Open Access

ARTICLE

Characterization of Non-Equibiaxial Residual Stresses via Machine Learning Enhanced Instrumented Indentation Testing

Jianwei Zhang^1,2,*, Ran Shen¹, Qianqi Zhang¹, Yuanxin Li^1,*, Shengchao Chen^3,4,*, Minghao Zhao^2,3, Lubing Shi⁴, Bing Wang⁵

1 School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou, China
2 Industrial Science & Technology Institute for Anti-Fatigue Manufacturing, Zhengzhou University, Zhengzhou, China
3 School of Mechanical and Power Engineering, Zhengzhou University, Zhengzhou, China
4 ZRIME Gearing Technology Co., Ltd., Zhengzhou, China
5 Key Laboratory of Testing for Manufacturing Process, Ministry of Education, School of Manufacturing Science and Engineering, Southwest University of Science and Technology, Mianyang, China

* Corresponding Authors: Jianwei Zhang. Email: ; Yuanxin Li. Email: ; Shengchao Chen. Email:

Computers, Materials & Continua 2026, 89(2), 19 https://doi.org/10.32604/cmc.2026.084790

Received 29 April 2026; Accepted 05 August 2026; Issue published 15 September 2026

Abstract

Non-equibiaxial residual stresses are prevalent in engineering components such as welding, additive manufacturing, and surface strengthening, making their accurate detection critical for ensuring structural integrity. This paper proposes a novel method capable of simultaneously identifying two principal stress components (${\sigma }_{\mathrm{x}}^{\mathrm{R}}$, ${\sigma }_{\mathrm{z}}^{\mathrm{R}}$) using only an individual instrumented indentation. First, the normalized total indentation work variation W_norm and the residual indentation ellipticity λ are extracted as sensitive features from the indentation responses through dimensional analysis. Subsequently, a finite element (FE) simulation database comprising 2400 datasets was established to train three types of neural networks: the single-target approach (ST-MLP), the classical multi-output multi-layer perceptron (MLP), and the parameter sharing-based deep network (DMTR). The outcomes of the training phase indicate that the overall error of the DMTR model is less than 5%, while those of the MLP and ST-MLP models are less than 7%. Furthermore, supplementary FE simulations were conducted on Al 7075, Al 2024, and Ti Grade 5 alloys for validation, showing that the MLP and DMTR prediction errors across all models are controlled within 11%. Finally, experimental validation was conducted on Al 7075 alloy and 18CrNiMo7-6 alloy cruciform specimens. The result is the DMTR model maintains a prediction error within 30 MPa. This study provides a feasible path for the rapid on-site detection of non-equibiaxial residual stress.

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Keywords

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