Formation of Bulk Tensile Regions in Metal Matrix Composites and Coatings under Uniaxial and Multiaxial Compression


This paper numerically investigates the mechanical behavior of an aluminum specimen with a TiC–Al6061 composite coating. The strain localization and fracture patterns are determined for different scale levels. The effects of the loading type, distance between titanium carbide particles, and metal matrix coating thickness are studied. A numerical method based on the experimental data is proposed for constructing three-dimensional structures of materials with complex-shaped particles. The method is applied to create three-dimensional structures of a material with a composite coating on different scale levels. Interfacial strain localization patterns are examined under multiaxial compression caused by cooling of the metal matrix/ceramic particle composite from the melt to room temperature, as well as under uniaxial compression. The formation mechanisms of bulk tensile regions under mechanical and thermal compression are investigated.

This is a preview of subscription content, log in to check access.

Fig. 1 (a), (b), (c).
Fig. 2 (a), (b), (c).
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.


  1. 1

    Gopinath Muvvala, Debapriya Patra Karmakar, and Ashish Kumar Nath, Online Assessment of TiC Decomposition in Laser Cladding of Metal Matrix Composite Coating, Mater. Design, 2017, vol. 121, pp. 310–320.

  2. 2

    Kadolkar,P.B., Watkins, T.R., De Hosson, J.Th.M., Kooi, B.J., and Dahotre, N.B., State of Residual Stress in Laser-Deposited Ceramic Composite Coatings on Aluminum Alloys,Acta Mater., 2007, vol. 55, no. 4, pp. 1203–1214.

  3. 3

    Liu, D., Hu, P., and Min, G., Interfacial Reaction in Cast WC Particulate Reinforced Titanium Metal Matrix Composites Coating Produced by Laser Processing, Optics Laser Technol., 2015, vol. 69, pp. 180–186.

  4. 4

    Yang-Feng Tao, Jun Li, Ying-Hao Lv, and Lie-Feng Hu, Effect of Heat Treatment on Residual Stress and Wear Behaviors of the TiNi/Ti2Ni Based Laser Cladding Composite Coatings, Optics Laser Technol., 2017, vol. 97, pp. 379–389.

  5. 5

    Peat, T., Galloway, A., Toumpis, A., McNutt, P., and Iqbal, N., The Erosion Performance of Particle Reinforced Metal Matrix Composite Coatings Produced by Co-Deposition Cold Gas Dynamic Spraying, Appl. Surf. Sci., 2017, vol. 396, pp. 1623–1634.

  6. 6

    Lee, Y.T.R., Ashrafizadeh, H., Fisher, G., and McDonald, A., Effect of Type of Reinforcing Particles on the Deposition Efficiency and Wear Resistance of Low-Pressure Cold-Sprayed Metal Matrix Composite Coatings, Surf. Coat. Technol., 2017, vol. 324, pp. 190–200.

  7. 7

    Physical Mesomechanics of Heterogeneous Media and Computer-Aided Design of Materials, Panin, V.E., Ed., Cambridge: Cambridge Interscience Publishing, 1998.

  8. 8

    Panin, V.E. and Egorushkin, V.E., Basic Physical Mesomechanics of Plastic Deformation and Fracture of Solids as Hierarchically Organized Nonlinear Systems, Phys. Mesomech., 2015, vol. 18, no. 4, pp. 377–390.

  9. 9

    Panin, V.E., Egorushkin, V.E., Moiseenko, D.D., et al., Functional Role of Polycrystal Grain Boundaries and Interfaces in Micromechanics of Metal Ceramic Composites under Loading, Comput. Mater. Sci., 2016, vol. 116, pp. 74–81.

  10. 10

    Surface Layers and Internal Interfaces in Heterogeneous Materials, Panin, V.E., Ed., Novosibirsk: Izd-vo SO RAN, 2006.

  11. 11

    Smirnov, S.V., An Investigation of the Mechanical Properties of Metal Surfaces and Coatings Using Modern Nanomechanical Test Systems: New Research Methods and Results, Vestnik Lobachevsky Univ. Nizhni Novgorod, 2011, no. 4(2), pp. 530–532.

  12. 12

    Marcin, K., Rakowski, W., Lackner, J.M., and Major, Ł., Analysis of Spherical Indentations of Coating–Substrate Systems: Experiments and Finite Element Modeling,Mater. Design, 2013, vol. 43, pp. 99–111.

  13. 13

    Maritza, G.J., Veprek-Heijman, and Stan Veprek, The Deformation of the Substrate During Indentation into Superhard Coatings Buckle’s Rule Revised, Surf. Coat. Technol., 2015, vol. 284, pp. 206–214.

  14. 14

    Reed, J.L., Dean, J., Aldrich-Smith, G., and Clyne, T.W., A Methodology for Obtaining Plasticity Characteristics of Metallic Coatings via Instrumented Indentation, Int. J. Solids Struct., 2016, vol. 80, pp. 128–136.

  15. 15

    Mohd Tobi, A.L., Shipway, P.H., and Leen, S.B., Finite Element Modelling of Brittle Fracture of Thick Coatings under Normal and Tangential Loading, Tribology Int., 2013, vol. 58, pp. 29–39.

  16. 16

    Lurie, S.A., Solyaev, Y.O., Rabinsky, L.N., Kondratova, Y.N., and Volov, M.I., Simulation of the Stress-Strain State of Thin Composite Coatings Based on Solutions of the Plane Problem of Strain-Gradient Elasticity for a Layer, PNRPU Mechanics Bulletin, 2013, no. 1, pp. 161–181.

  17. 17

    Smolin, A.Yu., Eremina, V.V. Sergeev, and Shilko, E.V., Three-Dimensional Movable Cellular Automata Simulation of Elastoplastic Deformation and Fracture of Coatings in Contact Interaction with a Rigid Indenter, Phys. Mesomech., 2014, vol. 17, no. 4, pp. 292–303.

  18. 18

    Wang, L., Wang, Z., Dong, S.M., Zhang, W., and Wang, Y., Finite Element Simulation of Stress Distribution and Development of Cf/SiC Ceramic–Matrix Composite Coated with Single Layer SiC Coating during Thermal Shock, Composites. B, 2013, vol. 51, pp. 204–214.

  19. 19

    Zhu, W., Yang, L., Guo, J.W., Zhou, Y.C., and Lu, C., Determination of Interfacial Adhesion Energies of Thermal Barrier Coatings by Compression Test Combined with a Cohesive Zone Finite Element Model, Int. J. Plasticity, 2015, vol. 64, pp. 76–87.

  20. 20

    Yussif, S.A.K., Panin, S.V., Lyukshin, P.A., and Sergeev, V.P., Stress-Strain State at the “Heat-Resistant Ceramic Coating–Copper Substrate” Interface, Fiz. Mezomekh., 2011, vol. 14, no. 4, pp. 81–94.

  21. 21

    Baker, M., Finite Element Simulation of Interface Cracks in Thermal Barrier Coatings, Comput. Mater. Sci., 2012, vol. 64, pp. 79–83.

  22. 22

    Ting, G.Sh., Zhong, Ch.G., Ping, W.H., and Mei, B.Y., Characterization of Local Mechanical Properties of Laser-Cladding H13–TiC Composite Coatings Using Nanoindentation and Finite Element Analysis, Mater. Design, 2012, vol. 39, pp. 72–80.

  23. 23

    Wang, L., Zhong, X.H., Yang, J.S., Tao, S.Y., Zhang, W., Wang, Y., and Sun, X.G., Finite Element Simulation of Surface Micro-Indentation Behavior of Yttria Stabilized Zirconia Thermal Barrier Coatings with Microstructural Characteristic of Columnar Grains and Sub-Grains Based on a Nonlinear Contact Model,Comput. Mater. Sci., 2014, vol. 82, pp. 244–256.

  24. 24

    Nayebpashaee, N., Seyedein, S.H., Aboutalebi, M.R., Sarpoolaky, H., and Hadavi, S.M.M., Finite Element Simulation of Residual Stress and Failure Mechanism in Plasma Sprayed Thermal Barrier Coatings Using Actual Microstructure as the Representative Volume, Surf. Coat. Technol., 2016, vol. 291, pp. 103–114.

  25. 25

    Donegan, S.P. and Rollett, A.D., Simulation of Residual Stress and Elastic Energy Density in Thermal Barrier Coatings Using Fast Fourier Transforms, Acta Mater., 2015, vol. 96, pp. 212–228.

  26. 26

    Holmberg, K., Laukkanen, A., Turunen, E., and Laitinen, T., Wear Resistance Optimisation of Composite Coatings by Computational Microstructural Modelling, Surf. Coat. Technol., 2014, vol. 247, pp. 1–13.

  27. 27

    ASM Engineered Materials Reference Book, Bauccio, M., Ed., Materials Park, OH: ASM Int., 1994.

  28. 28

    ASM Handbook. Vol. 2. Properties and Selection: Nonferrous Alloys and Special-Purpose Materials, ASM Handbook Committee, pp. 62–122.

  29. 29

    Balasundaram, A., Gokhale, A.M., Graham, S., and Horstemeyer, M.F., Three-Dimensional Particle Cracking Damage Development in an Al–Mg-Base Wrought Alloy, Mater. Sci. Eng. A, 2003, vol. 355, pp. 368–383.

  30. 30

    Ravnikar, D., Dahotre, N.B., and Grum, J., Laser Coating of Aluminum Alloy EN AW 6082-T651 with TiB2 and TiC: Microstructure and Mechanical Properties, Appl. Surf. Sci., 2013, vol. 282, pp. 914–922.

  31. 31

    Panin, V.E., Goldstein, R.V., and Panin, S.V., Mesomechanics of Multiple Cracking of Brittle Coatings in a Loaded Solid, Int. J. Fracture, 2008, vol. 150, no. 1–2, pp. 37–53.

Download references


The work was supported by the Russian Science Foundation (Project No. 18-19-00273). Fracture model described in Sect. 2 by Eq. (4) was developed by R. Balokhonov under the government statement of work for ISPMS SB RAS, Project No. III.23.1.1.

Author information



Corresponding author

Correspondence to R. R. Balokhonov.

Additional information

Russian Text © The Author(s), 2019, published in Fizicheskaya Mezomekhanika, 2019, Vol. 22, No. 1, pp. 69–80.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Balokhonov, R.R., Evtushenko, E.P., Romanova, V.A. et al. Formation of Bulk Tensile Regions in Metal Matrix Composites and Coatings under Uniaxial and Multiaxial Compression. Phys Mesomech 23, 135–146 (2020).

Download citation


  • computational mesomechanics
  • metal matrix composites
  • coated materials
  • residual tensile stresses
  • plastic deformation
  • fracture