Analytical solution to continuous contact problem for a functionally graded layer loaded through two dissimilar rigid punches

Meccanica ◽  
2018 ◽  
Vol 53 (14) ◽  
pp. 3565-3577 ◽  
Author(s):  
Alper Polat ◽  
Yusuf Kaya ◽  
Talat Şükrü Özşahin
Keyword(s):  
Analytical Solution ◽  
Contact Problem ◽  
Functionally Graded ◽  
Continuous Contact ◽  
Functionally Graded Layer

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.

Analytical Solution for the Bending of a Plate on a Functionally Graded Layer of Complex Structure

2011 ◽  
pp. 15-28 ◽  
Author(s):  
Sergey Aizikovich ◽  
Andrey Vasiliev ◽  
Igor Sevostianov ◽  
Irina Trubchik ◽  
Ludmila Evich ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Complex Structure ◽  
Functionally Graded ◽  
Functionally Graded Layer

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.

A receding contact problem between a functionally graded layer and two homogeneous quarter planes

2016 ◽  
Vol 227 (6) ◽  
pp. 1753-1766 ◽  
Author(s):  
Gökhan Adıyaman ◽  
Ahmet Birinci ◽  
Erdal Öner ◽  
Murat Yaylacı
Keyword(s):  
Contact Problem ◽  
Functionally Graded ◽  
Receding Contact ◽  
Functionally Graded Layer

Continuous and discontinuous contact problem of a functionally graded layer resting on a rigid foundation

2017 ◽  
Vol 228 (9) ◽  
pp. 3003-3017 ◽  
Author(s):  
Gökhan Adıyaman ◽  
Erdal Öner ◽  
Ahmet Birinci
Keyword(s):  
Contact Problem ◽  
Functionally Graded ◽  
Rigid Foundation ◽  
Functionally Graded Layer

scholarly journals Investigation of the contact problem for a partial functionally graded layer by using finite element method

2019 ◽  
Vol 1 (4) ◽  
pp. 185-193
Author(s):  
Alper Polat ◽  
Yusuf Kaya ◽  
Pınar Bora ◽  
Koudier Bendine ◽  
Talat Ş Özşahin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Problem ◽  
Functionally Graded ◽  
Functionally Graded Layer ◽  
Element Method
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