Elastic layer under axisymmetric indentation and surface energy effects

Intarit, Pong-in; Senjuntichai, Teerapong; Rungamornrat, Jaroon

doi:10.1007/s00033-018-0925-x

Cited by 15 publications

(12 citation statements)

References 38 publications

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“…For example, Vasu and Bhandakkar investigated the cylindrical indentation of a layer-substrate system, 21 and Rungamornrat research group analyzed an elastic layer under the action of different axisymmetric surface loads. 22–24 All researches reveal that the bulk material becomes stiffer with surface effects, and the surface residue stresses dominate in the normal deformation while the surface elasticity in the shear deformation. Since this paper concentrates on the frictionless normal contact problem, hence only the effect of surface residue stresses will be taken into account.…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric indentation problem of a transversely isotropic elastic medium with surface stresses

Wang

Shen

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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The frictionless contact problem between an axisymmetric rigid indenter and a layered transversely isotropic medium with surface stresses is considered. The contact pressure is represented as a product of two series based on the solutions of the bulk material and the elastic surface. By using Hankel transforms, the coefficients in the product-series representation are determined by the normal displacement condition inside the contact area and the finite-pressure condition at the contact edge. Taking the spherical indentation as a specific example, the effectiveness of the solution procedure is verified for various contact scenarios. Comparing with the Green’s function method, this solution procedure is not only computationally efficient but also may give the contact pressure in its analytical form. For some specific problems, the effects of the material anisotropy and the layer thickness on the contact process with surface stresses are investigated.

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Section: Introductionmentioning

confidence: 99%

Axisymmetric indentation problem of a transversely isotropic elastic medium with surface stresses

Wang

Shen

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Subsequently, Rungamornrat et al [29] revisited the axisymmetric case with both surface tension and surface elasticity, and also pointed out that surface tension plays a dominant role for normal frictionless contact problem. Most recently, Intarit et al [30] analyzed the axisymmetric indentations of an elastic layer with surface energy. In these works, the distributions of contact stresses and contact profiles were demonstrated for some particular cases, however, the indentation load-depth relation was absent, which is the basis for indentation tests but difficult to obtain analytically.…”

Section: Introductionmentioning

confidence: 99%

Indentation load–depth relation for an elastic layer with surface tension

Yuan

Ding

et al. 2018

Mathematics and Mechanics of Solids

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Load-depth relation is the fundamental requisite in nanoindentation tests for thin layers, however, the effects of surface tension are seldom included. This paper concerns micro-/nano-sized indentation of a bonded elastic layer by a rigid sphere. The surface Green's function with the incorporation of surface tension is first derived by applying the Hankel integral transform, and subsequently used to formulate the governing integral equation for the axisymmetric contact problem. By using a numerical method based on Gauss-Chebyshev quadrature formula, the singular integral equation is solved efficiently. Several numerical results are presented to investigate the influences of surface tension and layer thickness on contact pressure, surface deformation and bulk stress, respectively. It is found that when the size of contact is comparable to the ratio of surface tension to elastic modulus, the contribution of surface tension to the load-depth relation becomes quite prominent. With the help of a parametric study, explicit general expressions for the indentation load-depth relation as well as the load-contact radius relation are summarized, which provide the groundwork for practical applications.

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“…The Gurtin-Murdoch continuum-based model has been employed to study a variety of problems with the consideration of surface energy effects in the past (e.g. see [4][5][6][7][8][9][10][11][12][13][14]).…”

Section: Introductionmentioning

confidence: 99%

Variational Formulation of Interaction between Elastic Plate and Elastic Medium under the Influence of Surface Energy

et al. 2018

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A variational formulation of interaction problem is presented in this paper for the analysis of an elastic circular plate under axisymmetric vertical loading resting on an isotropic elastic half-space under the influence of surface energy. The Gurtin-Murdoch surface elasticity theory is adopted to take into account the surface energy effects. The contact surface between the plate and the half-space is assumed to be smooth, and the deflected shape of the plate is represented by a power series of the radial coordinate. The undetermined coefficients in the series are determined through the minimization of the total potential energy functional of the plate-half-space system. The accuracy of the present solution is verified by comparing with existing solutions, and selected numerical results are presented to portray the influence of surface energy effects on interaction between an elastic circular plate and an elastic half-space.

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Elastic layer under axisymmetric indentation and surface energy effects

Cited by 15 publications

References 38 publications

Axisymmetric indentation problem of a transversely isotropic elastic medium with surface stresses

Axisymmetric indentation problem of a transversely isotropic elastic medium with surface stresses

Indentation load–depth relation for an elastic layer with surface tension

Variational Formulation of Interaction between Elastic Plate and Elastic Medium under the Influence of Surface Energy

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