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Investigating the cold spraying process with the material point method

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Abstract

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.

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References

  • 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 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Bardenhagen, S.G.: Energy conservation error in the material point method for solid mechanics. J. Comput. Phys. 180(1), 383–403 (2002)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MathSciNet  Google Scholar 

  • Hon, Y.C., Schaback, R.: On unsymmetric collocation by radial basis functions. Appl. Math. Comput. 119(2–3), 177–186 (2001)

    MathSciNet  MATH  Google Scholar 

  • Hu, W., Chen, Z.: A multi-mesh MPM for simulating the meshing process of spur gears. Comput. Struct. 81(20), 1991–2002 (2003)

    Article  Google Scholar 

  • 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)

    MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Liu, G.R., Liu, M.: Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific, Singapore (2003)

    Book  MATH  Google Scholar 

  • Liu, W.K., Jun, S., Zhang, Y.F.: Reproducing kernel particle methods. Int. J. Numer. Methods Fluids 20(8–9), 1081–1106 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Liu, P., Liu, Y., Zhang, X.: Improved shielding structure with double honeycomb cores for hyper-velocity impact. Mech. Res. Commun. 69, 34–39 (2015a)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  MathSciNet  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • Meyers, M.A.: Dynamic Behavior of Materials. Wiley, New York (1994)

    Book  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Chapter  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Villafuerte, J.: Modern Cold Spray: Materials, Process, and Applications. Springer, Cham (2015)

    Book  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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 

  • 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)

    MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Zhang, X., Liu, Y.: Meshless Methods. Tsinghua University Press & Springer, Beijing (2004)

    Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

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Acknowledgements

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

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  1. School of Aerospace Engineering, Tsinghua University, Beijing, 100084, People’s Republic of China

    Yan Liu & Chenyang Xu

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  1. Yan Liu
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  2. Chenyang Xu
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Correspondence to Yan Liu.

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Liu, Y., Xu, C. Investigating the cold spraying process with the material point method. Int J Mech Mater Des 15, 361–378 (2019). https://doi.org/10.1007/s10999-018-9419-4

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  • DOI: https://doi.org/10.1007/s10999-018-9419-4

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