Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer

2013 ◽  
Vol 29 (2) ◽  
pp. 196-201 ◽  
Author(s):  
Sergey Volkov ◽  
Sergey Aizikovich ◽  
Yue-Sheng Wang ◽  
Igor Fedotov
Keyword(s):  
Analytical Solution ◽  
Contact Problem ◽  
Elastic Layer ◽  
Functionally Graded ◽  
Axisymmetric Contact Problem

Some Criteria for Coating Effectiveness in Heavily Loaded Line Elastohydrodynamically Lubricated Contacts—Part II: Lubricated Contacts

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Ilya I. Kudish ◽  
Sergey S. Volkov ◽  
Andrey S. Vasiliev ◽  
Sergey M. Aizikovich
Keyword(s):  
Analytical Solution ◽  
Contact Problem ◽  
Half Space ◽  
Contact Problems ◽  
Functionally Graded ◽  
Elastic Solids ◽  
Elastic Materials ◽  
Lubricated Contacts ◽  
Dry Contact ◽  
Appl Math

Contacts of indentors with functionally graded elastic solids may produce pressures significantly different from the results obtained for homogeneous elastic materials (Hertzian results). It is even more so for heavily loaded line elastohydrodynamically lubricated (EHL) contacts. The goal of the paper is to indicate two distinct ways the functionally graded elastic materials may alter the classic results for the heavily loaded line EHL contacts. Namely, besides pressure, the other two main characteristics which are influenced by the nonuniformity of the elastic properties of the contact materials are lubrication film thickness and frictional stress/friction force produced by lubricant flow. The approach used for analyzing the influence of functionally graded elastic materials on parameters of heavily loaded line EHL contacts is based on the asymptotic methods developed earlier by the authors such as Kudish (2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman & Hall/CRC Press, Boca Raton, FL), Kudish and Covitch (2010, Modeling and Analytical Methods in Tribology, Chapman & Hall/CRC Press, Boca Raton, FL), Aizikovich et al. (2002, “Analytical Solution of the Spherical Indentation Problem for a Half-Space With Gradients With the Depth Elastic Properties,” Int. J. Solids Struct., 39(10), pp. 2745–2772), Aizikovich et al. (2009, “Bilateral Asymptotic Solution of One Class of Dual Integral Equations of the Static Contact Problems for the Foundations Inhomogeneous in Depth,” Operator Theory: Advances and Applications, Birkhauser Verlag, Basel, p. 317), Aizikovich and Vasiliev (2013, “A Bilateral Asymptotic Method of Solving the Integral Equation of the Contact Problem for the Torsion of an Elastic Halfspace Inhomogeneous in Depth,” J. Appl. Math. Mech., 77(1), pp. 91–97), Volkov et al. (2013, “Analytical Solution of Axisymmetric Contact Problem About Indentation of a Circular Indenter Into a Soft Functionally Graded Elastic Layer,” Acta Mech. Sin., 29(2), pp. 196–201), Vasiliev et al. (2014, “Axisymmetric Contact Problems of the Theory of Elasticity for Inhomogeneous Layers,” Z. Angew. Math. Mech., 94(9), pp. 705–712), Aizikovich et al. (2008, “The Deformation of a Half-Space With a Gradient Elastic Coating Under Arbitrary Axisymmetric Loading,” J. Appl. Math. Mech., 72(4), pp. 461–467), and Aizikovich et al. (2010, “Inverse Analysis for Evaluation of the Shear Modulus of Inhomogeneous Media in Torsion Experiments,” Int. J. Eng. Sci., 48(10), pp. 936–942). More specifically, it is based on the analysis of contact problems for dry contacts of functionally graded elastic solids and the lubrication mechanisms in the inlet and exit zones as well as in the central region of heavily loaded lubricated contacts. The way the solution of the EHL problem for coated/functionally graded materials is obtained provides a very clear structure of the solution. The solution of the EHL problem in the Hertzian region is very close to the solution of the dry contact problem while in the inlet and exit zones the solutions of the EHL problem with the right asymptotes coming from the solution of the dry contact problem can be related to the solutions of the classic EHL problem for homogeneous materials.

scholarly journals An axisymmetric contact problem of an elastic layer on a rigid base with a cylindrical hole.

1989 ◽  
Vol 55 (516) ◽  
pp. 1800-1808
Author(s):  
Toshiaki HARA ◽  
Takao AKIYAMA ◽  
Toshikazu SHIBUYA ◽  
Takashi KOIZUMI
Keyword(s):  
Contact Problem ◽  
Elastic Layer ◽  
Cylindrical Hole ◽  
Rigid Base ◽  
Axisymmetric Contact Problem

scholarly journals The Axisymmetric Contact Problem of an Elastic Layer on a Rigid Base with an Annular Hole

1984 ◽  
Vol 27 (230) ◽  
pp. 1573-1578
Author(s):  
Toshiaki HARA ◽  
Toshikazu SHIBUYA ◽  
Takashi KOIZUMI ◽  
Eisuke TAKANO
Keyword(s):  
Contact Problem ◽  
Elastic Layer ◽  
Rigid Base ◽  
Axisymmetric Contact Problem

The Axisymmetric Contact Problem of an Elastic Layer on a Rigid Base with a Cylindrical Protrusion or Pit

1984 ◽  
Vol 27 (224) ◽  
pp. 159-164
Author(s):  
Toshiaki HARA ◽  
Toshikazu SHIBUYA ◽  
Takashi KOIZUMI ◽  
Katsuhiko IIDA
Keyword(s):  
Contact Problem ◽  
Elastic Layer ◽  
Rigid Base ◽  
Axisymmetric Contact Problem ◽  
Cylindrical Protrusion

scholarly journals MATHEMATICAL MODELING OF EXPERIMENT ON BERKOVICH NANOINDENTATION OF ZRN COATING ON STEEL SUBSTRATE

2020 ◽  
Vol 27 ◽  
pp. 18-21
Author(s):  
Evgeniy Sadyrin ◽  
Andrey Vasiliev ◽  
Sergei Volkov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Analytical Solution ◽  
Contact Problem ◽  
Half Space ◽  
Steel Substrate ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Good Agreement

In the present paper the experiment on Berkovich nanoindentation of ZrN coating on steel substrate is modelled using the proposed effective mathematical model. The model is intended for describing the experiments on indentation of samples with coatings (layered or functionally graded). The model is based on approximated analytical solution of the contact problem on indentation of an elastic half-space with a coating by a punch. It is shown that the results of the model and the experiment are in good agreement.

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