative volume elements, they tested different shapes and patterns of voids. In the early stages, the voids were small and spread out, which allowed hydrogen to move around more freely and spread deeper into the material. But as the voids grew larger and started clustering together, hydrogen got trapped between them. This trapping caused hydrogen to build up in certain spots, making it harder for it to diffuse and increasing the risk of cracks forming in those high-stress areas. Next, the authors studied how cracks actually start and grow in the steel. They found two main ways cracks form. The first, internal shearing, happens when cracks follow the larger stress patterns across the material, cutting straight through the steel and potentially causing a catastrophic failure. The second, internal necking, happens when the stress is concentrated around tightly packed clusters of voids. This causes the voids to coalesce and merge, forming isolated weak points that eventually rupture. The researchers noticed that the way the voids were arranged had a big impact—tight clusters of voids were more likely to cause necking, while spread-out voids were more likely to result in shearing. One of their most important findings was how hydrogen pressure inside the voids interacts with the pressure from the vessel itself. When the hydrogen pressure inside a void gets too high, it becomes a major factor in starting tiny cracks. This pressure doesn’t just weaken the steel—it also plays a role in determining how and where the cracks will grow. It’s like a tug-of-war between the hydrogen pressure and the external forces acting on the vessel. This dual effect of hydrogen—both chemically weakening the material and physically driving crack growth—turned out to be a crucial piece of the puzzle in understanding how RPVs degrade over time.

To sum it up, Professor Vincent Beng Chye Tan and his colleagues tackled a major issue in keeping RPVs safe—hydrogen-induced cracking, or HIC. This is a big deal because RPVs are essential for nuclear reactors to operate safely, and when they fail, the consequences can be disastrous. The team used a cutting-edge approach called Direct FE² multiscale modeling. What’s special about this method is that it connects what happens at a microscopic level, like hydrogen moving through tiny voids in steel, to how the entire structure holds up. This approach isn’t just effective—it’s fast and accurate, setting a new bar for how these problems are studied. One of the biggest takeaways from their research is how it could make nuclear reactors safer and more reliable. They figured out the exact conditions where hydrogen builds up and starts causing cracks. With this knowledge, we can start designing better materials—like steel that resists void formation or manages hydrogen buildup in a way that reduces damage. This could go a long way in cutting down the risks tied to hydrogen embrittlement, which is one of the main reasons RPVs fail. The team’s findings also have some practical benefits for maintaining and running reactors that are already in use. By understanding how tiny voids and hydrogen interact, operators can focus on monitoring these issues before they get out of hand. For example, adjusting pressure or temperature during reactor operations could slow down or even prevent cracks from forming. This means RPVs could last longer and experience fewer unexpected breakdowns, saving both time and money.