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Machine Learning-based Correlation of Charpy Impact Properties Between Sub-sized and Standard-sized Specimens for Nuclear Structural Materials

This study proposes a machine learning-based framework that accurately correlates Charpy impact properties between sub-sized and standard-sized specimens for nuclear structural materials by mapping absorbed energy across the ductile-to-brittle transition region, achieving superior performance over conventional methods in predicting upper shelf energy and ductile-to-brittle transition temperature without requiring full-sized data during inference.

Original authors: Yugandhar Kasala Sreenivasulu, Isshu Lee, John W. Merickel, Fei Xu, Yalei Tang, Joshua E. Rittenhouse, Aleksandar Vakanski, Rongjie Song

Published 2026-07-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yugandhar Kasala Sreenivasulu, Isshu Lee, John W. Merickel, Fei Xu, Yalei Tang, Joshua E. Rittenhouse, Aleksandar Vakanski, Rongjie Song

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to judge how tough a piece of metal is by hitting it with a giant swinging hammer. This is the Charpy impact test, a classic way to see if steel used in nuclear power plants will snap like a dry twig or bend like a rubber band when things get cold. Usually, you need a big, standard-sized block of metal to get the "real" answer. But here's the problem: in nuclear reactors, you often only have tiny, leftover scraps of metal, or you need to test materials that are so small they can't fit the big hammer test.

Scientists have tried to guess what the big block would do by testing these tiny scraps and using math formulas to "scale up" the results. Think of it like trying to guess how a full-sized pizza tastes by taking a tiny bite of a mini-pizza and doing some algebra. The problem? The old math formulas are like rigid, one-size-fits-all recipes. They assume all metals behave the same way and ignore the messy details of how the metal was cooked, how it was shaped, or how it was irradiated. The paper argues that these old formulas often get the answer wrong, especially when the metal is tricky or the conditions are weird.

The Big Idea: A Smart AI Translator
Instead of using rigid formulas, the researchers built a Machine Learning (ML) system. Think of this AI as a super-smart translator that has read thousands of stories about how different metals behave. It doesn't just look at the size of the tiny scrap; it looks at the metal's "DNA" (its chemical ingredients like carbon and nickel), how it was heated and cooled, how it was hit by radiation, and even the exact shape of the notch cut into it.

The AI's job is to take the data from the tiny "mini-pizza" (the sub-sized specimen) and translate it into what the "full-sized pizza" (the standard specimen) would have said. It does this in two clever steps:

Temperature Shift: It realizes that tiny pieces often act like they are warmer than they really are. So, it shifts the temperature data to line up the "tipping point" where the metal goes from tough to brittle.
Energy Scaling: It looks at the wiggles and bumps in the tiny metal's energy curve and stretches them out to match the size of the big metal's curve, keeping the unique personality of the data intact.

The Results: Beating the Old Formulas
The team tested this AI on 389 different test records for a specific steel called SA533B. They compared the AI's guesses against the actual results from full-sized tests.

The results were a clear win for the AI. When predicting the Upper Shelf Energy (USE)—which is basically the maximum energy the metal can soak up when it's warm—the AI got an accuracy score (R²) of 0.942. The old math formulas, even the best ones, only reached about 0.859.

For the Ductile-to-Brittle Transition Temperature (DBTT)—the specific temperature where the metal decides to snap instead of bend—the AI scored 0.892, while the best old formula only managed 0.661.

The paper explicitly rules out the idea that simple, fixed formulas are enough. It shows that methods relying on just the size of the specimen or simple linear math fail to capture the complex reality of how different metals react. The old formulas often need to be re-tuned for every new type of metal, making them unreliable for new situations. The AI, however, learned from a wide variety of conditions and didn't need to be re-tuned for every single test.

How Sure Are They?
The authors are quite confident in these numbers because they used a strict testing method called "cross-validation." They trained the AI on most of the data and then tested it on pieces of data it had never seen before, ensuring the AI wasn't just memorizing answers but actually learning the rules. They also ran statistical tests (Wilcoxon signed-rank tests) which showed that the difference between the AI's predictions and the real full-sized results was not statistically significant—meaning the AI's guesses were essentially indistinguishable from the real thing.

However, the paper is careful to note that this was tested specifically on SA533B steel. While the method looks promising, the authors suggest that expanding this to other types of metals and more data would be the next step to prove it works everywhere. They also mention that while they can estimate how much the AI might be "guessing" (uncertainty), the lack of repeated tests in the original data makes it hard to be 100% sure about the natural variability of the metal itself.

Why This Matters
This isn't just a math game. In the real world, nuclear power plants need to keep running safely for decades. They can't always cut out big chunks of metal to test them. This AI method means engineers can take tiny, leftover scraps, run a quick test, and get a highly reliable prediction of how the full-sized structure will hold up. It turns a "best guess" into a "smart prediction," helping keep nuclear reactors safe without needing to destroy more material than necessary.

Technical Summary: Machine Learning-based Correlation of Charpy Impact Properties Between Sub-sized and Standard-sized Specimens

Problem Statement
Reliable correlation of Charpy V-notch impact test results between sub-sized and full-sized specimens is critical for assessing the structural integrity of nuclear reactor pressure vessels (RPVs), particularly when material volume is restricted by spatial constraints or limited irradiation availability. While standards (e.g., ASTM A370, BS 7910) and numerous analytical methods exist to convert sub-sized data to full-sized equivalents, they suffer from significant limitations. These include:

Limited Accuracy: Analytical models often rely on linear or power-law formulations that fail to capture complex, nonlinear dependencies.
Lack of Generalizability: Many methods are calibrated for specific materials, heat treatments, or geometries and require re-calibration when applied to new conditions.
Inability to Capture Critical Factors: Traditional models struggle to incorporate variables such as microstructural variability, irradiation history, and specific manufacturing processes, which significantly influence Charpy behavior (e.g., Upper Shelf Energy [USE] varying from 51.8 J to 278 J for the same nominal material).
Systematic Errors: Existing analytical approaches often overestimate absorbed energies in the lower shelf region and underestimate them in the upper shelf region.

Methodology
The study proposes a data-driven Machine Learning (ML) framework to correlate Charpy impact properties across specimen sizes. The methodology involves three primary stages:

Dataset Compilation: A subset of a comprehensive open-access dataset was utilized, focusing on SA533B steel. The final dataset comprises 389 matched Charpy impact test records, linking sub-sized specimens (ranging from 1.5 mm to 5 mm thickness) to their corresponding full-sized counterparts (10 mm × 10 mm × 55 mm) under identical processing and testing conditions.
Data Transformation: To train the ML models, sub-sized data points were transformed to align with the full-sized domain. This involved:
- Temperature Shift: Shifting sub-sized temperatures ( $T_s$ ) by the difference in Ductile-to-Brittle Transition Temperature (DBTT) between full-sized and sub-sized specimens ( $\Delta T = DBTT_f - DBTT_s$ ) to align the transition regions.
- Scaled Residual Projection: Scaling the residuals (deviations from the fitted sigmoidal curve) of the sub-sized data by the ratio of full-sized to sub-sized Upper Shelf Energy ( $USE_f / USE_s$ ). These scaled residuals were added to the full-sized hyperbolic tangent (tanh) model to preserve the variability and scatter of the original sub-sized data while projecting it onto the full-sized response curve.
Machine Learning Modeling: A supervised multivariate regression approach was employed. The model takes 37 input parameters as features, including chemical composition, manufacturing/heat treatment details, irradiation conditions, specimen geometry, and the specific sub-sized test temperature and absorbed energy. The model jointly predicts the transformed temperature and absorbed energy for the full-sized domain. Seven ML algorithms were evaluated, including Random Forest, Gradient Boosting, CatBoost, XGBoost, LightGBM, Gaussian Process Regression, and Neural Networks.

Key Contributions

Novel ML Framework: This work presents the first application of ML specifically aimed at addressing size effects in Charpy impact testing, moving beyond previous ML applications focused on standard full-sized specimens or other mechanical tests (e.g., fatigue, tensile).
Indirect Parameter Estimation: The framework predicts the full temperature-energy profile first, from which USE and DBTT are extracted by fitting a hyperbolic tangent model. This allows for the inference of full-sized properties without requiring access to full-sized data during the prediction phase.
Comprehensive Evaluation: The study provides a rigorous comparative evaluation against established analytical methods (e.g., Lucas, Wallin, Uehira, Towers) using standard metrics ( $R^2$ , Pearson correlation $r$ , RMSE).
Uncertainty Quantification (UQ): Three strategies were introduced to estimate confidence and prediction intervals for USE and DBTT, addressing the reliability of correlated properties. These include coverage metrics based on fitted tanh functions and variance-weighted predictions.
Explainability: SHAP (SHapley Additive exPlanations) analysis was conducted to identify the most influential parameters, confirming that specimen dimensions, test temperature, and material composition (e.g., Carbon, Manganese) are dominant factors.

Results
The ML-based approach demonstrated superior performance compared to conventional analytical methods on the SA533B steel dataset:

Upper Shelf Energy (USE): The Gradient Boosting model achieved an $R^2$ of 0.942 and a Pearson correlation coefficient ( $r$ ) of 0.974, significantly outperforming the best analytical method (Wallin et al., $R^2 = 0.859$ ).
Ductile-to-Brittle Transition Temperature (DBTT): The Gradient Boosting model achieved an $R^2$ of 0.830 and $r$ of 0.913, compared to the best analytical method (Towers, $R^2 = 0.661$ ).
Statistical Significance: Wilcoxon signed-rank tests indicated that the differences between ML-predicted values and ground-truth full-sized values were not statistically significant ( $p > 0.05$ ), whereas several analytical methods showed statistically significant systematic biases.
Uncertainty Coverage: Strategy 2 (prediction intervals derived from ML-predicted data points) showed high coverage, with up to 96.2% of full-sized USE values and 80.8% of DBTT values falling within the predicted intervals for the Gradient Boosting model.

Significance and Claims
The paper claims that this ML-based framework offers a more flexible, accurate, and generalizable solution for correlating Charpy impact properties than existing analytical methods. By capturing complex, nonlinear dependencies across 37 input variables, the model overcomes the rigidity of geometry-based scaling laws.

The authors emphasize that the trained models do not require access to full-sized Charpy data during inference, making the approach highly suitable for:

Material Surveillance Programs: Enabling the use of sub-sized specimens to monitor reactor pressure vessel integrity over extended operational lifespans.
Accelerated Irradiation Testing: Facilitating data acquisition in test reactors with limited irradiation volumes.
Restricted Environments: Supporting mechanical characterization in spatially constrained regions (e.g., welded joints) or for components with limited material availability.

The study concludes that while the validation was performed on SA533B steel, the framework provides a robust foundation for addressing size effects in nuclear structural materials, provided that future work expands the dataset to include diverse materials and processing conditions to further enhance generalizability.

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