Skip to main content
SpringerLink
Log in

A Machine Learning Approach for Analyzing Residual Stress Distribution in Cold Spray Coatings

  • ORIGINAL RESEARCH ARTICLE
  • Published:
Journal of Thermal Spray Technology Aims and scope Submit manuscript

Abstract

This study establishes a machine learning (ML) model utilizing the expectation-maximization approach to predict maximum residual stresses, encompassing both tensile and compressive states, in the cold spraying process across various substrates. The main feature of the ML algorithm lies in its two-step iterative process, where the Expectation (E step) refines latent variable estimates, and the Maximization (M step) optimizes the model’s parameters, aligning them with the data. Based on the results, regression analysis highlighted the predictive capabilities of the proposed model for tensile and compressive residual stresses, exhibiting root mean square error values of 8.8 and 3.5%, along with determination coefficient values of 0.915 and 0.968, respectively, indicating higher prediction performance in the compression mode. This suggests higher predictability for residual stress within the depth of material’s body. Moreover, analyzing low residual stress levels underscored the significant impact of substrate and particle mechanical strength on prediction performance, whereas higher residual stress levels highlighted the strong influence of thermal conductivity. This correlation suggests that high stresses during the cold spray process generate more heat, thereby emphasizing the crucial role of thermal conductivity in predicting resultant residual stresses. Furthermore, a notable trend emerges as tensile stress increases, spotlighting the augmented influence of processing parameters in the prediction process. Conversely, at elevated compressive stresses, material properties’ weight factors assume a vital role in predictions. These findings offer insights into the intricate interplay between processing parameters and materials properties in determining resultant residual stresses during cold spraying.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Abbreviations

\(\bar{\sigma }\) :

Flow stress

A, B, C, m, and n :

Material constants

\({\overline{\varepsilon }}^{pl}\) :

Equivalent plastic strain

\({\dot{\varepsilon }}^{pl}\) :

Equivalent plastic strain rate

\({\dot{\varepsilon }}_{0}^{pl}\) :

Reference strain rate

T ref :

Reference temperature

T m :

Melting temperature of the material

\({\overline{\varepsilon }}_{{\text{pf}}}\) :

Equivalent plastic strain at material failure

p :

Contact pressure

q :

Von Mises stress

d1-d5:

Failure parameters

L new :

The normalized value of specified parameter

References

  1. H. Wang, P. Li, W. Guo, G. Ma, and H. Wang, Copper-Based Composite Coatings by Solid-State Cold Spray Deposition: A Review, Coatings, 2023, 13, p 479.

    Article  CAS  Google Scholar 

  2. W. Sun, X. Chu, H. Lan, R. Huang, J. Huang, Y. Xie, J. Huang, and G. Huang, Current Implementation Status of Cold Spray Technology: A Short Review, J. Therm. Spray Technol., 2022, 31, p 848-865.

    Article  PubMed  PubMed Central  Google Scholar 

  3. M.A. Adaan-Nyiak and A.A. Tiamiyu, Recent Advances on Bonding Mechanism in Cold Spray Process: A Review of Single-Particle Impact Methods, J. Mater. Res., 2023, 38, p 69-95.

    Article  CAS  PubMed  Google Scholar 

  4. D.C. Saha, J.V.S.N. Sripada, G.C. Saha, and H. Jahed, Microstructure and Interfacial Bonding Evolution of Cold Spray Deposited Graphene-Reinforced Composite Feedstock on AZ80 Magnesium Substrate, J. Therm. Spray Technol., 2023, 32, p 984-1001.

    Article  CAS  Google Scholar 

  5. S. Kumar, Influence of Processing Conditions on the Mechanical, Tribological and Fatigue Performance of Cold Spray Coating: A Review, Surf. Eng., 2022, 38, p 324-365.

    Article  CAS  Google Scholar 

  6. S. Yin, N. Fan, C. Huang, Y. Xie, C. Zhang, R. Lupoi, and W. Li, Towards High-Strength Cold Spray Additive Manufactured Metals: Methods, Mechanisms, and Properties, J. Mater. Sci. Technol., 2023, 170, p 47.

    Article  Google Scholar 

  7. A. Fardan, C.C. Berndt, and R. Ahmed, Numerical Modelling of Particle Impact and Residual Stresses in Cold Sprayed Coatings: A Review, Surf. Coatings Technol., 2021, 409, 126835. https://doi.org/10.1016/j.surfcoat.2021.126835

    Article  CAS  Google Scholar 

  8. X. Pan, W. He, L. Zhou, S. Shu, X. Ding, Q. Wang, S. Wen, N. Li, M. Yi, Y. Zhu, and J. Nan, Two Laser Beam Modulation of Microstructure and Residual Stress Field in Cold Sprayed Al Alloy for Recovering Fatigue Performance, Int. J. Plast., 2023, 164, 103598. https://doi.org/10.1016/j.ijplas.2023.103598

    Article  CAS  Google Scholar 

  9. A. Faheem, A. Tyagi, F. Hasan, A.A. Khan, Q. Murtaza, and K.K. Saxena, Residual Stress Investigation in the Metallic Coating Approach of Micro-sized Particles on the Substrate: Cold Spray Additive Manufacturing, Adv. Mater. Process. Technol., 2022, 8, p 4642-4658. https://doi.org/10.1080/2374068X.2022.2079250

    Article  Google Scholar 

  10. Z. Zhang, Z. Liu, J. Zhao, B. Wang, and Y. Cai, Numerical Analysis of Residual Stresses Induced by Cold Spray Fabricating cBN-reinforced Ni Matrix Composites, Surf. Coat. Technol., 2023, 467, 129672. https://doi.org/10.1016/j.surfcoat.2023.129672

    Article  CAS  Google Scholar 

  11. A. Vargas-Uscategui, P.C. King, M.J. Styles, M. Saleh, V. Luzin, and K. Thorogood, Residual Stresses in Cold Spray Additively Manufactured Hollow Titanium Cylinders, J. Therm. Spray Technol., 2020, 29, p 1508-1524. https://doi.org/10.1007/s11666-020-01028-3

    Article  CAS  Google Scholar 

  12. M. Daroonparvar, H.R. Bakhsheshi-Rad, A. Saberi, M. Razzaghi, A.K. Kasar, S. Ramakrishna, P.L. Menezes, M. Misra, A.F. Ismail, and S. Sharif, Surface Modification of Magnesium Alloys Using Thermal and Solid-State Cold Spray Processes: Challenges and Latest Progresses, J. Magn. Alloy., 2022, 10(8), p 2025-2061.

    Article  CAS  Google Scholar 

  13. K. Loke, Z.Q. Zhang, S. Narayanaswamy, P.K. Koh, V. Luzin, T. Gnaupel-Herold, and A.S.M. Ang, Residual Stress Analysis of Cold Spray Coatings Sprayed at Angles Using Through-Thickness Neutron Diffraction Measurement, J. Therm. Spray Technol., 2021, 30, p 1810-1826. https://doi.org/10.1007/s11666-021-01252-5

    Article  Google Scholar 

  14. B. Marzbanrad, E. Toyserkani, and H. Jahed, Customization of Residual Stress Induced in Cold Spray Printing, J. Mater. Process. Technol., 2021, 289, 116928. https://doi.org/10.1016/j.jmatprotec.2020.116928

    Article  CAS  Google Scholar 

  15. S. Lett, A. Quet, S. Hémery, J. Cormier, E. Meillot, and P. Villechaise, Residual Stresses Development During Cold Spraying of Ti-6Al-4V Combined with In Situ Shot Peening, J. Therm. Spray Technol., 2023, 32, p 1018-1032. https://doi.org/10.1007/s11666-022-01514-w

    Article  Google Scholar 

  16. D. Boruah, B. Ahmad, T.L. Lee, S. Kabra, A.K. Syed, P. McNutt, M. Doré, and X. Zhang, Evaluation of Residual Stresses Induced by Cold Spraying of Ti-6Al-4V on Ti-6Al-4V Substrates, Surf. Coat. Technol., 2019, 374, p 591-602. https://doi.org/10.1016/j.surfcoat.2019.06.028

    Article  CAS  Google Scholar 

  17. N.M. Dang, W.Y. Lin, Z.Y. Wang, S.A. Alidokht, R.R. Chromik, T.Y. Chen, and M.T. Lin, Mechanical Properties and Residual Stress Measurement of TiN/Ti Duplex Coating Using HiPIMS TiN on Cold Spray Ti, Coatings, 2022, 12, p 759. https://doi.org/10.3390/coatings12060759

    Article  CAS  Google Scholar 

  18. D. Shrestha, F. Azarmi, and X.W. Tangpong, Effect of Heat Treatment on Residual Stress of Cold Sprayed Nickel-Based Superalloys, J. Therm. Spray Technol., 2022, 31, p 197-205. https://doi.org/10.1007/s11666-021-01284-x

    Article  PubMed  Google Scholar 

  19. V. Luzin, O. Kirstein, S.H. Zahiri, and D. Fraser, Residual Stress Buildup in Ti Components Produced by Cold Spray Additive Manufacturing (CSAM), J. Therm. Spray Technol., 2020, 29, p 1498-1507. https://doi.org/10.1007/s11666-020-01048-z

    Article  CAS  Google Scholar 

  20. F. Meng, X. Fan, Z. Chi, S. Chen, and X. Chu, Modeling Parameters for Finite Element Simulation of Residual Stress in Cold Spray and the Stress Evolution and Distribution, J. Therm. Spray Technol., 2023 https://doi.org/10.1007/s11666-023-01640-z

    Article  Google Scholar 

  21. E. Lin, Q. Chen, O.C. Ozdemir, V.K. Champagne, and S. Müftü, Effects of Interface Bonding on the Residual Stresses in Cold-Sprayed Al-6061: A Numerical Investigation, J. Therm. Spray Technol., 2019, 28, p 472-483. https://doi.org/10.1007/s11666-019-00827-7

    Article  CAS  Google Scholar 

  22. K. Liu, M.F. Niri, G. Apachitei, M. Lain, D. Greenwood, and J. Marco, Interpretable Machine Learning for Battery Capacities Prediction and Coating Parameters Analysis, Control. Eng. Pract., 2022, 124, 105202.

    Article  Google Scholar 

  23. X. Xu, X. Wang, S. Wu, L. Yan, T. Guo, K. Gao, X. Pang, and A.A. Volinsky, Design of Super-Hard High-Entropy Ceramics Coatings Via Machine Learning, Ceram. Int., 2022, 48, p 32064-32072.

    Article  CAS  Google Scholar 

  24. Y. Gong, B. Cao, H. Zhang, F. Sun, and M. Fan, Terahertz Based Thickness Measurement of Thermal Barrier Coatings Using Hybrid Machine Learning. Nondestruct. Test. Eval., 2023, p 1-17.

  25. A.S. Mohammed, S. Dodla, J.K. Katiyar, and M.A. Samad, Prediction of Friction Coefficient of su-8 and Its Composite Coatings Using Machine Learning Techniques, Proc. Inst. Mech. Eng. Part J. J. Eng. Tribol., 2023, 237, p 943-953.

    Article  Google Scholar 

  26. Z. Wang, S. Cai, W. Chen, R.A. Ali, and K. Jin, Analysis of Critical Velocity of Cold Spray Based on Machine Learning Method with Feature Selection, J. Therm. Spray Technol., 2021, 30, p 1213-1225.

    Article  Google Scholar 

  27. K. Malamousi, K. Delibasis, B. Allcock, and S. Kamnis, Digital Transformation of Thermal and Cold Spray Processes with Emphasis on Machine Learning, Surf. Coat. Technol., 2022, 433, 128138. https://doi.org/10.1016/j.surfcoat.2022.128138

    Article  CAS  Google Scholar 

  28. H. Canales, I.G. Cano, and S. Dosta, Window of Deposition Description and Prediction of Deposition Efficiency Via Machine Learning Techniques in Cold Spraying, Surf. Coat. Technol., 2020, 401, 126143.

    Article  CAS  Google Scholar 

  29. K. Bobzin, W. Wietheger, H. Heinemann, S.R. Dokhanchi, M. Rom, and G. Visconti, Prediction of Particle Properties in Plasma Spraying Based on Machine Learning, J. Therm. Spray Technol., 2021, 30, p 1751-1764.

    Article  Google Scholar 

  30. G. Mauer and C. Moreau, Process Diagnostics and Control in Thermal Spray, J. Therm. Spray Technol., 2022, 31, p 818-828.

    Article  Google Scholar 

  31. R. Valente, A. Ostapenko, B.C. Sousa, J. Grubbs, C.J. Massar, D.L. Cote, and R. Neamtu, Classifying Powder Flowability for Cold Spray Additive Manufacturing Using Machine Learning, in 2020 IEEE International Conference on Big Data (Big Data), (IEEE, 2020), pp 2919-2928

  32. R. Ghelichi, S. Bagherifard, D. MacDonald, I. Fernandez-Pariente, B. Jodoin, and M. Guagliano, Experimental and Numerical Study of Residual Stress Evolution in Cold Spray Coating, Appl. Surf. Sci., 2014, 288, p 26-33.

    Article  CAS  Google Scholar 

  33. W.K.W. Tai, R. Chakrabarty, S. Pinches, X. Huang, J. Lang, J. Song, and A.S.M. Ang, Comparing Relative Bond Characteristics Between Spherical and Elongated Morphologies for Cold Spray Process Using SPH Simulation, J. Therm. Spray Technol., 2022, 31, p 2489-2504.

    Article  Google Scholar 

  34. R. Chakrabarty and J. Song, A Modified Johnson-Cook Material Model with Strain Gradient Plasticity Consideration for Numerical Simulation of Cold Spray Process, Surf. Coat. Technol., 2020, 397, 125981.

    Article  CAS  Google Scholar 

  35. G.R. Johnson and W.H. Cook, Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures, Eng. Fract. Mech., 1985, 21, p 31-48.

    Article  Google Scholar 

  36. A.S.M. Ang and C.C. Berndt, A Review of Testing Methods for Thermal Spray Coatings, Int. Mater. Rev., 2014, 59, p 179-223.

    Article  CAS  Google Scholar 

  37. A. Mehta, H. Vasudev, and L. Thakur, Applications of Numerical Modelling Techniques in Thermal Spray Coatings: A Comprehensive Review. Int. J. Interact. Des. Manuf., 2023, p 1-21.

  38. N. Ferguen, W. Leclerc, and E.S. Lamini, Numerical Investigation of Thermal Stresses Induced Interface Delamination in Plasma-Sprayed Thermal Barrier Coatings, Surf. Coat. Technol., 2023, 461, 129449.

    Article  CAS  Google Scholar 

  39. T.C. Chen, Expectation–Maximization Machine Learning Model for Micromechanical Evaluation of Thermally-Cycled Solder Joints in a Semiconductor, J. Phys. Condens. Matter, 2023, 35, 305901. https://doi.org/10.1088/1361-648X/accdab

    Article  Google Scholar 

  40. M. Bocquet, J. Brajard, A. Carrassi, and L. Bertino, Bayesian Inference of Chaotic Dynamics by Merging Data Assimilation, Machine Learning and Expectation-Maximization. ArXiv Prepr. ArXiv2001.06270. (2020).

  41. K. Greff, S. Van Steenkiste, and J. Schmidhuber, Neural Expectation Maximization. Adv. Neural Inf. Process. Syst., 2017, 30.

  42. D. Singh and B. Singh, Investigating the Impact of Data Normalization on Classification Performance, Appl. Soft Comput., 2020, 97, 105524.

    Article  Google Scholar 

  43. Y. Chauvin and D.E. Rumelhart, Backpropagation: Theory, Architectures, and Applications, Psychology Press, London, 2013.

    Book  Google Scholar 

  44. L. Xu, M. Jordan, and G.E. Hinton, An Alternative Model for Mixtures of Experts. Adv. Neural Inf. Process. Syst., 1994, 7.

  45. V. Samavatian, M. Fotuhi-Firuzabad, M. Samavatian, P. Dehghanian, and F. Blaabjerg, Correlation-Driven Machine Learning for Accelerated Reliability Assessment of Solder Joints in Electronics, Sci. Rep., 2020, 10, p 14821. https://doi.org/10.1038/s41598-020-71926-7

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. B. Marzbanrad, H. Jahed, and E. Toyserkani, On the Evolution of Substrate’s Residual Stress During Cold Spray Process: A Parametric Study, Mater. Des., 2018, 138, p 90-102.

    Article  CAS  Google Scholar 

  47. O.C. Ozdemir, C.A. Widener, M.J. Carter, and K.W. Johnson, Predicting the Effects of Powder Feeding Rates on Particle Impact Conditions and Cold Spray Deposited Coatings, J. Therm. Spray Technol., 2017, 26, p 1598-1615.

    Article  CAS  Google Scholar 

  48. Y. Zhang and C. Ling, A Strategy to Apply Machine Learning to Small Datasets in Materials Science, Npj Comput. Mater., 2018, 4, p 25.

    Article  CAS  Google Scholar 

  49. B. Szabó and I. Babuška, Finite Element Analysis: Method Verification and Validation, Wiley, New Jersey, 2021.

    Book  Google Scholar 

  50. H. Yeom, B. Maier, G. Johnson, T. Dabney, M. Lenling, and K. Sridharan, High Temperature Oxidation and Microstructural Evolution of Cold Spray Chromium Coatings on Zircaloy-4 in Steam Environments, J. Nucl. Mater., 2019, 526, 151737.

    Article  CAS  Google Scholar 

  51. C. Singhal and Q. Murtaza, Simulation of Critical Velocity of Cold Spray Process with Different Turbulence Models, Mater. Today Proc., 2018, 5, p 17371-17379.

    Article  Google Scholar 

  52. L. Palodhi and H. Singh, On the Dependence of Critical Velocity on the Material Properties During Cold Spray Process, J. Therm. Spray Technol., 2020, 29, p 1863-1875.

    Article  CAS  Google Scholar 

  53. M.R. Rokni, S.R. Nutt, C.A. Widener, V.K. Champagne, and R.H. Hrabe, Review of Relationship Between Particle Deformation, Coating Microstructure, and Properties in High-Pressure Cold Spray, J. Therm. Spray Technol., 2017, 26, p 1308-1355.

    Article  Google Scholar 

  54. Z. Arabgol, M.V. Vidaller, H. Assadi, F. Gärtner, and T. Klassen, Influence of Thermal Properties and Temperature of Substrate on the Quality of Cold-Sprayed Deposits, Acta Mater., 2017, 127, p 287-301.

    Article  CAS  Google Scholar 

  55. V.S. Bhattiprolu, K.W. Johnson, O.C. Ozdemir, and G.A. Crawford, Influence of Feedstock Powder and Cold Spray Processing Parameters on Microstructure and Mechanical Properties of Ti-6Al-4V Cold Spray Depositions, Surf. Coat. Technol., 2018, 335, p 1-12.

    Article  CAS  Google Scholar 

  56. S. Singh, R.K.S. Raman, C.C. Berndt, and H. Singh, Influence of Cold Spray Parameters on Bonding Mechanisms: A Review, Metals (Basel), 2021, 11, p 2016.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Academic Department of Engineering, National University José María Arguedas, Andahuaylas-Apurímac, Peru

    Rosa Huaraca Aparco

  2. Academic Departamento of Agroindustrial Engineering and Technology, José María Arguedas National University, Andahuaylas, Perú

    Fidelia Tapia-Tadeo

  3. National Amazonian University of Madre de Dios, Puerto Maldonado, Peru

    Yajhayda Bellido Ascarza & Alexis León Ramírez

  4. Academic Department of Basic Sciences, National Amazonian University of Madre de Dios, Puerto Maldonado, Peru

    Yersi-Luis Huamán-Romaní

  5. Academic Department of Engineering, National University Micaela Bastidas of Apurímac, Abancay, Peru

    Calixto Cañari Otero

Authors
  1. Rosa Huaraca Aparco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fidelia Tapia-Tadeo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yajhayda Bellido Ascarza
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alexis León Ramírez
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yersi-Luis Huamán-Romaní
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Calixto Cañari Otero
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Rosa Huaraca Aparco or Fidelia Tapia-Tadeo.

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

Aparco, R.H., Tapia-Tadeo, F., Ascarza, Y.B. et al. A Machine Learning Approach for Analyzing Residual Stress Distribution in Cold Spray Coatings. J Therm Spray Tech (2024). https://doi.org/10.1007/s11666-024-01776-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11666-024-01776-6

Keywords

Search

Navigation