Contact problems for functionally graded materials of complicated structure

Aizikovich, S. M.; Vasil'ev, A. M.; Krenev, L. I.; Trubchik, Irina; Селезнев, Н М

doi:10.1007/s11029-011-9232-8

Cited by 11 publications

(11 citation statements)

References 7 publications

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“…They can reduce the magnitude of residual and thermal stresses, mitigate stress concentration and increase fracture toughness [1]. In the past few years, many experimental and numerical results have shown that controlling a material property gradient in FGMs could lead to a significant improvement in the resistance to the contact deformation and damage [2][3][4][5][6][7][8][9][10][11][12]. This potential application motivates the study of the contact mechanics of FGMs.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic instability of functionally graded materials in frictionless contact

Mao

Wang

2015

Acta Mech

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This paper investigates the static thermoelastic instability between a functionally graded material (FGM) half-plane and a homogeneous half-plane under the plane strain state using the perturbation method. Two frictionless half-planes are pressed together by a uniform pressure and transmit a uniform heat flux at their interface where a pressure-dependent thermal contact resistance is taken into account. The material properties of the FGMs are assumed to be of an exponential form. The characteristic equation is derived to determine the thermoelastic instability behavior of two half-planes. The instabilities are categorized into three types based on the ratio of the material properties. The effects of the gradient index, thermal contact resistance and material combination on the critical heat flux are discussed by the parametric studies. It is indicated that the use of FGMs can improve the thermoelastic instability behavior of systems.

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Section: Introductionmentioning

confidence: 99%

Thermoelastic instability of functionally graded materials in frictionless contact

Mao

Wang

2015

Acta Mech

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“…Obviously, for sufficiently thin coatings away from the contact boundaries x c = ± a 0 c the pressure distribution p 0 c ( x c ) is very close to the Hertzian distribution 1 − x 2 , while close to these boundaries p 0 c ( x c ) is small (see Figures 8 and 9 from Part 1 of this series of papers [11]). Therefore, for thin coatings and Q s > 0 the value of the ratio of the integrals falsefalse ∫ − a 0 c a 0 c exp ( β − 1 ∕ 2 Q s p 0 c ( x ) ) dx ∕ falsefalse ∫ − 1 1…”

Section: Some Criteria For Coating Effectiveness In Ehl Contacts Omentioning

confidence: 99%

“…As part of the study, criteria of coating effectiveness are introduced and discussed. The approach used for achieving this goal is based on the recently developed asymptotic solution method [1–3] for the steady isothermal EHL problems for heavily loaded point contacts, as well as on a semi-analytical method for the solution of contact problems for elastic functionally graded materials without the presence of lubrication in contacts (dry contacts) [4–12]. A detailed review of the current state of methodologies used for the solution of EHL problems for line and point contacts of homogeneous elastic materials, as well as certain advantages including solution regularization and the drawbacks of numerical and asymptotic methods are presented in previous works [1–3].…”

Section: Introductionmentioning

confidence: 99%

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

Kudish

Volkov

Vasiliev

et al. 2017

Mathematics and Mechanics of Solids

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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 cr...

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“…Substituting (2) to the equation (1), differential equation of elasticity in terms of displacements is obtained:…”

Section: Problem Statementmentioning

confidence: 99%

“…From the mid-20th century functionally graded inhomogeneity of materials is accounted for in analysis of plates, foundations [1,2] etc. In modern times, FGMs, apart from the civil engineering, are widely used in industry, especially in microelectronics [3,4], where traditional materials like alumina, silicon etc.…”

Section: Introductionmentioning

confidence: 99%

On the problem of shear of a functionally graded half-space by a punch

Zelentsov

2017

MATEC Web Conf.

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Contact problem on shear of a functionally graded half-space by a strip bunch was considered. Shear modulus of the half-space is exponentially increasing by depth. The contact problem was reduced to a convolution integral equation of the first kind. Solution of the integral equation was constructed by asymptotic methods over the characteristic parameter of the problem. Dependence of the obtained problem solution and its main characteristics on the shear modulus of the half-space was analysed. Expressions for the main characteristics of the problem are given.

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Contact problems for functionally graded materials of complicated structure

Cited by 11 publications

References 7 publications

Thermoelastic instability of functionally graded materials in frictionless contact

Thermoelastic instability of functionally graded materials in frictionless contact

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

On the problem of shear of a functionally graded half-space by a punch

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