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Journal of Thermal Spray Technology

, Volume 27, Issue 4, pp 641–653 | Cite as

High-Strain-Rate Material Behavior and Adiabatic Material Instability in Impact of Micron-Scale Al-6061 Particles

  • Qiyong Chen
  • Arash Alizadeh
  • Wanting Xie
  • Xuemei Wang
  • Victor Champagne
  • Andrew Gouldstone
  • Jae-Hwang Lee
  • Sinan Müftü
Peer Reviewed

Abstract

Impact of spherical particles onto a flat sapphire surface was investigated in 50-950 m/s impact speed range experimentally and theoretically. Material parameters of the bilinear Johnson–Cook model were determined based on comparison of deformed particle shapes from experiment and simulation. Effects of high-strain-rate plastic flow, heat generation due to plasticity, material damage, interfacial friction and heat transfer were modeled. Four distinct regions were identified inside the particle by analyzing temporal variation of material flow. A relatively small volume of material near the impact zone becomes unstable due to plasticity-induced heating, accompanied by severe drop in the flow stress for impact velocity that exceeds ~ 500 m/s. Outside of this region, flow stress is reduced due to temperature effects without the instability. Load carrying capacity of the material degrades and the material expands horizontally leading to jetting. The increase in overall plastic and frictional dissipation with impact velocity was found to be inherently lower than the increase in the kinetic energy at high speeds, leading to the instability. This work introduces a novel method to characterize HSR (109 s−1) material properties and also explains coupling between HSR material behavior and mechanics that lead to extreme deformation.

Keywords

adiabatic shear instability Al-6061 cold spray high strain rate Johnson–Cook model material instability particle impact 

List of symbols

A

Static yield stress, MPa

Ac

Contact area, m2

B

Coefficient of strain hardening, MPa

c

Specific heat, J/kg K

C

Bilinear strain rate coefficient

D1

Height of deformed particle, m

D2

Diameter of deformed particle, m

Dp

Diameter of particle, m

e

Coefficient of restitution

E

Elastic modulus, error between experiment and simulation aspect ratios

Ek

Kinetic energy of particle, J

Er

Recovered strain energy, J

k

Thermal conductivity, W/m K

m

Index of thermal softening

mp

Mass of particle, kg

n

Index of strain-rate hardening

Re

Experimental aspect ratio

Rs

Simulated aspect ratio

T

Temperature, K

T*

Homologous temperature

Tm

Melting temperature, K

TR

Reference temperature, K

Up

Energy dissipated due to plastic action, J

vi

Impact velocity, m/s

vr

Rebound velocity, m/s

Wf

Work done against friction, J

x

Optimization variable vector

Greek letters

α

Thermal expansion ratio, K−1

β

Inelastic heat fraction

\(\varepsilon_{f}\)

Failure shear strain

\(\varepsilon_{\text{p}}\)

Equivalent plastic strain

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

Reference strain rate, s−1

\(\dot{\varepsilon }_{\text{c}}\)

Critical reference strain rate, s−1

\(\dot{\varepsilon }_{\text{p}}\)

Equivalent plastic strain rate, s−1

µ

Kinetic friction coefficient

ν

Poisson’s ratio

ρ

Mass density, kg/m3

σY

Yield (flow) stress, MPa

Subscripts

r

Material properties at room temperature

Acronyms

CS

Cold spray

FEA

Finite element analysis

GZ

Gao-Zhang

HSR

High strain rate

JC

Johnson–Cook

KHL

Khan–Huang–Liang

LIPIT

Laser-induced projectile impact test

PDMS

Polydimethylsiloxane

PTW

Preston–Tonk–Wallace

VA

Voyiadjis–Abed

ZA

Zerilli–Armstrong

References

  1. 1.
    S.V. Klinkov, V.F. Kosarev, and M. Rein, Cold Spray Deposition: Significance of Particle Impact Phenomena, Aerosp. Sci. Technol., 2005, 9(7), p 582-591CrossRefGoogle Scholar
  2. 2.
    M.A. Meyers, Dynamic Behavior of Materials, Wiley, New York, 1994CrossRefGoogle Scholar
  3. 3.
    G.T. Gray, Classic Split-Hopkinson Pressure Bar Testing, ASM International, Materials Park, OH, 2000, p 462-476Google Scholar
  4. 4.
    H. Kolsky, An Investigation of the Mechanical Properties of Materials at Very High Rates of Loading, Proc. Phys. Soc. Lond. B, 1949, 62(11), p 676CrossRefGoogle Scholar
  5. 5.
    J. Harding, E. Wood, and J. Campbell, Tensile Testing of Materials at Impact Rates of Strain, J. Mech. Eng. Sci., 1960, 2(2), p 88-96CrossRefGoogle Scholar
  6. 6.
    F.E. Hauser, Techniques for Measuring Stress-Strain Relations at High Strain Rates, Exp. Mech., 1966, 6(8), p 395-402CrossRefGoogle Scholar
  7. 7.
    U. Lindholm and L. Yeakley, High Strain-Rate Testing: Tension and Compression, Exp. Mech., 1968, 8(1), p 1-9CrossRefGoogle Scholar
  8. 8.
    D. Rittel, S. Lee, and G. Ravichandran, A Shear-Compression Specimen for Large Strain Testing, Exp. Mech., 2002, 42(1), p 58-64CrossRefGoogle Scholar
  9. 9.
    J. Zhao, H. Li, and Y. Zhao, Dynamic Strength Tests of the Bukit Timah Granite, Nanyang Technological University, Singapore, 1998Google Scholar
  10. 10.
    S. Huang, X. Feng, and K. Xia, A Dynamic Punch Method to Quantify the Dynamic Shear Strength of Brittle Solids, Rev. Sci. Instrum., 2011, 82(5), p 053901CrossRefGoogle Scholar
  11. 11.
    J. Zhao, An Overview of Some Recent Progress in Rock Dynamics Research, Advances in Rock Dynamics and Applications. CRC Press, Boca Raton, 2011, p 5-33Google Scholar
  12. 12.
    R. Armstrong and F. Zerilli, Dislocation Mechanics Aspects of Plastic Instability and Shear Banding, Mech. Mater., 1994, 17(2-3), p 319-327CrossRefGoogle Scholar
  13. 13.
    C. Gao and L. Zhang, Constitutive Modelling of Plasticity of FCC Metals Under Extremely High Strain Rates, Int. J. Plast., 2012, 32, p 121-133CrossRefGoogle Scholar
  14. 14.
    G.R. Johnson, and W.H. Cook, A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures, Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands, 1983Google Scholar
  15. 15.
    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
  16. 16.
    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
  17. 17.
    D.L. Preston, D.L. Tonks, and D.C. Wallace, Model of Plastic Deformation for Extreme Loading Conditions, J. Appl. Phys., 2003, 93(1), p 211-220CrossRefGoogle Scholar
  18. 18.
    G.Z. Voyiadjis and F.H. Abed, Microstructural Based Models for BCC and FCC Metals with Temperature and Strain Rate Dependency, Mech. Mater., 2005, 37(2), p 355-378CrossRefGoogle Scholar
  19. 19.
    M. Grujicic, C. Zhao, W. 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
  20. 20.
    T. Hu, S. Zhalehpour, A. Gouldstone, S. Muftu, and T. Ando, A Method for the Estimation of the Interface Temperature in Ultrasonic Joining, Metall. Mater. Trans. A, 2014, 45(5), p 2545-2552CrossRefGoogle Scholar
  21. 21.
    V.K. Champagne, Jr., D. Helfritch, P. Leyman, S. Grendahl, and B. Klotz, Interface Material Mixing Formed by the Deposition of Copper on Aluminum by Means of the Cold Spray Process, J. Therm. Spray Technol., 2005, 14(3), p 330-334CrossRefGoogle Scholar
  22. 22.
    M. Grujicic, J. Saylor, D. Beasley, W. 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), p 211-227CrossRefGoogle Scholar
  23. 23.
    S. Guetta, M.-H. Berger, F. Borit, V. Guipont, M. Jeandin, M. Boustie, Y. Ichikawa, K. Sakaguchi, and K. Ogawa, Influence of Particle Velocity on Adhesion of Cold-Sprayed Splats, J. Therm. Spray Technol., 2009, 18(3), p 331-342CrossRefGoogle Scholar
  24. 24.
    T. Hussain, D. McCartney, P. Shipway, and D. Zhang, Bonding Mechanisms in Cold Spraying: The Contributions of Metallurgical and Mechanical Components, J. Therm. Spray Technol., 2009, 18(3), p 364-379CrossRefGoogle Scholar
  25. 25.
    H. Assadi, F. Gärtner, T. Stoltenhoff, and H. Kreye, Bonding Mechanism in Cold Gas Spraying, Acta Mater., 2003, 51(15), p 4379-4394CrossRefGoogle Scholar
  26. 26.
    W.-Y. Li, H. Liao, C.-J. Li, G. Li, C. Coddet, and X. Wang, On High Velocity Impact of Micro-sized Metallic Particles in Cold Spraying, Appl. Surf. Sci., 2006, 253(5), p 2852-2862CrossRefGoogle Scholar
  27. 27.
    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 794CrossRefGoogle Scholar
  28. 28.
    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
  29. 29.
    W. Li, D. Zhang, C. Huang, S. Yin, M. Yu, F. Wang, and H. Liao, Modelling of Impact Behaviour of Cold Spray Particles: Review, Surf. Eng., 2014, 30(5), p 299-308CrossRefGoogle Scholar
  30. 30.
    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 4858-4868CrossRefGoogle Scholar
  31. 31.
    B. Yildirim, H. Fukanuma, T. Ando, A. Gouldstone, and S. Müftü, A Numerical Investigation into Cold Spray Bonding Processes, J. Tribol., 2015, 137(1), p 011102CrossRefGoogle Scholar
  32. 32.
    S. Müftü, S. Zhalehpour, A. Gouldstone, and T. Ando, Assessment of Interface Energy in High Velocity Particle Impacts, 38th Annual Meeting of The Adhesion Society. Savannah, GA, 2015Google Scholar
  33. 33.
    B. Yildirim, S. Müftü, and A. Gouldstone, On Cohesion of Micron Scale Metal Particles in High Velocity Impact with a Metal Substrate, ASME/STLE 2011 International Joint Tribology Conference, American Society of Mechanical Engineers, 2011Google Scholar
  34. 34.
    W.-Y. Li, C. Zhang, X. Guo, C.-J. Li, H. Liao, and C. Coddet, Study on Impact Fusion at Particle Interfaces and Its Effect on Coating Microstructure in Cold Spraying, Appl. Surf. Sci., 2007, 254(2), p 517-526CrossRefGoogle Scholar
  35. 35.
    A. Alkhimov, A. Gudilov, V. Kosarev, and N. Nesterovich, Specific Features of Microparticle Deformation Upon Impact on a Rigid Barrier, J. Appl. Mech. Tech. Phys., 2000, 41(1), p 188-192CrossRefGoogle Scholar
  36. 36.
    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
  37. 37.
    S. Schoenfeld and T. Wright, A Failure Criterion Based on Material Instability, Int. J. Solids Struct., 2003, 40(12), p 3021-3037CrossRefGoogle Scholar
  38. 38.
    T.W. Wright and J.W. Walter, On Stress Collapse in Adiabatic Shear Bands, J. Mech. Phys. Solids, 1987, 35(6), p 701-720CrossRefGoogle Scholar
  39. 39.
    T. Wright and H. Ockendon, A Scaling Law for the Effect of Inertia on the Formation of Adiabatic Shear Bands, Int. J. Plast., 1996, 12(7), p 927-934CrossRefGoogle Scholar
  40. 40.
    T. Wright, Shear Band Susceptibility: Work Hardening Materials, Int. J. Plast., 1992, 8(5), p 583-602CrossRefGoogle Scholar
  41. 41.
    B. Yildirim, S. Muftu, and A. Gouldstone, Modeling of High Velocity Impact of Spherical Particles, Wear, 2011, 270(9-10), p 703-713CrossRefGoogle Scholar
  42. 42.
    W. Xie, A. Alizadeh-Dehkharghani, Q. Chen, V.K. Champagne, X. Wang, A.T. Nardi, S. Kooi, S. Müftü, and J.-H. Lee, Dynamics and Extreme Plasticity of Metallic Microparticles in Supersonic Collisions, Sci. Rep., 2017, 7, p 5073CrossRefGoogle Scholar
  43. 43.
    J.-H. Lee, P.E. Loya, J. Lou, and E.L. Thomas, Dynamic Mechanical Behavior of Multilayer Graphene Via Supersonic Projectile Penetration, Science, 2014, 346(6213), p 1092-1096CrossRefGoogle Scholar
  44. 44.
    J.-H. Lee, D. Veysset, J.P. Singer, M. Retsch, G. Saini, T. Pezeril, K.A. Nelson, and E.L. Thomas, High Strain Rate Deformation of Layered Nanocomposites, Nature communications, 2012, 3, p 1164CrossRefGoogle Scholar
  45. 45.
    S. Barradas, V. Guipont, R. Molins, M. Jeandin, M. Arrigoni, M. Boustie, C. Bolis, L. Berthe, and M. Ducos, Laser Shock Flier Impact Simulation of Particle-Substrate Interactions in Cold Spray, J. Therm. Spray Technol., 2007, 16(4), p 548-556CrossRefGoogle Scholar
  46. 46.
    M. Arrigoni, M. Boustie, C. Bolis, S. Barradas, L. Berthe, and M. Jeandin, Shock Mechanics and Interfaces, Mechanics of Solid Interfaces, M. Braccini and M. Dupeux, Eds., John Wiley & Sons, Inc., Hoboken, NJ, USA, 2012.  https://doi.org/10.1002/9781118561669.ch7
  47. 47.
    M. Jeandin, D.K. Christoulis, F. Borit, M.-H. Berger, S. Guetta, G. Rolland, V. Guipont, F. N’Guyen, D. Jeulin, and E. Irissou, A Socratic Approach to Surface Modification: The Example of Thermal Spray, 24th International Conference on Surface Modification Technologies, SMT 24, 2010Google Scholar
  48. 48.
    M. Hassani-Gangaraj, D. Veysset, K.A. Nelson, and C.A. Schuh, In-situ Observations of Single Micro-particle Impact Bonding, Scripta Mater., 2018, 145, p 9-13CrossRefGoogle Scholar
  49. 49.
    Dassault Systèmes Simulia Corp., P., RI, USA, ABAQUS/Explicit 6.13 User Manual. 2013Google Scholar
  50. 50.
    Dehkharghani, A.A., Tuning Johnson–Cook Material Model Parameters for Impact of High Velocity, Micron Scale Aluminum Particles, Department of Mechanical and Industrial Engineering. 2016, MS Thesis, Northeastern University.Google Scholar
  51. 51.
    Yildirim, B., Mechanistic Modeling of High Velocity Micro-particle Impacts: Application to Material Deposition by Cold Spray Process, in Department of Mechanical and Industrial Engineering. 2013, PhD Thesis, Northeastern UniversityGoogle Scholar
  52. 52.
    T. Belytschko, J.S.-J. Ong, W.K. Liu, and J.M. Kennedy, Hourglass Control in Linear and Nonlinear Problems, Comput. Methods Appl. Mech. Eng., 1984, 43(3), p 251-276CrossRefGoogle Scholar
  53. 53.
    JAHM Software Inc., I., MPDB Material Database Software, 1998Google Scholar
  54. 54.
    A. Manes, D. Lumassi, L. Giudici, and M. Giglio, An Experimental–Numerical Investigation on Aluminium Tubes Subjected to Ballistic Impact with Soft Core 7.62 Ball Projectiles, Thin-Walled Structures, 2013, 73, p 68-80CrossRefGoogle Scholar
  55. 55.
    A. Manes, L. Peroni, M. Scapin, and M. Giglio, Analysis of Strain Rate Behavior of an Al 6061 T6 Alloy, Procedia Engineering, 2011, 10, p 3477-3482CrossRefGoogle Scholar
  56. 56.
    R.G. Munro, Evaluated Material Properties for a Sintered alpha-Alumina, J. Am. Ceram. Soc., 1997, 80(8), p 1919-1928CrossRefGoogle Scholar
  57. 57.
    S.P. Keeler and W.A. Backofen, Plastic Instability and Fracture in Sheets Stretched Over Rigid Punches, Asm. Trans. Q., 1963, 56(1), p 25-48Google Scholar
  58. 58.
    Z. Marciniak and K. Kuczyński, Limit Strains in the Processes of Stretch-Forming Sheet Metal, Int. J. Mech. Sci., 1967, 9(9), p 609IN1613-612IN2620CrossRefGoogle Scholar
  59. 59.
    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
  60. 60.
    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
  61. 61.
    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(9), p 963-980CrossRefGoogle Scholar
  62. 62.
    S. Rahmati and A. Ghaei, The Use of Particle/Substrate Material Models in Simulation of Cold-Gas Dynamic-Spray Process, J. Therm. Spray Technol., 2014, 23(3), p 530-540CrossRefGoogle Scholar
  63. 63.
    D.R. Lesuer, G. Kay, and M. LeBlanc, Modeling Large-Strain, High-Rate Deformation in Metals, Third Biennial Tri-Laboratory Engineering Conference on Modeling and Simulation, Lawrence Livermore National Laboratory: Pleasanton, CA (US), 2001Google Scholar
  64. 64.
    L. Pun, Introduction to Optimization Practice, Wiley, New York, 1969Google Scholar
  65. 65.
    L.R. Grace and M. Altan, Characterization of Anisotropic Moisture Absorption in Polymeric Composites Using Hindered Diffusion Model, Compos. A Appl. Sci. Manuf., 2012, 43(8), p 1187-1196CrossRefGoogle Scholar
  66. 66.
    K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge Cambridgeshire; New York, 1985, p 452CrossRefGoogle Scholar
  67. 67.
    B. Yildirim, H. Yang, A. Gouldstone, and S. Müftü, Rebound Mechanics of Micrometre-Scale, Spherical Particles in High-Velocity Impacts, Proc. R. Soc. A., 2017, 473, p 20160936CrossRefGoogle Scholar

Copyright information

© ASM International 2018

Authors and Affiliations

  • Qiyong Chen
    • 1
  • Arash Alizadeh
    • 1
  • Wanting Xie
    • 2
    • 3
  • Xuemei Wang
    • 4
  • Victor Champagne
    • 5
  • Andrew Gouldstone
    • 1
  • Jae-Hwang Lee
    • 2
  • Sinan Müftü
    • 1
  1. 1.Department of Mechanical and Industrial EngineeringNortheastern UniversityBostonUSA
  2. 2.Department of Mechanical and Industrial EngineeringUniversity of MassachusettsAmherstUSA
  3. 3.Department of PhysicsUniversity of MassachusettsAmherstUSA
  4. 4.United Technologies Research CenterEast HartfordUSA
  5. 5.United States Army Research LaboratoryAberdeen Proving GroundAberdeenUSA

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