Skip to main content
Log in

A FEM-guided data-driven machine learning model for residual stress characterization in ultrasonic surface rolling of lightweight alloys

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

This work proposes the development of a Bayesian-regularized machine learning (ML) model tailored for predicting residual stresses in compressive and tensile modes during ultrasonic rolling of lightweight alloys. Training data were acquired through finite element method (FEM) simulations covering various parameters and alloys. The model exhibited high performance, with R2 values of 0.973 and 0.926, and corresponding RMSE values of 0.038 and 0.070 for compressive and tensile modes, respectively. The successful outcome was attributed to the effective implementation of Bayesian optimization, showcasing its proficiency in scenarios with limited data volumes. Furthermore, a delicate balance between the relevance scores of material properties and rolling processing parameters was identified for optimal prediction performance. Specifically, higher tensile stress values correlated with elevated relevance scores of static pressure, frequency, amplitude of ultrasonic vibration, compressive strength, Poisson ratio, and material density. In contrast, higher compressive stress values were well-predicted with increased relevance scores of rolling depth, amplitude of ultrasonic vibration, yield stress, and Poisson ratio. The study also elucidates the rationale behind these relevance scores and provides a compelling case study demonstrating the fine-tuning of input parameters to achieve target residual stress levels.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Q. Xu, J. Zhou, D. Jiang, X. Yang, Z. Qiu, Improved low-temperature mechanical properties of FH36 marine steel after ultrasonic surface rolling process. J. Alloys Compd. 937, 168401 (2023)

    Article  Google Scholar 

  2. J. Yang, D. Liu, Z. Ren, Y. Zhi, X. Zhang, R. Zhao, D. Liu, X. Xu, K. Fan, C. Liu, Grain growth and fatigue behaviors of GH4169 superalloy subjected to excessive ultrasonic surface rolling process. Mater. Sci. Eng. A 839, 142875 (2022)

    Article  Google Scholar 

  3. Z. Li, X. Guo, Z. Yang, Z. Cai, Y. Jiao, Effect of ultrasonic surface rolling process on the microstructure and corrosion behavior of zirconium alloy in high-temperature water condition. Mater. Chem. Phys. 311, 128546 (2024)

    Article  Google Scholar 

  4. P. Sun, S. Qu, C. Duan, X. Hu, X. Li, Improving the high cycle fatigue property of Ti6Al4V ELI alloy by optimizing the surface integrity through electric pulse combined with ultrasonic surface rolling process. J. Mater. Sci. Technol. 170, 103–121 (2024)

    Article  Google Scholar 

  5. X. Li, B. Guan, Y.-L. Wang, Y.-L. Wei, B. Li, Ascertaining the microstructural evolution and strengthening mechanisms of the gradient nanostructured pure titanium fabricated by ultrasonic surface rolling process. Surf. Coat. Technol. (2023) 130047

  6. H. Shi, D. Liu, T. Jia, X. Zhang, W. Zhao, Effect of the ultrasonic surface rolling process and plasma electrolytic oxidation on the hot salt corrosion fatigue behavior of TC11 alloy. Int. J. Fatigue. 168, 107443 (2023)

    Article  Google Scholar 

  7. L. Chen, W. Li, Y. Sun, M. Luo, Effect of microstructure evolution on the mechanical properties of a Mg–Y–Nd–Zr alloy with a gradient nanostructure produced via ultrasonic surface rolling processing. J. Alloys Compd. 923, 166495 (2022)

    Article  Google Scholar 

  8. Y. Zhao, B. Gong, Y. Liu, W. Zhang, C. Deng, Fatigue behaviors of ultrasonic surface rolling processed AISI 1045: the role of residual stress and gradient microstructure. Int. J. Fatigue. 178, 107993 (2024)

    Article  Google Scholar 

  9. Z. Liu, Z. Wang, C. Gao, X. Liu, R. Liu, Z. Xiao, J. Sanderson, Enhanced rolling contact fatigue behavior of selective electron beam melted Ti6Al4V using the ultrasonic surface rolling process. Mater. Sci. Eng. A 833, 142352 (2022)

    Article  Google Scholar 

  10. Z. Xiong, Y. Jiang, M. Yang, Y. Zhang, L. Lei, Achieving superior strength and ductility in 7075 aluminum alloy through the design of multi-gradient nanostructure by ultrasonic surface rolling and aging. J. Alloys Compd. 918, 165669 (2022)

    Article  Google Scholar 

  11. J. Tang, Y. Shi, J. Zhao, L. Chen, Z. Wu, Numerical modeling considering initial gradient mechanical properties and experiment verification of residual stress distribution evolution of 12Cr2Ni4A steel generated by ultrasonic surface rolling. Surf. Coat. Technol. 452, 129127 (2023)

    Article  Google Scholar 

  12. H. Wang, X. Wang, Y. Tian, Y. Ling, Study on surface residual stress of 42CrMo steel treated by ultrasonic rolling extrusion. Sci. Rep. 13, 6956 (2023)

    Article  ADS  Google Scholar 

  13. F. Jiao, S. Lan, B. Zhao, Y. Wang, Theoretical calculation and experiment of the surface residual stress in the plane ultrasonic rolling. J. Manuf. Process. 50, 573–580 (2020). https://doi.org/10.1016/j.jmapro.2019.12.058

    Article  Google Scholar 

  14. X. Peng, Y. Liang, X. Qin, J. Gu, The effect of ultrasonic surface rolling process on tension-tension fatigue limit of small diameter specimens of Inconel 718 superalloy. Int. J. Fatigue. 162, 106964 (2022)

    Article  Google Scholar 

  15. M. Zhang, J. Deng, Z. Liu, Y. Zhou, Investigation into contributions of static and dynamic loads to compressive residual stress fields caused by ultrasonic surface rolling. Int. J. Mech. Sci. 163, 105144 (2019). https://doi.org/10.1016/j.ijmecsci.2019.105144

    Article  Google Scholar 

  16. H. Liu, J. Zheng, Y. Guo, L. Zhu, Residual stresses in high-speed two-dimensional ultrasonic rolling 7050 aluminum alloy with thermal-mechanical coupling. Int. J. Mech. Sci. 186, 105824 (2020). https://doi.org/10.1016/j.ijmecsci.2020.105824

    Article  Google Scholar 

  17. J. Zheng, Y. Shang, Y. Guo, H. Deng, L. Jia, Analytical model of residual stress in ultrasonic rolling of 7075 aluminum alloy. J. Manuf. Process. 80, 132–140 (2022). https://doi.org/10.1016/j.jmapro.2022.05.049

    Article  Google Scholar 

  18. X. Xu, D. Liu, X. Zhang, C. Liu, D. Liu, Mechanical and corrosion fatigue behaviors of gradient structured 7B50-T7751 aluminum alloy processed via ultrasonic surface rolling. J. Mater. Sci. Technol. 40, 88–98 (2020). https://doi.org/10.1016/j.jmst.2019.08.030

    Article  Google Scholar 

  19. Z. Meng, Z. Yuanxi, Z. Yang, Theoretical and experimental analysis of compressive residual stress field on 6061 aluminum alloy after ultrasonic surface rolling process, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 233 (2019) 5363–5376. https://doi.org/10.1177/0954406219850218

  20. J. Geng, Z. Yan, H. Zhang, Y. Liu, P. Dong, S. Yuan, W. Wang, Microstructure and Mechanical properties of AZ31B Magnesium Alloy via Ultrasonic Surface Rolling process. Adv. Eng. Mater. 23, 2100076 (2021). https://doi.org/10.1002/adem.202100076

    Article  Google Scholar 

  21. K. Fan, D. Liu, X. Zhang, D. Liu, W. Zhao, J. Yang, A. Ma, M. Li, Y. Qi, J. Xiang, M. Abdel, Wahab, Effect of residual stress induced by ultrasonic surface rolling on fretting fatigue behaviors of Ti-6Al-4V alloy. Eng. Fract. Mech. 259, 108150 (2022). https://doi.org/10.1016/j.engfracmech.2021.108150

    Article  Google Scholar 

  22. C. Liu, D. Liu, X. Zhang, G. He, X. Xu, N. Ao, A. Ma, D. Liu, On the influence of ultrasonic surface rolling process on surface integrity and fatigue performance of Ti-6Al-4V alloy, surf. Coat. Technol. 370, 24–34 (2019). https://doi.org/10.1016/j.surfcoat.2019.04.080

    Article  Google Scholar 

  23. J. Park, G. An, N. Ma, S.-J. Kim, Prediction of transverse welding residual stress considering transverse and bending constraints in butt welding. J. Manuf. Process. 102, 182–194 (2023)

    Article  Google Scholar 

  24. A. Coraddu, L. Oneto, S. Li, M. Kalikatzarakis, O. Karpenko, Surrogate models to unlock the optimal design of stiffened panels accounting for ultimate strength reduction due to welding residual stress. Eng. Struct. 293, 116645 (2023)

    Article  Google Scholar 

  25. E. Polyzos, H. Pulju, P. Mäckel, M. Hinderdael, J. Ertveldt, D. Van Hemelrijck, L. Pyl, Measuring and Predicting the effects of residual stresses from full-Field Data in Laser-Directed Energy Deposition. Mater. (Basel). 16, 1444 (2023)

    Article  ADS  Google Scholar 

  26. S.E. Mirazimzadeh, S. Pazireh, J. Urbanic, O. Jianu, Unsupervised clustering approach for recognizing residual stress and distortion patterns for different parts for directed energy deposition additive manufacturing. Int. J. Adv. Manuf. Technol. 125, 5067–5087 (2023)

    Article  Google Scholar 

  27. M. John, A.M. Ralls, S.C. Dooley, A.K.V. Thazhathidathil, A.K. Perka, U.B. Kuruveri, P.L. Menezes, Ultrasonic surface rolling process: Properties, characterization, and applications. Appl. Sci. 11, 10986 (2021)

    Article  Google Scholar 

  28. F. Wang, X. Men, Y. Liu, X. Fu, Experiment and simulation study on influence of ultrasonic rolling parameters on residual stress of Ti-6Al-4V alloy. Simul. Model. Pract. Theory. 104, 102121 (2020). https://doi.org/10.1016/j.simpat.2020.102121

    Article  Google Scholar 

  29. X. Zhang, W. Liu, S. Wang, K. Wang, D. Wang, L. Liu, Effect of Ultrasonic Rolling on Properties of GCr15 Bearing Steel, in: J. Phys. Conf. Ser., IOP Publishing, 2022: p. 12044

  30. Y. Liu, L. Wang, D. Wang, Finite element modeling of ultrasonic surface rolling process. J. Mater. Process. Technol. 211, 2106–2113 (2011)

    Article  Google Scholar 

  31. F. Didi, H. Pallathadka, S. Abdullaev, R.R. Asaad, S. Askar, N.H. Haroon, Probing the impact of process variables in laser-welded aluminum alloys: a machine learning study. Mater. Today Commun. 38, 107660 (2024)

    Article  Google Scholar 

  32. V. Samavatian, M. Fotuhi-Firuzabad, M. Samavatian, P. Dehghanian, F. Blaabjerg, Correlation-driven machine learning for accelerated reliability assessment of solder joints in electronics. Sci. Rep. 10, 14821 (2020). https://doi.org/10.1038/s41598-020-71926-7

    Article  ADS  Google Scholar 

  33. H. Guo, X. Zhuang, T. Rabczuk, A deep collocation method for the bending analysis of Kirchhoff plate, ArXiv Prepr. ArXiv2102.02617. (2021)

  34. X. Zhuang, H. Guo, N. Alajlan, H. Zhu, T. Rabczuk, Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning. Eur. J. Mech. - A/Solids. 87, 104225 (2021). https://doi.org/10.1016/j.euromechsol.2021.104225

    Article  MathSciNet  Google Scholar 

  35. E. Samaniego, C. Anitescu, S. Goswami, V.M. Nguyen-Thanh, H. Guo, K. Hamdia, X. Zhuang, T. Rabczuk, An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications, Comput. Methods Appl. Mech. Eng. 362, 112790 (2020). https://doi.org/10.1016/j.cma.2019.112790

    Article  Google Scholar 

  36. R.B. Araujo, T. Edvinsson, Supervised AI and deep neural networks to Evaluate High-Entropy alloys as reduction catalysts in aqueous environments. ACS Catal. 14, 3742–3755 (2024)

    Article  Google Scholar 

  37. H. Guo, Z.-Y. Yin, A novel physics-informed deep learning strategy with local time-updating discrete scheme for multi-dimensional forward and inverse consolidation problems. Comput. Methods Appl. Mech. Eng. 421, 116819 (2024). https://doi.org/10.1016/j.cma.2024.116819

    Article  ADS  MathSciNet  Google Scholar 

  38. S. Deng, S. Hosseinmardi, L. Wang, D. Apelian, R. Bostanabad, Data-driven physics-constrained recurrent neural networks for multiscale damage modeling of metallic alloys with process-induced porosity. Comput. Mech. (2024) 1–31

  39. W. Liang, M. Lou, Y. Wang, C. Zhang, S. Chen, C. Cui, A fatigue crack growth prediction method on small datasets based on optimized deep neural network and Delaunay data augmentation, Theor. Appl. Fract. Mech. 129, 104218 (2024)

    Article  Google Scholar 

  40. A.L. Caterini, D.E. Chang, Deep Neural Networks in a Mathematical Framework (Springer, 2018)

  41. S.Y. Lee, S. Byeon, H.S. Kim, H. Jin, S. Lee, Deep learning-based phase prediction of high-entropy alloys: optimization, generation, and explanation. Mater. Des. 197, 109260 (2021)

    Article  Google Scholar 

  42. S. Li, W. Chen, K.S. Bhandari, D.W. Jung, X. Chen, Flow behavior of AA5005 alloy at high temperature and low strain rate based on arrhenius-type equation and back propagation artificial neural network (BP-ANN) model, materials (Basel). 15 (2022) 3788

  43. G. Xiao, J. Xing, Y. Zhang, Surface roughness prediction model of GH4169 superalloy abrasive belt grinding based on multilayer perceptron (MLP). Procedia Manuf. 54, 269–273 (2021)

    Article  Google Scholar 

  44. Z. Ji, M. Dudík, R.E. Schapire, M. Telgarsky, Gradient descent follows the regularization path for general losses, in: Conf. Learn. Theory, PMLR, 2020: pp. 2109–2136

  45. D. Khatamsaz, R. Neuberger, A.M. Roy, S.H. Zadeh, R. Otis, R. Arróyave, A physics informed bayesian optimization approach for material design: application to NiTi shape memory alloys. Npj Comput. Mater. 9, 221 (2023). https://doi.org/10.1038/s41524-023-01173-7

    Article  ADS  Google Scholar 

  46. N. Wang, M. Samavatian, V. Samavatian, H. Sun, Bayesian machine learning-aided Approach bridges between dynamic elasticity and compressive strength in the cement-based mortars. Mater. Today Commun. 106283 (2023). https://doi.org/10.1016/j.mtcomm.2023.106283

  47. M. Sucker, P. Ochs, PAC-Bayesian Learning of Optimization Algorithms, in: Int. Conf. Artif. Intell. Stat., PMLR, 2023: pp. 8145–8164

  48. B. Lei, T.Q. Kirk, A. Bhattacharya, D. Pati, X. Qian, R. Arroyave, B.K. Mallick, Bayesian optimization with adaptive surrogate models for automated experimental design. Npj Comput. Mater. 7, 194 (2021)

    Article  ADS  Google Scholar 

  49. X. Pei, Y. hong Zhao, L. Chen, Q. Guo, Z. Duan, Y. Pan, H. Hou, Robustness of machine learning to color, size change, normalization, and image enhancement on micrograph datasets with large sample differences. Mater. Des. 232, 112086 (2023)

    Article  Google Scholar 

  50. J. Xiong, S.-Q. Shi, T.-Y. Zhang, A machine-learning approach to predicting and understanding the properties of amorphous metallic alloys. Mater. Des. 187, 108378 (2020). https://doi.org/10.1016/j.matdes.2019.108378

    Article  Google Scholar 

  51. M. Ghorbani, M. Boley, P.N.H. Nakashima, N. Birbilis, A machine learning approach for accelerated design of magnesium alloys. Part B: regression and property prediction. J. Magnes Alloy. 11, 4197–4205 (2023)

    Article  Google Scholar 

  52. M. Zhang, Z. Liu, J. Deng, M. Yang, Q. Dai, T. Zhang, Optimum design of compressive residual stress field caused by ultrasonic surface rolling with a mathematical model. Appl. Math. Model. 76, 800–831 (2019)

    Article  MathSciNet  Google Scholar 

  53. D. Dai, T. Xu, X. Wei, G. Ding, Y. Xu, J. Zhang, H. Zhang, Using machine learning and feature engineering to characterize limited material datasets of high-entropy alloys. Comput. Mater. Sci. 175, 109618 (2020)

    Article  Google Scholar 

  54. Z. Yu, S. Ye, Y. Sun, H. Zhao, X.-Q. Feng, Deep learning method for predicting the mechanical properties of aluminum alloys with small data sets. Mater. Today Commun. 28, 102570 (2021)

    Article  Google Scholar 

  55. S. Lin, H. Zheng, B. Han, Y. Li, C. Han, W. Li, Comparative performance of eight ensemble learning approaches for the development of models of slope stability prediction. Acta Geotech. 17, 1477–1502 (2022). https://doi.org/10.1007/s11440-021-01440-1

    Article  Google Scholar 

  56. S. Lin, Z. Liang, S. Zhao, M. Dong, H. Guo, H. Zheng, A comprehensive evaluation of ensemble machine learning in geotechnical stability analysis and explainability. Int. J. Mech. Mater. Des. 20, 331–352 (2024). https://doi.org/10.1007/s10999-023-09679-0

    Article  Google Scholar 

  57. Y. Zhang, C. Ling, A strategy to apply machine learning to small datasets in materials science. Npj Comput. Mater. 4, 25 (2018)

    Article  ADS  Google Scholar 

  58. M. Sahnoune Chaouche, H.K. Al-Mohair, S. Askar, B.S. Abdullaeva, N.A. Hussien, A.H. Alawadi, A micromechanical nested machine learning model for characterizing materials behaviors of bulk metallic glasses. J. Non Cryst. Solids. 625, 122733 (2024). https://doi.org/10.1016/j.jnoncrysol.2023.122733

    Article  Google Scholar 

  59. P. Bharti, R. Singh, J.R. Sahoo, A. Tripathi, S. Mishra, Yield strength modeling of an Al-Cu-Li alloy through circle rolling and flow stress superposition approach. J. Alloys Compd. 964, 171343 (2023)

    Article  Google Scholar 

  60. J.L. González-Velázquez, Mechanical Behavior and Fracture of Engineering Materials (Springer, 2020)

  61. P. Rambabu, N. Eswara Prasad, V.V. Kutumbarao, R.J.H. Wanhill, Aluminium alloys for aerospace applications, Aerosp. Mater. Mater. Technol. Vol. 1 Aerosp. Mater. (2017) 29–52

Download references

Author information

Authors and Affiliations

Authors

Contributions

Rahul Pradhan played a key role in conceptualization, modeling, and simulation, as well as contributing to data analysis. Farag M. A. Altalbawy contributed significantly to investigation, literature review, and data analysis. Renas Rajab Asaad’s expertise was evident in modeling and simulation, investigation, and writing. Carlos Rodriguez-Benites made contributions to data analysis and literature review. Ahmed Raza Khan was involved in investigation, and numerical modeling. Finally, M. K. Sharma played a crucial role in conceptualization and data analysis. All authors contributed to the manuscript preparation and writing.

Corresponding author

Correspondence to Farag M. A. Altalbawy.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pradhan, R., Altalbawy, F.M.A., Khan, A.R. et al. A FEM-guided data-driven machine learning model for residual stress characterization in ultrasonic surface rolling of lightweight alloys. Appl. Phys. A 130, 400 (2024). https://doi.org/10.1007/s00339-024-07577-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-024-07577-6

Keywords

Navigation