Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Conical Punch

Andrey S. Vasiliev, Sergey S. Volkov, Evgeniy V. Sadyrin and Sergei M. Aizikovich
Additional contact information
Andrey S. Vasiliev: Research and Education Center “Materials”, Don State Technical University, 344000 Rostov-on-Don, Russia
Sergey S. Volkov: Research and Education Center “Materials”, Don State Technical University, 344000 Rostov-on-Don, Russia
Evgeniy V. Sadyrin: Research and Education Center “Materials”, Don State Technical University, 344000 Rostov-on-Don, Russia
Sergei M. Aizikovich: Research and Education Center “Materials”, Don State Technical University, 344000 Rostov-on-Don, Russia

Mathematics, 2020, vol. 8, issue 6, 1-14

Abstract: The contact problem on indentation of an elastic coated half-space by a conical punch is considered. To obtain an explicit analytical solution suitable for applications, the bilateral asymptotic method is used in a simplified form. For that purpose, kernel transform of the integral equation is approximated by a ratio of two quadratic functions containing only one parameter. Such an approach allows us to obtain explicit analytical expressions for the distribution of contact stresses and relations between the indentation force, depth, stiffness and contact radius. The obtained solution is suitable both for homogeneous and functionally graded coatings. The dependence of the characteristics of contact interaction on a relative Young’s modulus of the coating and relative coating thickness is analyzed and illustrated by the numerical examples. Ranges of values of elastic and geometrical parameters are obtained, for which the presence of a coating sufficiently changes the contact characteristics. The accuracy of the obtained simplified expressions is studied in detail. Results of the paper sufficiently simplify engineering calculations and are suitable for inverse analysis, e.g., analysis of indentation experiments of coated materials using either a conical or a pyramidal (Berkovich) indenter.

Keywords: contact problem; indentation; coatings; analytical solutions; simplified solutions; conical indenter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/6/983/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/6/983/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:6:p:983-:d:372287

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().