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Open Access

ARTICLE

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

Jianwei Zhang1,2,*, Ran Shen1, Qianqi Zhang1, Yuanxin Li1,*, Shengchao Chen3,4,*, Minghao Zhao2,3, 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 Author: Jianwei Zhang. Email: email; Yuanxin Li. Email: email; Shengchao Chen. Email: email

Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.084790

Received 29 April 2026; Accepted 05 August 2026; Published online 21 August 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 (σxR, σzR) using only an individual instrumented indentation. First, the normalized total indentation work variation Wnorm 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.

Keywords

Non-equibiaxial residual stress; spherical indentation; machine learning

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