Investigating the cold spraying process with the material point method

  • Yan LiuEmail author
  • Chenyang Xu


High-velocity impacts of micro copper particles on the copper substrate in the cold spraying process are simulated and investigated with the material point method (MPM). Both the single-particle and the multiple-particle models are built and simulated. The large deformation and fracture phenomena induced by the impact can be well simulated with the MPM owing to its meshfree feature. The final configurations of the sprayed particle and the substrate agree well with the experimental results reported in the literature and the results of other numerical methods. It is observed that the interlocking between the particles and the substrate may be an important contributor to the bonding mechanism. Influences of the impact velocities and impact angles are investigated numerically in detail.


Cold spray High-velocity impact Metal jetting Mechanical interlocking Meshfree particle methods Material point method 



Supported by National Natural Science Foundation of China (Grant Nos. 11772171 and 11472153).


  1. Aldwell, B., Kelly, E., Wall, R., Amaldi, A., O’Donnell, G.E., Lupoi, R.: Machinability of Al 6061 deposited with cold spray additive manufacturing. J. Therm. Spray Technol. 26(3), 1–12 (2017)Google Scholar
  2. Bae, G., Xiong, Y., Kumar, S., Kang, K., Lee, C.: General aspects of interface bonding in kinetic sprayed coatings. Acta Mater. 56, 4858–4868 (2008)CrossRefGoogle Scholar
  3. Bae, G., Kang, K., Na, H., Kim, J.J., Lee, C.: Effect of particle size on the microstructure and properties of kinetic sprayed nickel coatings. Surf. Coat. Technol. 204, 3326–3335 (2010)CrossRefGoogle Scholar
  4. Bardenhagen, S.G.: Energy conservation error in the material point method for solid mechanics. J. Comput. Phys. 180(1), 383–403 (2002)zbMATHCrossRefGoogle Scholar
  5. Bardenhagen, S.G., Brackbill, J.U., Sulsky, D.: The material-point method for granular materials. Comput. Methods Appl. Mech. Eng. 187(3), 529–541 (2000)zbMATHCrossRefGoogle Scholar
  6. Duan, Q., Belytschko, T.: Gardient and dilatational stabilizations for stress-point integration in the element-free Galerkin method. Int. J. Numer. Methods Eng. 77(6), 776–798 (2009)zbMATHCrossRefGoogle Scholar
  7. Gong, W., Liu, Y., Zhang, X., Ma, H.: Numerical investigation on dynamical response of aluminum foam subject to hypervelocity impact with material point method. Comput. Model. Eng. Sci. 83(5), 527–545 (2012)Google Scholar
  8. Grujicic, M., Zhao, C.L., DeRosset, W.S., Helfritch, D.: Adiabatic shear instability based mechanism for particles/substrate bonding in the cold-gas dynamic-spray process. Mater. Des. 25, 681–688 (2004)CrossRefGoogle Scholar
  9. He, N., Liu, Y., Zhang, X.: Seamless coupling of molecular dynamics and material point method via smoothed molecular dynamics. Int. J. Numer. Methods Eng. 112, 380–400 (2017)MathSciNetCrossRefGoogle Scholar
  10. Hon, Y.C., Schaback, R.: On unsymmetric collocation by radial basis functions. Appl. Math. Comput. 119(2–3), 177–186 (2001)MathSciNetzbMATHGoogle Scholar
  11. Hu, W., Chen, Z.: A multi-mesh MPM for simulating the meshing process of spur gears. Comput. Struct. 81(20), 1991–2002 (2003)CrossRefGoogle Scholar
  12. Huang, P., Zhang, X., Ma, S., Wang, H.K.: Shared memory openmp parallelization of explicit mpm and its application to hypervelocity impact. Comput. Model. Eng. Sci. 38(2), 119–147 (2008)zbMATHGoogle Scholar
  13. Huang, P., Zhang, X., Ma, S., Huang, X.: Contact algorithms for the material point method in impact and penetration simulation. Int. J. Numer. Methods Eng. 85(4), 498–517 (2011)zbMATHCrossRefGoogle Scholar
  14. Johnson, G.R., Cook, W.H.: Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng. Fract. Mech. 21(1), 31–48 (1985)CrossRefGoogle Scholar
  15. King, P.C., Bae, G., Zahiri, S.H., Jahedi, M., Lee, C.: An experimental and finite element study of cold spray copper impact onto two aluminum substrates. J. Therm. Spray Technol. 19(3), 620–635 (2010)CrossRefGoogle Scholar
  16. Lemiale, V., King, P.C., Rudman, M., Prakash, M., Cleary, P.W., Jahedi, M.Z., Gulizia, S.: Temperature and strain rate effects in cold spray investigated by smoothed particle hydrodynamics. Surf. Coat. Technol. 254(10), 121–130 (2014)CrossRefGoogle Scholar
  17. Li, W.Y., Gao, W.: Some aspects on 3d numerical modeling of high velocity impact of particles in cold spraying by explicit finite element analysis. Appl. Surf. Sci. 255, 7878–7892 (2009)CrossRefGoogle Scholar
  18. Li, W.Y., Liao, H., Li, C.J., Li, G., Coddet, C., Wang, X.: On high velocity impact of micro-sized metallic particles in cold spraying. Appl. Surf. Sci. 253(5), 2852–2862 (2006)CrossRefGoogle Scholar
  19. Li, W.Y., Yin, S., Wang, X.F.: Numerical investigations of the effect of oblique impact on particle deformation in cold spraying by the SPH method. Appl. Surf. Sci. 256(12), 3725–3734 (2010)CrossRefGoogle Scholar
  20. Liu, G.R., Liu, M.: Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific, Singapore (2003)zbMATHCrossRefGoogle Scholar
  21. Liu, W.K., Jun, S., Zhang, Y.F.: Reproducing kernel particle methods. Int. J. Numer. Methods Fluids 20(8–9), 1081–1106 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  22. Liu, Y., Zhang, X., Lu, M.W.: A meshless method based on least-squares approach for steady- and unsteady-state heat conduction problems. Numer. Heat Transf. Part B Fundam. 47(3), 257–275 (2005)CrossRefGoogle Scholar
  23. Liu, Y., Hon, Y.C., Liew, K.M.: A meshfree hermite-type radial point interpolation method for kirchhoff plate problems. Int. J. Numer. Methods Eng. 66, 1153–1178 (2006)zbMATHCrossRefGoogle Scholar
  24. Liu, Y., Wang, H.K., Zhang, X.: A multiscale framework for high-velocity impact process with combined material point method and molecular dynamics. Int. J. Mech. Mater. Des. 9(2), 127–139 (2013)CrossRefGoogle Scholar
  25. Liu, P., Liu, Y., Zhang, X.: Improved shielding structure with double honeycomb cores for hyper-velocity impact. Mech. Res. Commun. 69, 34–39 (2015a)CrossRefGoogle Scholar
  26. Liu, P., Liu, Y., Zhang, X.: Internal-structure-model based simulation research of shielding properties of honeycomb sandwich panel subjected to high-velocity impact. Int. J. Impact Eng. 77, 120–133 (2015b)CrossRefGoogle Scholar
  27. Liu, P., Liu, Y., Zhang, X., Guan, Y.: Investigation on high-velocity impact of micron particles using material point method. Int. J. Impact Eng. 75, 241–254 (2015c)CrossRefGoogle Scholar
  28. Liu, P., Liu, Y., Zhang, X.: Simulation of hyper-velocity impact on double honeycomb sandwich panel and its staggered improvement with internal-structure model. Int. J. Mech. Mater. Des. 12(2), 241–254 (2016)MathSciNetCrossRefGoogle Scholar
  29. Ma, S., Zhang, X., Qiu, X.M.: Comparison study of MPM and SPH in modeling hypervelocity impact problems. Int. J. Impact Eng. 36(2), 272–282 (2009)CrossRefGoogle Scholar
  30. Ma, Z.T., Zhang, X., Huang, P.: An object-oriented mpm framework for simulation of large deformation and contact of numerous grains. Comput. Model. Eng. Sci. 55(1), 61–87 (2010)Google Scholar
  31. Manap, A., Ogawa, K., Okabe, T.: Numerical analysis of interfacial bonding of al-si particle and mild steel substrate by cold spray technique using the SPH method. J. Solid Mech. Mater. Eng. 6(3), 241–250 (2012)CrossRefGoogle Scholar
  32. Meyers, M.A.: Dynamic Behavior of Materials. Wiley, New York (1994)zbMATHCrossRefGoogle Scholar
  33. Profizi, P., Combescure, A., Ogawa, K.: SPH modeling of adhesion in fast dynamics: application to the cold spray process. C.R. Mec. 344, 211–224 (2016)CrossRefGoogle Scholar
  34. Saleh, M., Luzin, V., Spencer, K.: Analysis of the residual stress and bonding mechanism in the cold spray technique using experimental and numerical methods. Surf. Coat. Technol. 252, 15–28 (2014)CrossRefGoogle Scholar
  35. Sova, A., Grigoriev, S., Okunkova, A., Smurov, I.: Potential of cold gas dynamic spray as additive manufacturing technology. Int. J. Adv. Manuf. Technol. 69(9–12), 2269–2278 (2013)CrossRefGoogle Scholar
  36. Sulsky, D., Gong, M.: Improving the material-point method. In: Weinberg, K., Pandolfi, A. (eds.) Innovative Numerical Approaches for Multi-Field and Multi-Scale Problems. Lecture Notes in Applied and Computational Mechanics, vol. 81, pp. 217–240. Springer, Cham (2016)CrossRefGoogle Scholar
  37. Sulsky, D., Chen, Z., Schreyer, H.L.: A particle method for history-dependent materials. Comput. Methods Appl. Mech. Eng. 118(1–2), 179–196 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  38. Tao, J., Zheng, Y., Chen, Z., Zhang, H.: Generalized interpolation material point method for coupled thermo-mechanical processes. Int. J. Mech. Mater. Des. 12, 577–595 (2016)CrossRefGoogle Scholar
  39. Villafuerte, J.: Modern Cold Spray: Materials, Process, and Applications. Springer, Cham (2015)CrossRefGoogle Scholar
  40. Wang, J.G., Liu, G.R.: A point interpolation meshless method based on radial basis functions. Int. J. Numer. Methods Eng. 54, 1623–1648 (2002)zbMATHCrossRefGoogle Scholar
  41. Wu, X.K., Zhou, X.L., Cui, H., Zhang, J.S.: Morphology prediction of cold-sprayed Cu and Al coatings through multi-particles deposition simulation. J. Univ. Sci. Technol. Beijing 34(12), 1391–1399 (2012)Google Scholar
  42. Yang, G., Han, X., Hu, D.: Computer simulation of two-dimensional linear-shaped charge jet using smoothed particle hydrodynamics. Eng. Comput. 28(1–2), 58–75 (2011)zbMATHGoogle Scholar
  43. Yin, S., Wang, X.F., Li, W.Y., Xu, B.P.: Numerical investigation on effects of interactions between particles on coating formation in cold spraying. J. Therm. Spray Technol. 18, 686–693 (2009)CrossRefGoogle Scholar
  44. Yin, S., Wang, X.F., Li, Y.: High-velocity impact process between particle and substrate in cold spraying. Explos. Shock Waves 30(5), 546–550 (2010)Google Scholar
  45. Yin, S., Wang, X.F., Li, W.Y., Jie, H.E.: Effect of substrate hardness on the deformation behavior of subsequently incidient particles in cold spraying. Appl. Surf. Sci. 257, 7560–7565 (2011)CrossRefGoogle Scholar
  46. Yin, S., Suo, X., Su, J., Guo, Z., Liao, H., Wang, X.: Effects of substrate hardness and spray angle on the deposition behavior of cold-sprayed ti particles. J. Therm. Spray Technol. 23(1–2), 76–84 (2014)CrossRefGoogle Scholar
  47. Yin, S., Xie, Y., Suo, X., Liao, H., Wang, X.: Interfacial bonding features of Ni coating on Al substrate with different surface pretreatments in cold spray. Mater. Lett. 138, 143–147 (2015)CrossRefGoogle Scholar
  48. Zhang, X., Liu, Y.: Meshless Methods. Tsinghua University Press & Springer, Beijing (2004)Google Scholar
  49. Zhang, X., Song, K.Z., Lu, M.W., Liu, X.: Meshless methods based on collocation with radial basis functions. Comput. Mech. 26(4), 333–343 (2000)zbMATHCrossRefGoogle Scholar
  50. Zhang, X., Sze, K.Y., Ma, S.: An explicit material point finite element method for hyper-velocity impact. Int. J. Numer. Methods Eng. 66(4), 689–706 (2006)zbMATHCrossRefGoogle Scholar
  51. Zhang, M.Y., Zhang, H., Zheng, L.L.: Simulation of droplet spreading, splashing and solidification using smoothed particle hydrodynamics method. Int. J. Heat Mass Transf. 51, 3410–3419 (2008)zbMATHCrossRefGoogle Scholar
  52. Zhang, Z., Wu, H., Hao, W., Bao, Y., Chai, G.: A systematic AMF-FEM coupled method for the thermo-elasto-plastic contact analysis of the plasma sprayed ha-coated biocomposite. Int. J. Mech. Mater. Des. 9, 227–238 (2013)CrossRefGoogle Scholar
  53. Zhang, X., Chen, Z., Liu, Y.: The Material Point Method: A Continuum-Based Particle Method for Extreme Loading Cases. Academic Press, Beijing (2016)Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Aerospace EngineeringTsinghua UniversityBeijingPeople’s Republic of China

Personalised recommendations