The effect of substrate on the elastic properties of films determined by the indentation test — axisymmetric boussinesq problem

Yu, Hao; Sanday, S. C.; Rath, B. B.

doi:10.1016/0022-5096(90)90038-6

Cited by 155 publications

(85 citation statements)

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“…As mentioned in the introduction, the elastic indentation of a layered half-space is mathematically a mixed boundary value problem that can be reduced to a Fredholm integral equation of the second kind [10]:…”

Section: Yu's Analysis: Elastic Indentation Problem and Solutionmentioning

confidence: 99%

“…(5) can be solved numerically in the form of a Chebyshev series using El-Gendi's method [10,14]. For conical and spherical indenters, the boundary condition of vanishing pressure at the contact periphery is expressed as .…”

Section: Yu's Analysis: Elastic Indentation Problem and Solutionmentioning

confidence: 99%

“…A number of studies with several different approaches to modeling the substrate effect have been reported [7][8][9][10][11][12][13]. King used numerical techniques to model the elastic indentation of a layered half space with flat-ended punches of various cross-sections [8].…”

Section: Introductionmentioning

confidence: 99%

“…Yu et al solved the elastic contact problem of an axisymmetric indenter -flat, conical or spherical in shape -on a layered half space by first reducing the mixed boundary value problem to a Fredholm integral equation of the second kind using the Papkovich-Neuber potentials, and then solving the integral equation numerically [10,14]. Yu's solution can be regarded as a generalization of Sneddon's solution for a film/substrate composite and can be used to calculate the relations between indentation load, depth and contact stiffness for any combination of film and substrate.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation

Vlassak

2009

J. Mater. Res.

166

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The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Abstract -A data analysis procedure has been developed to estimate the contact area in an elasto-plastic indentation of a thin film bonded to a substrate. The procedure can be used to derive the elastic modulus and hardness of the film from the indentation load, displacement, and contact stiffness data at indentation depths that are a significant fraction of the film thickness. The analysis is based on Yu's elastic solution for the contact of a rigid conical punch on a layered half-space and uses an approach similar to the Oliver-Pharr method for bulk materials. The methodology is demonstrated for both compliant films on stiff substrates and the reverse combination and shows improved accuracy over previous methods.

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Section: Yu's Analysis: Elastic Indentation Problem and Solutionmentioning

confidence: 99%

Section: Yu's Analysis: Elastic Indentation Problem and Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation

Vlassak

2009

J. Mater. Res.

166

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“…First, in view of the local character of the indentation problem, we introduce a suitable parameter b representing the radius in which the contact phenomenon is contained. In such a way, we write the components of the displacement field by means of Dini and Fourier-Bessel expansions, so avoiding the use of the Hankel integral transforms and, consequently, the problem of their inversions [Yu et al 1990]. We shall subsequently show that, under suitable conditions, the specific value assumed for the parameter b is not relevant.…”

Section: Introductionmentioning

confidence: 99%

Elastic indentation problems in thin films on substrate systems

Sburlati

2006

JOMMS

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In this paper an analytical solution of an elastic isotropic thin-film on an elastic substrate under an axisymmetric loading on the plane surface is presented. The analysis is intended to model the micronanoindentation tests to evaluate some of the relevant properties of thin films and provide information about the influence of interface conditions between the film and the substrate.The theoretical solution of the equations of three-dimensional elasticity is obtained by using Dini and Fourier-Bessel expansions for the displacement field.To describe the elastic mechanical interaction between the indenter and the film for low load, we make use of the pressure distribution for contact between two homogeneous bodies, and the corresponding displacement field is solved in explicit form. The contact law is obtained with two different ideal interface conditions between the film and the substrate: perfectly bonded and frictionless contact.This form of the elastic solution may be utilized for different axisymmetric pressure distributions performed to model the interaction between the indenter and the film, thus obtaining an analytical framework for comparing experimental and numerical results.

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Oscillating Contact of Isotropic Elastic Half‐spaces

2007

Particle and Continuum Aspects of Mesomechanics

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The effect of substrate on the elastic properties of films determined by the indentation test — axisymmetric boussinesq problem

Cited by 155 publications

References 10 publications

Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation

Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation

Elastic indentation problems in thin films on substrate systems

Oscillating Contact of Isotropic Elastic Half‐spaces

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