Study on Residual Stress Reconstruction Method Based on Surface Data

doi:10.3901/JME.260543

Abstract

Abstract: Reconstructing residual stress based on surface measurement data enables obtaining the full-field residual stress distribution without damaging the component，providing a new approach for residual stress characterization. The eigenstrain method naturally satisfies mechanical constraints and is one of the mainstream methods for residual stress reconstruction. However，with the increase in component structural complexity and the decrease in the amount of measurement data，the ill-posedness of the inversion matrix intensifies，affecting the reliability of reconstruction. To address this，an improved eigenstrain reconstruction method is proposed：adaptive generation of radial basis function (Radial Basis Function，RBF) centers based on finite element mesh nodes is adopted to enhance the geometric adaptability of eigenstrain parameterization; a regularization parameter selection strategy based on GCV(Generalized Cross-Validation, GCV) rough screening-L curve fine-tuning is designed to suppress matrix ill-posedness. The residual stress fields of two-dimensional and three-dimensional components such as four-point bending components，ball-head indentation components，and quenched curved surface components are effectively reconstructed by this method. The coefficients of determination (R²) between the reconstructed values and ABAQUS simulation values are 0.943 5，0.903 7，and 0.939 6 respectively，with consistent distribution trends. Moreover，the reconstructed residual stress fields exhibit better smoothness and are closer to the continuous distribution characteristics of residual stress. Further，the effects of basis functions，shape deviations，and input data on reconstruction accuracy are analyzed. The results show that the power exponential RBF combined with the RBF center selection strategy based on finite element mesh nodes achieves the optimal accuracy; shape deviations exacerbate matrix ill-posedness，but the final reconstruction results differ slightly; when the input data is reduced or noise is introduced，the distribution trend of the reconstruction results is still basically consistent with the simulation values，with a slight decrease in reconstruction accuracy. These results indicate that the proposed method has strong robustness.

Key words: residual stress reconstruction, radial basis function, eigenstrain method, surface data, regularization

CLC Number:

TG306

WANG Jiani, FAN Xiaoguang, ZHAN Mei, YU Yangzhen, ZENG Xiangyi, WANG Zhijun. Study on Residual Stress Reconstruction Method Based on Surface Data[J]. Journal of Mechanical Engineering, 2026, 62(14): 231-240.

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URL: http://www.cjmenet.com.cn/EN/10.3901/JME.260543

http://www.cjmenet.com.cn/EN/Y2026/V62/I14/231

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