<p>The fracture strengths of grain boundaries (GBs) determine the failure mechanisms of polycrystalline materials during plastic deformation. We perform atomistic simulations to determine the ultimate strengths and corresponding strains of GBs under tensile loading in copper. A dataset is built based on a total of 17,374 GB configurations with 57 orientations. Using this dataset, three machine learning (ML) algorithms, including gradient boosting decision trees (GBDT), random forests (RF), and support vector regression (SVR), are employed to develop models for predicting the fracture strengths and strains of GBs based on ten input features related to GB structure and its local atomic environment. Among these three ML models, the RF algorithm serves as the most robust baseline, yielding <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${R}^{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> values of 0.9025 for fracture strength and 0.8560 for fracture strain. Following optimization via particle swarm optimization (PSO), the hybrid RF–PSO model elevates this accuracy to an exceptional level, achieving <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${R}^{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> values of 0.9551 and 0.9554, respectively. This performance significantly outperforms the GBDT (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">${R}^{2}\approx 0.84$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> <mo>≈</mo> <mn>0.84</mn> </mrow> </math></EquationSource> </InlineEquation> for both targets) and SVR (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">${R}^{2}<0.70$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> <mo><</mo> <mn>0.70</mn> </mrow> </math></EquationSource> </InlineEquation>) benchmarks. Our analysis indicates that grain boundary energy (GBE) and maximum Schmid factor dominate GB strength and its ultimate strain, respectively. These results establish a translation-space strength landscape for efficient screening of metastable GB configurations, offering a practical route toward the design of high-strength polycrystalline materials.</p>

Machine Learning-Based Prediction of Grain Boundary Strengths in Copper

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发表日期：

2026年6月26日

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Zhaolong Zhang,
Wu-Rong Jian,
Shuozhi Xu,
Xiaohu Yao

摘要

The fracture strengths of grain boundaries (GBs) determine the failure mechanisms of polycrystalline materials during plastic deformation. We perform atomistic simulations to determine the ultimate strengths and corresponding strains of GBs under tensile loading in copper. A dataset is built based on a total of 17,374 GB configurations with 57 orientations. Using this dataset, three machine learning (ML) algorithms, including gradient boosting decision trees (GBDT), random forests (RF), and support vector regression (SVR), are employed to develop models for predicting the fracture strengths and strains of GBs based on ten input features related to GB structure and its local atomic environment. Among these three ML models, the RF algorithm serves as the most robust baseline, yielding ${R}^{2}$ $R^{2}$ values of 0.9025 for fracture strength and 0.8560 for fracture strain. Following optimization via particle swarm optimization (PSO), the hybrid RF–PSO model elevates this accuracy to an exceptional level, achieving ${R}^{2}$ $R^{2}$ values of 0.9551 and 0.9554, respectively. This performance significantly outperforms the GBDT ( ${R}^{2}\approx 0.84$ $R^{2} \approx 0.84$ for both targets) and SVR ( ${R}^{2}<0.70$ $R^{2} < 0.70$ ) benchmarks. Our analysis indicates that grain boundary energy (GBE) and maximum Schmid factor dominate GB strength and its ultimate strain, respectively. These results establish a translation-space strength landscape for efficient screening of metastable GB configurations, offering a practical route toward the design of high-strength polycrystalline materials.