Effectiveness of Coatings With Constant, Linearly, and Exponentially Varying Elastic Parameters in Heavily Loaded Line Elastohydrodynamically Lubricated Contacts

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Ilya I. Kudish ◽  
Sergey S. Volkov ◽  
Andrey S. Vasiliev ◽  
Sergey M. Aizikovich
Keyword(s):  
Asymptotic Methods ◽  
Functionally Graded ◽  
Problem Solution ◽  
Elastic Materials ◽  
Elastic Parameters ◽  
Graded Materials ◽  
Lubrication Film ◽  
Lubricated Contacts ◽  
Homogeneous Materials ◽  
The One

In contacts of functionally graded elastic solids, the conditions produced are significantly different from the ones in similar contacts of homogeneous elastic materials. Especially it is true for heavily loaded lubricated contacts. The situation is even more diverse due to different dependences of the material elastic parameters on material depth. In the previous papers, the cases of lubricated contacts with coatings made of homogeneous materials are considered using asymptotic and semi-analytical methods. The goal of the paper is to determine the behavior of the coating effectiveness criteria in heavily loaded elastohydrodynamically lubricated (EHL) contacts for coatings with elastic modulus varying linearly and exponentially across the coating thickness as well as to compare the results with the case of coatings made of homogeneous materials. The above criteria include the criteria on the lubrication film thickness and friction force. 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 earlier developed by the authors. The analysis is based on splitting the problem into two distinct parts: the problem for dry (nonlubricated) contacts and a problem for lubricated contacts. The bridge between the two problems is the asymptotic behavior of pressure in the vicinity of the end points of the contacts. More specifically, in the central part of the contact the solution of the EHL problem for functionally graded materials is close to the one for the dry contact of these materials while in the narrow zones near the inlet and exit points of the contact the lubrication effects become comparable to the effects due to the elasticity of the solids. This approach to the EHL problem solution reveals its structure.

Lubricated point heavily loaded contacts of functionally graded materials. Part 2. Lubricated contacts

2017 ◽  
Vol 23 (7) ◽  
pp. 1081-1103 ◽  
Author(s):  
Ilya I Kudish ◽  
Sergey S Volkov ◽  
Andrey S Vasiliev ◽  
Sergey M Aizikovich
Keyword(s):  
Functionally Graded Materials ◽  
Central Region ◽  
Contact Problems ◽  
Functionally Graded ◽  
Problem Solution ◽  
Elastic Materials ◽  
Graded Materials ◽  
Lubrication Film ◽  
Lubricated Contacts ◽  
Lubricated Contact

The paper presents a study of the effectiveness of functionally graded materials in heavily loaded point elastohydrodynamically lubricated contacts with straight lubricant entrainment. As part of the study, some criteria of coating effectiveness are introduced and discussed. The approach used for achieving this goal is based on the recently developed asymptotic solution method for steady isothermal elastohydrodynamically lubricated problems of heavily loaded point contacts, as well as on a semi-analytical method for the solutions of contact problems for elastic functionally graded materials without the presence of lubrication in the contacts (dry contacts). For line elastohydrodynamically lubricated contacts such a problem has already been studied. The solution process can be subdivided into two stages: the solution of the contact problems for dry contacts and a solution of the problem for lubricated contacts. The solution of dry contact problems for functionally graded materials is described in detail in Part 1 of the paper. As in the case of homogeneous contact materials in the analysis of the elastohydrodynamically lubricated problem for functionally graded elastic materials, it is shown that the whole contact region can be subdivided into three subregions: the central one which is adjacent to the other two regions occupied by the ends of the zones. The central region can be subdivided into the Hertzian region and adjacent to it the inlet and exit zones which, in turn, are adjacent to the inlet and exit boundaries of the contact, respectively. In the Hertzian region the elastohydrodynamically lubricated problem solution is very close to the solution of the corresponding dry (i.e. non-lubricated) contact problem for functionally graded elastic materials which have been analyzed in Part 1 of the paper. In the central region in the inlet and exit zones of the heavily loaded point elastohydrodynamically lubricated contact, the elastohydrodynamically lubricated problem for functionally graded elastic materials using certain similarity transforms can be reduced to asymptotically valid equations identical to the ones obtained in the inlet and exit zones of the heavily loaded line elastohydrodynamically lubricated contacts for homogeneous elastic materials. Therefore, many of the well known properties of heavily loaded line elastohydrodynamically lubricated contacts for homogeneous elastic materials are also valid for heavily loaded point elastohydrodynamically lubricated contacts for functionally graded elastic materials. These asymptotically valid equations can be analyzed and numerically solved based on stable methods using a specific regularization approach which was developed for lubricated line contacts. Also, this asymptotic analysis leads to the easy analytical derivation of equations for the lubrication film thickness which take into account the inhomogeneity of the elastic materials. As a result of this analysis, criteria for an increase in lubrication film and friction force reduction are proposed. These criteria depend on lubricant properties, as well as the properties of functionally graded elastic materials involved in lubricated contacts.

Lubricated point heavily loaded contacts of functionally graded materials. Part 1. Dry contacts

2017 ◽  
Vol 23 (7) ◽  
pp. 1061-1080 ◽  
Author(s):  
Ilya I Kudish ◽  
Sergey S Volkov ◽  
Andrey S Vasiliev ◽  
Sergey M Aizikovich
Keyword(s):  
Contact Problem ◽  
Film Thickness ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Elastic Materials ◽  
Graded Materials ◽  
Lubrication Film ◽  
Lubricated Contacts ◽  
Dry Contact ◽  
Lubricated Contact

Over the last couple decades coatings attract more and more attention in practical applications. The present study addresses a question which is not well studied: how coated surfaces behave in lubricated contacts? In other words, this is a study of the effectiveness of functionally graded materials in heavily loaded point elastohydrodynamically lubricated contacts with straight lubricant entrainment. As a part of the study, some criteria of coating effectiveness are introduced and discussed. More specifically, the behavior of main parameters such as the lubrication film thickness and the frictional force in point heavily loaded lubricated contacts of functionally graded elastic materials are considered. The problem is studied based on the method of matched asymptotic expansions which allows us to split the problem into two separate problems: a dry contact problems for functionally graded elastic materials and an elastohydrodynamically lubricated problem for functionally graded materials. The elastohydrodynamically lubricated problem uses as input data not only the operational and physical parameters of the materials and lubricant but also the asymptotic behavior of the dry contact problem solution near the contact boundaries. Therefore, a sequence of two problems must be solved: the dry contact problems for functionally graded elastic materials and the elastohydrodynamically lubricated problem for functionally graded materials. Similar methods have been used for the analysis of an elastohydrodynamically lubricated problem for heavily loaded line contacts of functionally graded materials. The dry contact problem will be analyzed in Part 1 of the paper based on a semi-analytical bilateral method which produces correct asymptotic solutions for thin and thick coatings. The analytical expressions for contact pressure are obtained and analyzed for various combinations of coating thicknesses and elastic properties. The elastohydrodynamically lubricated problem will be considered in Part 2 of the paper based on the method of matched asymptotic expansions. In the analysis of the elastohydrodynamically lubricated problem, as in the case of homogeneous contact materials, it is shown that the whole contact region can be subdivided into three subregions: the central one which is adjacent to the other two regions occupied by the ends of the zones. The central region can be subdivided into the Hertzian region and then adjacent to it inlet and exit zones which, in turn, are adjacent to the inlet and exit boundaries of the contact, respectively. In the Hertzian region the elastohydrodynamically lubricated problem solution is very close to the solution of the corresponding dry (i.e. non-lubricated) contact problem for functionally graded elastic materials which have been analyzed. In the central region in the inlet and exit zones of a heavily loaded point elastohydrodynamically lubricated contact, the elastohydrodynamically lubricated problem for functionally graded elastic materials using certain scaling transforms can be reduced to asymptotically valid equations identical to the ones obtained in the inlet and exit zones of heavily loaded line elastohydrodynamically lubricated contacts for homogeneous elastic materials. Therefore, many of the well known properties of heavily loaded line elastohydrodynamically lubricated contacts for homogeneous elastic materials are also valid for heavily loaded point elastohydrodynamically lubricated contacts for functionally graded elastic materials. These asymptotically valid equations can be analyzed and numerically solved based on stable methods using a specific regularization approach, which were developed for lubricated line contacts. Also, this asymptotic analysis leads to an easy analytical derivation of formulas for the lubrication film thickness which take into account the inhomogeneity of the elastic materials. As a result of this analysis, some criteria for lubrication film thickness increase and friction force reduction are proposed. These criteria depend on lubricant properties as well as the properties of functionally graded elastic materials involved in lubricated contacts. Such a sequential solution of the elastohydrodynamically lubricated problem for functionally graded materials makes it perfectly clear what the dependence is of elastohydrodynamically lubricated contact parameters on the solid material (including the coating) and lubricant properties.

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

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Ilya I. Kudish ◽  
Sergey S. Volkov ◽  
Andrey S. Vasiliev ◽  
Sergey M. Aizikovich
Keyword(s):  
New York ◽  
Asymptotic Methods ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
Functionally Graded ◽  
Frictional Stress ◽  
Elastic Solids ◽  
Elastic Materials ◽  
Lubrication Film ◽  
Lubricated Contacts

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 earlier developed by authors (Kudish, 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman & Hall/CRC Press, New York; Kudish and Covitch, 2010, Modeling and Analytical Methods in Tribology, Chapman & Hall/CRC Press, New York; and Aizikovich et al., 2006, Contact Problems of Elasticity for Functionally Graded Materials, Fizmatlit, Moscow, Russia). 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 lubricated contacts.

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 Calculation of Stress Intensity Factor for an Internal Circumferential Crack in a Rotating Functionally Graded Thick-Walled Hollow Circular Cylinder under Thermal Shock

2017 ◽  
Vol 64 (4) ◽  
pp. 455-479 ◽  
Author(s):  
Mohammad Reza Ghafoor Elahi ◽  
Masoud Mahdizadeh Rokhi
Keyword(s):  
Stress Intensity ◽  
Functionally Graded ◽  
Problem Solution ◽  
Mechanical Shock ◽  
Axially Symmetric ◽  
Extended Finite Element ◽  
Dynamic Stress Intensity Factors ◽  
Graded Materials ◽  
Circumferential Crack ◽  
The Time Domain

Abstract In this article, the fracture behavior of functionally graded thick-walled cylinder under thermo-mechanical shock is investigated. For this purpose, classical coupled thermoelastic equations are used in calculations. First, these equations are discretized with extended finite element method (XFEM) in the space domain and then they are solved by the Newmark method in the time domain. The most general form of interaction integral is extracted for axially symmetric circumferential crack in a cylinder under thermal and mechanical loads in functionally graded materials and is used to calculate dynamic stress intensity factors (SIFs). The problem solution has been implemented in MATLAB software.

Inversion of Functionally Graded Materials to Improve the Elastic Ultimate Bearing Capacity of Thick-Walled Hollow Cylinder

2011 ◽  
Vol 378-379 ◽  
pp. 116-120 ◽  
Author(s):  
Ai Zhong Lu ◽  
Ning Zhang
Keyword(s):  
Bearing Capacity ◽  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Functionally Graded Materials ◽  
Young's Modulus ◽  
Ultimate Bearing Capacity ◽  
Functionally Graded ◽  
The Body ◽  
Graded Materials ◽  
Homogeneous Materials

Thick-walled hollow cylinder is an important class of engineering structure, the stress state of which depends on the loads and properties of the body materials. Under the assumptions of σθ-σr=c (σθ and σr denote the hoop stress and radial stress, respectively, c is a constant), inverse analysis of thick-walled hollow cylinder composed of functionally graded materials with uniform pressure acting on the outer surface is carried out. Analytical solutions for the Young’s modulus variation in the radial direction are obtained. It is found that only when the Young’s modulus E(r) is a specific monotone increasing function of the radius r, the pre-specified stress distribution can be satisfied. Comparing with classical homogeneous materials, stress concentration at the inner surface of hollow cylinder composed of functionally graded materials can be alleviated. Hence the elastic ultimate bearing capacity of hollow cylinder can be improved strikingly. For functionally graded materials, the elastic ultimate bearing capacity can be improved strikingly by increasing the thickness of cylinder, which is not so obvious for classical homogeneous materials.

scholarly journals An improved radial point interpolation method applied for elastic problem with functionally graded material

2015 ◽  
Vol 18 (2) ◽  
pp. 131-138
Author(s):  
Viet Quoc Phung ◽  
Nha Thanh Nguyen ◽  
Thien Tich Truong
Keyword(s):  
Interpolation Method ◽  
Functionally Graded ◽  
Thin Plates ◽  
Graded Materials ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Graded Material ◽  
Point Interpolation ◽  
Support Domain ◽  
The One

A meshless method based on radial point interpolation was developed as an effective tool for solving partial differential equations, and has been widely applied to a number of different problems. Besides its advantages, in this paper we introduce a new way to improve the speed and time calculations, by construction and evaluation the support domain. From the analysis of two-dimensional thin plates with different profiles, structured conventional isotropic materials and functional graded materials (FGM), the results are compared with the results had done before that indicates: on the one hand shows the accuracy when using the new way, on the other hand shows the time count as more economical

Creep Property of Functionally Graded Materials

2005 ◽  
Vol 492-493 ◽  
pp. 599-604 ◽  
Author(s):  
Peng Cheng Zhai ◽  
Gang Chen ◽  
Qing Jie Zhang
Keyword(s):  
Functionally Graded Materials ◽  
Creep Property ◽  
Pure Metal ◽  
Functionally Graded ◽  
Ceramic Component ◽  
Metal Component ◽  
Graded Materials ◽  
Temperature Environment ◽  
The One ◽  
Graded Interlayer

The present paper investigates the creep phenomenon of the functionally graded materials under high temperature environment by the computational micromechanical method (CMM). Based on the real microstructure of the functionally graded interlayer with different component volume fractions, the emulation experiment is implemented for the creep test numerically and the creep parameters are obtained. A further series of simulation works are carried out to investigate the creep phenomenon of FGM interlayers in more detail. Numerical results show that the creep phenomenon is obvious not only for the metal-rich interlayers but also for the ceramic-rich interlayers. The creep property of ceramic/metal interlayer depends on the material’s properties of the ceramic obviously. It is remarkable that the creep strain rate of the ceramic/metal interlayer is larger than the corresponding one of pure metal under the same load when the modulus of the ceramic component is lower than the one of the metal component.

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