Journal of Thermal Spray Technology

, Volume 23, Issue 3, pp 530–540 | Cite as

The Use of Particle/Substrate Material Models in Simulation of Cold-Gas Dynamic-Spray Process

Peer Reviewed


Cold spray is a coating deposition method in which the solid particles are accelerated to the substrate using a low temperature supersonic gas flow. Many numerical studies have been carried out in the literature in order to study this process in more depth. Despite the inability of Johnson-Cook plasticity model in prediction of material behavior at high strain rates, it is the model that has been frequently used in simulation of cold spray. Therefore, this research was devoted to compare the performance of different material models in the simulation of cold spray process. Six different material models, appropriate for high strain-rate plasticity, were employed in finite element simulation of cold spray process for copper. The results showed that the material model had a considerable effect on the predicted deformed shapes.


cold spray high strain rate simulation 


  1. 1.
    H. Assadi, F. Gärtner, T. Stoltenhoff, and H. Kreye, Bonding Mechanism in Cold Gas Spraying, Acta Mater., 2003, 51(15), p 4379-4394CrossRefGoogle Scholar
  2. 2.
    M. Grujicic, C.L. Zhao, W.S. DeRosset, and D. Helfritch, Adiabatic Shear Instability Based Mechanism for Particles/Substrate Bonding in the Cold-Gas Dynamic-Spray Process, Mater. Des., 2004, 25(8), p 681-688CrossRefGoogle Scholar
  3. 3.
    M. Grujicic, J.R. Saylor, D.E. Beasley, W.S. DeRosset, and D. Helfritch, Computational Analysis of the Interfacial Bonding Between Feed-Powder Particles and the Substrate in the Cold-Gas Dynamic-Spray Process, Appl. Surf. Sci., 2003, 219(3-4), p 211-227CrossRefGoogle Scholar
  4. 4.
    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 729-742CrossRefGoogle Scholar
  5. 5.
    G. Bae, S. Kumar, S. Yoon, K. Kang, H. Na, H.-J. Kim, and C. Lee, Bonding Features and Associated Mechanisms in Kinetic Sprayed Titanium Coatings, Acta Mater., 2009, 57(19), p 5654-5666CrossRefGoogle Scholar
  6. 6.
    P.C. King, G. Bae, S.H. Zahiri, M. Jahedi, and C. Lee, An Experimental and Finite Element Study of Cold Spray Copper Impact onto Two Aluminum Substrates, J. Thermal Spray Technol., 2010, 19(3), p 620-634CrossRefGoogle Scholar
  7. 7.
    J. Kocimski, R.G. Maev, and V. Leshchynsky, Modeling of Particle Consolidation by Cold Spray, International Thermal Spray Conference & Exposition 2010, Thermal Spray: Global Solutions for Future Application. DVS-ASM, Materials Park, 2010, p. 774-779Google Scholar
  8. 8.
    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, ASM Int., 2009, 18, p 921-933Google Scholar
  9. 9.
    W.-Y. Li, S. Yin, and X.-F. Wang, Numerical Investigations of the Effect of Oblique Impact on Particle Deformation in Cold Spraying by the SPH Method, Appl. Surf. Sci., 2010, 256(12), p 3725-3734CrossRefGoogle Scholar
  10. 10.
    R. Ghelichi, S. Bagherifard, M. Guagliano, and M. Verani, Numerical Simulation of Cold Spray Coating, Surf. Coat. Technol., 2011, 205(23-24), p 5294-5301CrossRefGoogle Scholar
  11. 11.
    A. Moridi, S. 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 617-624CrossRefGoogle Scholar
  12. 12.
    B. Hopkinson, A Method of Measuring the Pressure Produced in the Detonation of High Explosives or by the Impact of Bullets, Proc. R. Soc. Lond. Ser. A, 1914, 89(612), p 411-413CrossRefGoogle Scholar
  13. 13.
    P.S. Follansbee and U.F. Kocks, A Constitutive Description of the Deformation of Copper Based on the Use of the Mechanical Threshold Stress as an Internal State Variable, Acta Mater., 1987, 36, p 81-93CrossRefGoogle Scholar
  14. 14.
    W. Tong and R.J. Clifton, Pressure-Shear Impact Investigation of Strain Rate History Effects in Oxygen-Free High-Conductivity Copper, Mech. Phys. Solids, 1991, 40, p 1251-1294CrossRefGoogle Scholar
  15. 15.
    S. Huang, and R.J. Clifton, Macro and Micro-Mechanics of High Velocity Deformation and Fracture, IUTAM Symposium on MMMHVDF, Tokyo, 1985, p. 63Google Scholar
  16. 16.
    M.A. Meyers, F. Gregori, B.K. Kad, M.S. Schneider, D.H. Kalantar, B.A. Remington, G. Ravichandran, T. Boehly, and J.S. Wark, Laser-Induced Shock Compression of Monocrystalline Copper: Characterization and Analysis, Acta Mater., 2003, 51(5), p 1211-1228CrossRefGoogle Scholar
  17. 17.
    W.J. Murphy, A. Higginbotham, G. Kimminau, B. Barbrel, E.M. Bringa, J. Hawreliak, R. Kodama, M. Koenig, W. McBarron, M.A. Meyers, B. Nagler, N. Ozaki, N. Park, B. Remington, S. Rothman, S.M. Vinko, T. Whitcher, and J.S. Wark, The Strength of Single Crystal Copper Under Uniaxial Shock Compression at 100 GPa, J. Phys., 2010, 22, p 1-6Google Scholar
  18. 18.
    E.M. Bringa, K. Rosolankova, R.E. Rudd, B.A. Remington, J.S. Wark, M. Duchaineau, D.H. Kalantar, J. Hawreliak, and J. Belak, Shock Deformation of Face-Centred-Cubic Metals on Subnanosecond Timescales, Nat. Mater., 2006, 5(10), p 805-809CrossRefGoogle Scholar
  19. 19.
    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(1), p 31-48CrossRefGoogle Scholar
  20. 20.
    C.Y. Gao and L.C. Zhang, Constitutive Modelling of Plasticity of fcc Metals Under Extremely High Strain Rates, Int. J. Plast., 2012, 32-33, p 121-133CrossRefGoogle Scholar
  21. 21.
    J.-B. Kim and H. Shin, Comparison of Plasticity Models for Tantalum and a Modification of the PTW Model for Wide Ranges of Strain, Strain Rate, and Temperature, Int. J. Impact Eng., 2009, 36(5), p 746-753CrossRefGoogle Scholar
  22. 22.
    R. Liang and A.S. Khan, A Critical Review of Experimental Results and Constitutive Models for BCC and FCC Metals Over a Wide Range of Strain Rates and Temperatures, Int. J. Plast., 1999, 15, p 963-980CrossRefGoogle Scholar
  23. 23.
    F.H. Abed, G.Z. Voyiadjis, B. Rouge, and Louisiana, A Consistent Modified Zerilli-Armstrong Flow Stress Model for BCC and FCC Metals for Elevated Temperatures, Acta Mech., 2005, 175, p 1-18CrossRefGoogle Scholar
  24. 24.
    G.Z. Voyiadjis and F.H. Abed, Microstructural Based Models for bcc and fcc Metals with Temperature and Strain Rate Dependency, Mech. Mater., 2003, 37, p 355-378CrossRefGoogle Scholar
  25. 25.
    D.L. Preston, D.L. Tonks, and D.C. Wallace, Model of Plastic Deformation for Extreme Loading Conditions, Appl. Phys., 2003, 93, p 211-220CrossRefGoogle Scholar
  26. 26.
    H. Huh, H. Lee, and J. Song, Dynamic Hardening Equation of the Auto-Body Steel Sheet with the Variation of Temperature, Int. J. Automot. Technol., 2012, 13(1), p 43-60CrossRefGoogle Scholar
  27. 27.
    M. Grujicic, B. Pandurangan, C.F. Yen, and B. Cheeseman, Modifications in the AA5083 Johnson-Cook Material Model for Use in Friction Stir Welding Computational Analyses, J. Mater. Eng. Perform., 2012, 21(11), p 2207-2217CrossRefGoogle Scholar
  28. 28.
    R. Armstrong and F. Zerilli, Dislocation Mechanics Aspects of Plastic Instability and Shear Banding, Mech. Mater., 1994, 17(2), p 319-327CrossRefGoogle Scholar
  29. 29.
    F.J. Zerilli and R.W. Armstrong, Dislocation Mechanics Based Constitutive Relations for Material Dynamics Calculations, J. Appl. Phys., 1987, 61(5), p 1816-1825CrossRefGoogle Scholar
  30. 30.
    A.S. Khan and R. Liang, Behaviors of Three BCC Metal Over a Wide Range of Strain Rates and Temperatures: Experiments and Modeling, Int. J. Plast., 1999, 15(10), p 1089-1109CrossRefGoogle Scholar
  31. 31.
    A.S. Khan and R. Liang, Behaviors of Three BCC Metals During Non-proportional Multi-axial Loadings: Experiments and Modeling, Int. J. Plast., 2000, 16(12), p 1443-1458CrossRefGoogle Scholar
  32. 32.
    H. Huh, J.H. Song, and H.J. Lee, Dynamic Tensile Tests of Auto-Body Steel Sheets with the Variation of Temperature, Solid State Phenom., 2006, 116, p 259-262Google Scholar
  33. 33.
    D. Simulia, ABAQUS 6.11 Analysis User’s Manual, Abaqus 6.11 Documentation, 2011, p 22.22Google Scholar
  34. 34.
    E.P. De Garmo, J.T. Black, and R.A. Kohser, DeGarmo’s Materials and Processes in Manufacturing, Wiley, New Jersey, 2011Google Scholar
  35. 35.
    W.Y. Li, Study on Effect of Particle Parameters on Deposition Behavior, Microstructure Evolution and Properties in Cold Spraying. Xi’an Jiotong University, ChinaGoogle Scholar
  36. 36.
    D. Rittel, G. Ravichandran, and S. Lee, Large Strain Constitutive Behavior of OFHC Copper over a Wide Range of Strain Rates Using the Shear Compression Specimen, Mech. Mater., 2002, 34(10), p 627-642CrossRefGoogle Scholar
  37. 37.
    K. Ahn, H. Huh, and L. Park, Comparison of Dynamic Hardening Equations for Metallic Materials with the Variation of Crystalline Structures, ICHSF2012, 2012, p. 176-187Google Scholar
  38. 38.
    R.A. MacDonald and W.M. MacDonald, Thermodynamic Properties of fcc Metals at High Temperatures, Phys. Rev. B, 1981, 24(4), p 1715-1724CrossRefGoogle Scholar
  39. 39.
    A.C. Mitchell and W.J. Nellis, Shock Compression of Aluminum, Copper, and Tantalum, J. Appl. Phys., 1981, 52(5), p 3363-3374CrossRefGoogle Scholar

Copyright information

© ASM International 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIsfahan University of TechnologyIsfahanIran

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