Cite this article as:

Vatulyan A. O., Plotnikov D. K., Poddubny A. A. On Some Models of Indentation for Functionally-Graded Coatings . Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics, 2018, vol. 18, iss. 4, pp. 421-432. DOI: https://doi.org/10.18500/1816-9791-2018-18-4-421-432


Language: 
Russian
Heading: 
UDC: 
539.3

On Some Models of Indentation for Functionally-Graded Coatings

Abstract: 

The paper presents approximate models of deformation for an inhomogeneous elastic strip. Approximate models reflect the distribution features of the inhomogeneous structure properties over the thickness. The models are based on hypotheses about the nature of the change in the components of the displacement field, which allows to consider arbitrary laws of heterogeneity: continuous, as well as discontinuous or having a strong gradient. Solutions of the contact problem for different inhomogeneity laws are constructed. Comparative analysis of the models is carried out. The results of the solutions are compared with the solution based on the FE model.

References

1. Grainger S., Blunt. J. Engineering Coatings: Design and Application. Woodhead Publ. Ltd, UK, 1998. 336 p.
2. Naebe M., Shirvanimoghaddam K. Functionally graded materials: A review of fabrication and properties. Applied Materials Today, 2016, vol. 5, pp. 223–245. DOI: https://doi.org/10.1016/j.apmt.2016.10.001
3. Golovin Yu. I. Nanoindentation and mechanical properties of solids in submicrovolumes, thin near-surface layers, and films: A Review. Physics of the Solid State, 2008, vol. 50, iss. 12, pp. 2205–2236. DOI: https://doi.org/10.1134/S1063783408120019
4. Oliver W. C., Pharr G. M. Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res., 2004, vol. 19, no. 1, pp. 3–20. DOI: https://doi.org/10.1557/jmr.2004.19.1.3
5. Vorovich I. I., Alexandrov V. M., Babeshko V. A. Neklassicheskie smeshannie zadachi teorii uprugosti. [Non-classical mixed problems in elasticity theory]. Moscow, Nauka, 1974. 456 p. (in Russian).

6. Kontaktnie zadachi teorii uprugosti dlya neodnorodnih sred [Contact problems of theory of elasticity for inhomogeneous media] / S. M. Aizikovich, V. M. Aleksandrov, A. V. Belokon, L. I. Krenev, I. S. Trubchik. Moscow, Fizmatlit, 2006. 240 p. (in Russian).
7. Volkov S. S., Vasilev A. S, Aizikovich S. M., Seleznev N. M., Leonteva A .V. Stressstrain state of an elastic soft functionally graded coating during the indentation of a spherical indenter. PNRPU Mechanics Bulletin, 2016, no. 4, pp. 20–34 (in Russian). DOI: https://doi.org/10.15593/perm.mech/2016.4.02
8. Alexandrov V. M., Mhitaryan S. M. Kontaktnie zadachi dlya tel s tonkimi pokritiyami i podlozhkami [Contact problems for bodies with thin coatings and layers]. Moscow, Nauka, 1983. 488 p. (in Russian).
9. Vatulyan A. O., Plotnikov D. K. On indentation of heterogeneous strip. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2017, no. 3, pp. 22–29 (in Russian).
10. Vatul’yan A. O., Kossovich E. L., Plotnikov D. K. Some specific characteristics of indentation of cracked layered structures. Mechanics of Solids, 2017, no. 4, pp. 429–434. DOI: https://doi.org/10.3103/S0025654417040094

Short text (in English): 
Full text: