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<p>This study addresses the multi-field coupling errors induced by geometric distortion and pile-up effects during tilted micro-indentation testing of 6005&#xa0;A-T6 aluminum alloy. To mitigate these errors, an indentation analysis correction function was developed by combining a geometric correction of the contact area with a pile-up compensation algorithm based on plastic work. Furthermore, cubic spline interpolation under physical constraints was employed to perform small-sample data augmentation. Based on these analyses and the plastic work conservation equation, a Support Vector Regression (SVR) model was constructed. The micro-indentation experiments were designed with five tilt angles (0°–4°, in 1° increments) and four indentation depths (20–50&#xa0;μm, in 10&#xa0;μm increments), resulting in 20 groups of baseline small-sample tests. On this basis, physically consistent spline interpolation and small perturbation expansion were applied, ultimately yielding 63 datasets, of which 43 were augmented. Experimental results demonstrated that the corrected indentation analysis model substantially improved the prediction accuracy of hardness and elastic modulus, exhibiting outstanding performance. Specifically, the prediction of hardness achieved a mean squared error (MSE) as low as 0.04, a mean absolute error (MAE) of 0.05, and a mean absolute percentage error (MAPE) of only 2.2%, with the coefficient of determination (R²) reaching 0.94, nearly ideal fitting. Similarly, the prediction of elastic modulus showed excellent precision, with an MSE of 0.34, an MAE of 0.27, a MAPE of only 3.4%, and an R² of 0.89, fully validating the reliability and accuracy of the corrected model. This work demonstrates that integrating small-sample data with well-established geometric–physical relationships and machine learning techniques can significantly enhance the characterization accuracy of hardness and elastic modulus in micro-indentation testing. It thus provides a novel methodological approach for micro-indentation analysis.</p>

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Hybrid Geometry and Physics-Informed Small Sample Data SVR for Tilted Micro-Indentation Characterization of 6005 A-T6 Aluminum Alloy

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • J. Qian,
  • Z. Zhang,
  • J. Li,
  • C. Li

摘要

This study addresses the multi-field coupling errors induced by geometric distortion and pile-up effects during tilted micro-indentation testing of 6005 A-T6 aluminum alloy. To mitigate these errors, an indentation analysis correction function was developed by combining a geometric correction of the contact area with a pile-up compensation algorithm based on plastic work. Furthermore, cubic spline interpolation under physical constraints was employed to perform small-sample data augmentation. Based on these analyses and the plastic work conservation equation, a Support Vector Regression (SVR) model was constructed. The micro-indentation experiments were designed with five tilt angles (0°–4°, in 1° increments) and four indentation depths (20–50 μm, in 10 μm increments), resulting in 20 groups of baseline small-sample tests. On this basis, physically consistent spline interpolation and small perturbation expansion were applied, ultimately yielding 63 datasets, of which 43 were augmented. Experimental results demonstrated that the corrected indentation analysis model substantially improved the prediction accuracy of hardness and elastic modulus, exhibiting outstanding performance. Specifically, the prediction of hardness achieved a mean squared error (MSE) as low as 0.04, a mean absolute error (MAE) of 0.05, and a mean absolute percentage error (MAPE) of only 2.2%, with the coefficient of determination (R²) reaching 0.94, nearly ideal fitting. Similarly, the prediction of elastic modulus showed excellent precision, with an MSE of 0.34, an MAE of 0.27, a MAPE of only 3.4%, and an R² of 0.89, fully validating the reliability and accuracy of the corrected model. This work demonstrates that integrating small-sample data with well-established geometric–physical relationships and machine learning techniques can significantly enhance the characterization accuracy of hardness and elastic modulus in micro-indentation testing. It thus provides a novel methodological approach for micro-indentation analysis.