Axisymmetric contact problem for an elastic inhomogeneous half-space in the presence of cohesion

Popov, G. Ya.

doi:10.1016/0021-8928(73)90070-1

Cited by 20 publications

(17 citation statements)

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“…However, as closed form solutions of this kind are unwieldy and difficult to handle numerically (cf. [52,53] regarding elliptical contact situation or [54][55][56] in the case of a certain gradient structure) or simply do not exist in sufficiently general manner, we prefer the use of load dots as introduced in [57] or [58]. With this approach, a solution of the problem given above can be constructed by combining the superposition of various elastic or visco-elastic spaces as given in [57] with the introduction of interconnected load dots [57,58].…”

Section: The Extension Of the Oliver And Pharr Methods To Analyze Nanomentioning

confidence: 99%

Completely Analytical Tools for the Next Generation of Surface and Coating Optimization

Schwarzer¹

2014

Coatings

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Usually, some severe efforts are required to obtain tribological parameters like Archard's wear depth parameter k d . Complex tribological experiments have to be performed and analyzed. The paper features an approach where such parameters are extracted from effective interaction potentials in combination with more physical-oriented measurements, such as Nanoindentation and physical scratch. Thereby, the effective potentials are built up and fed from such tests. By using effective material potentials one can derive critical loading situations leading to failure (decomposition strength) for any contact situation. A subsequent connection of these decomposition or failure states with the corresponding stress or strain distributions allows the development of rather comprehensive tribological parameter models, applicable in wear and fatigue simulations, as demonstrated in this work. From this, a new relatively general wear model has been developed on the basis of the effective indenter concept by using the extended Hertzian approach for a great variety of loading situations. The models do not only allow to analyze certain tribological experiments, such as the well known pin-on disk test or the more recently developed nano-fretting test, but also to forward simulate such tests and even give hints for structured optimization or result in better component life-time prediction. The work will show how the procedure has to be applied in general and a small selection of practical examples will be presented.

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Section: The Extension Of the Oliver And Pharr Methods To Analyze Nanomentioning

confidence: 99%

Completely Analytical Tools for the Next Generation of Surface and Coating Optimization

Schwarzer¹

2014

Coatings

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“…According to Popov (1973), the exact solution of the integral equation in Eq. (4) can be expressed as a series of Jacobi polynomials, that is…”

Section: Problem Statement and The Solution Approachmentioning

confidence: 99%

“…Using the surface elastic Green's function, the relation between the surface displacements of the half-space ( u r ðrÞ ¼ À R r 0 eðsÞds and u z ðrÞ) and the corresponding interfacial tractions within the contact region (p(r) = r zz (r) and q(r) = s rz (r)) can be established as follows (Popov, 1973 …”

Section: Problem Statement and The Solution Approachmentioning

confidence: 99%

Mechanics of non-slipping adhesive contact on a power-law graded elastic half-space

Gao

Jin

Gao

2011

International Journal of Solids and Structures

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a b s t r a c tIn previous work about axisymmetric adhesive contact on power-law graded elastic materials, the contact interface was often assumed to be frictionless, which is, however, not always the case in practical applications. In order to elucidate the effect of friction and the coupling between normal and tangential deformations, in the present paper, the problem of a rigid punch with a parabolic shape in non-slipping adhesive contact with a power-law graded half-space is studied analytically via singular integral equation method. A series of closed-form analytical solutions, which include the frictionless and homogeneous solutions as special cases, are obtained. Our results show that, compared with the frictionless case, the interfacial friction tends to reduce the contact area and the indentation depth during adhesion. The magnitude of the coupling effect depends on both the Poisson ratio and the gradient exponent of the half-space. This effect vanishes for homogeneous incompressible as well as for linearly graded materials but becomes significant for auxetic materials with negative Poisson's ratio. Furthermore, influence of mode mixity on the adhesive behavior of power-law graded materials, which was seldom touched in literature, is discussed in details.

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“…Solutions to some mixed boundary value problems in nonhomogeneous materials have been obtained by Kassir [2], Kassir and Chuaprasert [3], Popov [4], and Singh [5]. All the above authors have considered only unidirectional nonhomogeneity.…”

Section: Introductionmentioning

confidence: 99%

On the theory of elssticity of a nonhomogeneous medium

Dhaliwal

Singh

1978

J Elasticity

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In this paper the equation of equilibrium for a nonhomogeneous isotropic elastic solid under shear has been solved in rectangular Cartesian coordinates as well as in cylindrical polar coordinates. The modulus of rigidity of the material is assumed to vary in lateral as well as vertical directions. As an example, the above solution has been used to solve the problem of a Griffith crack in an infinite solid under shear.

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Axisymmetric contact problem for an elastic inhomogeneous half-space in the presence of cohesion

Cited by 20 publications

References 1 publication

Completely Analytical Tools for the Next Generation of Surface and Coating Optimization

Completely Analytical Tools for the Next Generation of Surface and Coating Optimization

Mechanics of non-slipping adhesive contact on a power-law graded elastic half-space

On the theory of elssticity of a nonhomogeneous medium

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