Elastic indentation problems in thin films on substrate systems

Sburlati, Roberta

doi:10.2140/jomms.2006.1.541

Cited by 8 publications

(6 citation statements)

References 11 publications

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“…It is remarked that the mathematical approach utilized to find the contact law in section 2 is very powerful and has been utilized also in [9] to find the indentation in a film/substrate system. …”

Section: Numerical Results and Conclusionmentioning

confidence: 99%

Elastodynamic contact in plate-like bodies

Sburlati¹

2006

WIT Transactions on the Built Environment, Vol 87

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In this paper the dynamic problem of the frictionless normal low velocity impact of a rigid sphere against an elastic plate-like body is studied by assuming that the period of duration of the impact is much larger than the time employed by the elastic waves in traversing the plate after the first impact, using a static contact law taking into account the thickness of the plate and a Hertzian pressure distribution between the sphere and the plate is adopted. A non-linear second order ordinary differential equation for the dynamical value of the indentation is obtained and, by using a perturbative technique, numerical solutions concerning the contact period, the maximum contact force and the maximum indentation in terms of the plate thickness are obtained. Numerical investigations show how the time of collision decreases with the increasing of the thickness-to plate radius ratio, the maximum indentation decreases and the maximum contact force increases. All these values approach Hertz's values when the plate thickness increases. It is remarked that the solution presented here is valid only when the contact area radius is "small" in comparison to the plate thickness; if this assumption is not satisfied, the contact pressure distribution deviates significantly from the Hertzian prediction.

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Section: Numerical Results and Conclusionmentioning

confidence: 99%

Elastodynamic contact in plate-like bodies

Sburlati¹

2006

WIT Transactions on the Built Environment, Vol 87

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“…Furthermore, this solution provides a good description of localized effects in some mechanical problems [15][16][17].…”

Section: Stress and Displacement Field In The Cylindermentioning

confidence: 97%

Three-Dimensional Analytical Solution for an Axisymmetric Biharmonic Problem

Sburlati

2009

J Elasticity

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In this paper, we propose a method for the solution of the axisymmetric boundary value problem for a finite elastic cylinder with assigned stress and/or displacements acting on the ends and side. The technique utilizes the Love representation, which allows for reduction of the solution of the elastic problem to the search for a biharmonic function on a cylindrical domain. In the solution method suggested here, we write the Love function with a Bessel expansion and analyze in detail the conditions under which it is possible to differentiate the expansion term by term. We show that this is possible only for a restricted class of elastic solutions. In the general case, we introduce two new auxiliary functions of the z-coordinate. In this way, we obtain the general form of the axisymmetric biharmonic function, which is discussed in relation to certain specific boundary conditions applied on the side and ends of the cylinder. We obtain an exact explicit solution of practical interest for a cylinder with free ends and assigned displacements applied to the side.

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“…To explicitly find the elastic solution (2.7 and 2.8), in the next section, we assume boundary conditions on the free surface and on the interface film/substrate (Sburlati, 2006).…”

Section: Elastic Solutionmentioning

confidence: 99%

“…With this motivation, in this paper we propose a semi-inverse method in which we consider a perfectly elastic thin film (with and without adhesion) where, instead of assuming the displacement field in the contact area as input data, we assume the pressure distributions and the contact area radii known in the literature for the corresponding half-space models (Sburlati, 2006). This assumption allows us to overcome the mathematical difficulties involved in the exact analytical method (as a contact problem; Sneddon, 1966) and to extend the Hertzian, JKR, DMT, and MD half-space adhesion models to thin elastic films coated on elastic substrates.…”

Section: Introductionmentioning

confidence: 99%

Adhesive elastic contact between a symmetric indenter and an elastic film

Sburlati¹

2009

International Journal of Solids and Structures

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a b s t r a c tThis paper examines the frictionless adhesive elastic contact problem of a rigid sphere indenting a thin film deposited on a substrate. The result is then used to model the elastic phase of micro-nanoscale indentation tests performed to determine the mechanical properties of coatings and films. We investigate the elastic response including the effects of adhesion, which, as the scale decreases to the nano level, become an important issue. In this paper, we extend the Johnson-Kendall-Roberts, Derjaguin-MullerToporov, and Maugis-Dugdale half-space adhesion models to the case of a finite thickness elastic film coated on an elastic substrate. We propose a simplified model based on the assumption that the pressure distribution is that of the corresponding half-space models; in doing so, we investigate the contact radius/film thickness ratio in a range where it is usually assumed the half-space model. We obtain an analytical solution for the elastic response that is useful for evaluating the effects of the film-thickness, the interface film-substrate conditions, and the adhesion forces. This study provides a guideline for selecting the appropriate film thickness and substrate to determine the elastic constants of film in the indentation tests.

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Elastic indentation problems in thin films on substrate systems

Cited by 8 publications

References 11 publications

Elastodynamic contact in plate-like bodies

Elastodynamic contact in plate-like bodies

Three-Dimensional Analytical Solution for an Axisymmetric Biharmonic Problem

Adhesive elastic contact between a symmetric indenter and an elastic film

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