Skip to main content
SpringerLink
Log in

On the Dependence of Critical Velocity on the Material Properties During Cold Spray Process

  • PEER REVIEWED
  • Published:
Journal of Thermal Spray Technology Aims and scope Submit manuscript

Abstract

Optimization of the cold spray process is extremely challenging due to the involvement of a large number of process parameters as well as material properties. Modern approaches for modeling the cold spray process have relied largely on numerical simulations. In this paper, we shall present a simplified mathematical model which will be benchmarked against experimental and numerical measurements available in the literature and demonstrate that the model shows reasonable agreement with real-world observations. We will present a parametric study using this model and identify the factors that strongly affect the cold spray process, which can be used for identifying and optimizing the process parameters and the material properties.

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

Similar content being viewed by others

Abbreviations

\(\varepsilon\) :

Plastic strain

\(\varepsilon_{\text{f}}\) :

Final strain

k :

Strength coefficient

σ :

Stress

n :

Strain hardening exponent

U se :

Strain energy

U re :

Rebound energy

e :

Coefficient of restitution

e r :

Recoil coefficient

m p :

Particle mass

v p :

Particle velocity

v cr :

Critical velocity

σ yp :

Effective yield stress

E p :

Elastic modulus of the particle

E s :

Elastic modulus of the substrate

E* :

Effective elastic modulus

Δγ :

Difference in interface energy between the colliding bodies

μ s :

Poisson’s ratio of the substrate

μ p :

Poisson’s ratio of the particle

ρ p :

Particle density

d p :

Particle diameter

a :

Contact radius

R p :

Radius of the particle

R s :

Radius of the substrate

R :

Effective radius on elastic collision

F :

Applied force on the substrate

r :

Radius of the spherical cap

h :

Height of the spherical cap

C d :

Particle drag coefficient

C 2 :

Fitting parameter

R g :

Gas constant

L d :

Nozzle divergent length

P 0 :

Inlet pressure/gas stagnation pressure

T 0 :

Inlet temperature/gas stagnation temperature

A :

Yield stress

B :

Hardening constant

C :

Strain rate constant

m :

Thermal softening exponent

\(\dot{\varepsilon }\) :

Strain rate

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

Normalizing reference strain rate

T* :

Normalized reference temperature

T m :

Melting temperature

T r :

Reference temperature

References

  1. T. Schmidt, H. Assadi, F. Gärtner, H. Richter, T. Stoltenhoff, H. Kreye, and T. Klassen, From Particle Acceleration to Impact and Bonding in Cold Spraying, J. Therm. Spray Technol., 2009, 18(5-6), p 794

    Article  Google Scholar 

  2. F. Gärtner, T. Stoltenhoff, T. Schmidt, and H. Kreye, The Cold Spray Process and Its Potential for Industrial Applications, J. Therm. Spray Technol., 2006, 15(2), p 223-232

    Article  Google Scholar 

  3. J. Wu, H. Fang, S. Yoon, C. Lee, and H. Kim, Critical Velocities for High Speed Particle Deposition in Kinetic Spraying, Mater. Trans., 2006, 47(7), p 1723-1727

    Article  CAS  Google Scholar 

  4. H. Assadi, T. Schmidt, H. Richter, J.-O. Kliemann, K. Binder, F. Gärtner, T. Klassen, and H. Kreye, On Parameter Selection in Cold Spraying, J. Therm. Spray Technol., 2011, 20(6), p 1161-1176

    Article  CAS  Google Scholar 

  5. T. Stoltenhoff, H. Kreye, and H.J. Richter, An Analysis of the Cold Spray Process and Its Coatings, J. Therm. Spray Technol., 2002, 11(4), p 542-550

    Article  CAS  Google Scholar 

  6. H. Assadi, F. Gärtner, T. Stoltenhoff, and H. Kreye, Bonding Mechanism in Cold Gas Spraying, Acta Mater., 2003, 51(15), p 4379-4394

    Article  CAS  Google Scholar 

  7. T. Schmidt, F. Gärtner, H. Assadi, and H. Kreye, Development of a Generalized Parameter Window for Cold Spray Deposition, Acta Mater., 2006, 54(3), p 729-742

    Article  CAS  Google Scholar 

  8. C.-J. Li, W.-Y. Li, and H. Liao, Examination of the Critical Velocity for Deposition of Particles in Cold Spraying, J. Therm. Spray Technol., 2006, 15(2), p 212-222

    Article  CAS  Google Scholar 

  9. F.F. Wang, W.Y. Li, M. Yu, and H.L. Liao, Prediction of Critical Velocity During Cold Spraying Based on a Coupled Thermomechanical Eulerian Model, J. Therm. Spray Technol., 2014, 23(1-2), p 60-67

    Article  Google Scholar 

  10. G. Bae, Y. Xiong, S. Kumar, K. Kang, and C. Lee, General Aspects of Interface Bonding in Kinetic Sprayed Coatings, Acta Mater., 2008, 56(17), p 4858-4868

    Article  CAS  Google Scholar 

  11. A. Moridi, S.M. Hassani-Gangaraj, and M. Guagliano, A Hybrid Approach to Determine Critical and Erosion Velocities in the Cold Spray Process, Appl. Surf. Sci., 2013, 273, p 617-624

    Article  CAS  Google Scholar 

  12. F. Meng, S. Yue, and J. Song, Quantitative Prediction of Critical Velocity and Deposition Efficiency in Cold-Spray: A Finite-Element Study, Scr. Mater., 2015, 107, p 83-87

    Article  CAS  Google Scholar 

  13. M. Hassani-Gangaraj, D. Veysset, V.K. Champagne, K.A. Nelson, and C.A. Schuh, Adiabatic Shear Instability is Not Necessary for Adhesion in Cold Spray, Acta Mater., 2018, 158, p 430-439

    Article  CAS  Google Scholar 

  14. H. Assadi, F. Gärtner, T. Klassen, and H. Kreye, Comment on ‘Adiabatic Shear Instability is Not Necessary for Adhesion in Cold Spray’, Scr. Mater., 2019, 162, p 512-514

    Article  CAS  Google Scholar 

  15. C. Sun, X. Zhou, C. Xie, and B. Liu, Investigating Hard/Soft Combinations of Cold Spraying by Eulerian Approach, Surf. Eng., 2020, 36(10), p 1049-1057

    Article  CAS  Google Scholar 

  16. S. Yin, H.L. Liao, and X.F. Wang, Euler Based Finite Element Analysis on High Velocity Impact Behaviour in Cold Spraying, Surf. Eng., 2014, 30(5), p 309-315

    Article  CAS  Google Scholar 

  17. M. Hassani-Gangaraj, D. Veysset, K.A. Nelson, and C.A. Schuh, In Situ Observations of Single Micro-particle Impact Bonding, Scr. Mater., 2018, 145, p 9-13

    Article  CAS  Google Scholar 

  18. B. Yildirim, Mechanistic Modeling of High Velocity Micro-particle Impacts: Application to Material Deposition by Cold Spray Process, Northeastern University, Boston, 2013

    Google Scholar 

  19. R.K. Nutor, N.K. Adomako, and Y.Z. Fang, Using the Hollomon Model to Predict Strain-Hardening in Metals, Am. J. Mater. Synth. Process., 2017, 2(1), p 1-4

    Google Scholar 

  20. G.R. Johnson and W.H. Cook, in Proceedings of the 7th International Symposium on Ballistics, The Hague, Netherlands, 1983 (International Ballistics Society, 1983)

  21. R.C. Dykhuizen and M.F. Smith, Gas Dynamic Principles of Cold Spray, J. Therm. Spray Technol., 1998, 7(2), p 205-212

    Article  CAS  Google Scholar 

  22. A.C. Fischer-Cripps, E.F. Gloyna, and W.H. Hart, Introduction to Contact Mechanics, Springer, Berlin, 2000

    Google Scholar 

  23. B.V. Derjaguin, V.M. Muller, and Y.P. Toporov, Effect of Contact Deformations on the Adhesion of Particles, J. Colloid Interface Sci., 1975, 53(2), p 314-326

    Article  CAS  Google Scholar 

  24. B.V. Derjaguin, V.M. Muller, and Y.P. Toporov, Effect of Contact Deformations on the Adhesion of Particles, Prog. Surf. Sci., 1994, 45(1-4), p 131-143

    Article  Google Scholar 

  25. A. Nastic, M. Vijay, A. Tieu, S. Rahmati, and B. Jodoin, Experimental and Numerical Study of the Influence of Substrate Surface Preparation on Adhesion Mechanisms of Aluminum Cold Spray Coatings on 300 M Steel Substrates, J. Therm. Spray Technol., 2017, 26(7), p 1461-1483

    Article  CAS  Google Scholar 

  26. R. Nikbakht, S.H. Seyedein, S. Kheirandish, H. Assadi, and B. Jodoin, Asymmetrical Bonding in Cold Spraying of Dissimilar Materials, Appl. Surf. Sci., 2018, 444, p 621-632

    Article  CAS  Google Scholar 

  27. L. Zhu, T.-C. Jen, Y.-T. Pan, and H.-S. Chen, Particle Bonding Mechanism in Cold Gas Dynamic Spray: A Three-Dimensional Approach, J. Therm. Spray Technol., 2017, 26(8), p 1859-1873

    Article  CAS  Google Scholar 

  28. W.-Y. Li, C. Zhang, C.-J. Li, and H. Liao, Modeling Aspects of High Velocity Impact of Particles in Cold Spraying by Explicit Finite Element Analysis, J. Therm. Spray Technol., 2009, 18(5-6), p 921

    Article  CAS  Google Scholar 

  29. A. Manap, O. Nooririnah, H. Misran, T. Okabe, and K. Ogawa, Experimental and SPH Study of Cold Spray Impact Between Similar and Dissimilar Metals, Surf. Eng., 2014, 30(5), p 335-341

    Article  CAS  Google Scholar 

  30. J. Xie, D. Nélias, W.-L. Berre, K. Ogawa, and Y. Ichikawa, Simulation of the Cold Spray Particle Deposition Process, J. Tribol., 2015, 137(4), p 041101

  31. S. Rahmati and B. Jodoin, Physically Based Finite Element Modeling Method to Predict Metallic Bonding in Cold Spray, J. Therm. Spray Technol., 2020, 29, p 611-629

    Article  CAS  Google Scholar 

  32. F. Raletz, M. Vardelle, and G. Ezo’o, Critical Particle Velocity Under Cold Spray Conditions, Surf. Coat. Technol., 2006, 201(5), p 1942-1947

    Article  CAS  Google Scholar 

  33. K. Kang, S. Yoon, Y. Ji, and C. Lee, Oxidation Dependency of Critical Velocity for Aluminum Feedstock Deposition in Kinetic Spraying Process, Mater. Sci. Eng. A, 2008, 486(1-2), p 300-307

    Article  Google Scholar 

Download references

Acknowledgments

This work is funded through Faculty Research and Innovation Award (FRIA) grant, for which the authors are grateful to Indian Institute of Technology Ropar, Rupnagar (India).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Ropar, Rupnagar, Punjab, 140001, India

    Lopamudra Palodhi & Harpreet Singh

Authors
  1. Lopamudra Palodhi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Harpreet Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lopamudra Palodhi.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Palodhi, L., Singh, H. On the Dependence of Critical Velocity on the Material Properties During Cold Spray Process. J Therm Spray Tech 29, 1863–1875 (2020). https://doi.org/10.1007/s11666-020-01105-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11666-020-01105-7

Keywords

Search

Navigation