Contact problems and depth-sensing nanoindentation for frictionless and frictional boundary conditions

Borodich, Feodor M.; Keer, Leon M.

doi:10.1016/j.ijsolstr.2003.12.012

Cited by 101 publications

(64 citation statements)

References 38 publications

(61 reference statements)

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“…For example, the indentation by sharp pyramidal indenters is used to estimate the elastic modulus of a tested material by measuring the slope S of the unloading branch of the diagram and employing the semi-empirical BASh (Bulychev-Alekhin-Shorshorov) formula or its modifications [11,12] …”

Section: Depth-sensing Indentation and Adhesive Contactmentioning

confidence: 99%

Evaluation of adhesive and elastic properties of materials by depth-sensing indentation of spheres

et al. 2012

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Work of adhesion is the crucial material parameter for application of theories of adhesive contact. It is usually determined by experimental techniques based on the direct measurements of pull-off force of a sphere. These measurements are unstable due to instability of the loaddisplacement diagrams at tension, and they can be greatly affected by roughness of contacting solids. We show how the values of work of adhesion and elastic contact modulus of materials may be quantified using a new indirect approach (the Borodich-Galanov (BG) method) based on an inverse analysis of a stable region of the force-displacements curve obtained from the depth-sensing indentation of a sphere into an elastic sample. Using numerical simulations it is shown that the BG method is simple and robust. The crucial difference between the proposed method and the standard direct experimental techniques is that the BG method may be applied only to compressive parts of the force-displacements curves. Finally, the work of adhesion and the elastic modulus F.M. Borodich ( ) · Mof soft polymer (polyvinylsiloxane) samples are extracted from experimental load-displacement diagrams.

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Section: Depth-sensing Indentation and Adhesive Contactmentioning

confidence: 99%

Evaluation of adhesive and elastic properties of materials by depth-sensing indentation of spheres

et al. 2012

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“…For non-elastic materials, (1) 2 becomes an approximate relation and S may be affected by the residual stress field and by adhesion of materials [Borodich and Galanov 2008]. Application of the depth sensing indentation techniques in indentation analysis confirmed the link provided by classical linear elastic contact mechanics solutions [Hertz 1882;Boussinesq 1885;Love 1939;Galin 1961;Sneddon 1965;Borodich and Keer 2004] for a rigid indenter of axysmmetric shape that can be described by a monomial function of the form z = Br n :…”

Section: Introductionmentioning

confidence: 81%

Indentation analysis of fractional viscoelastic solids

Shahsavari

Ulm

2009

J. Mech. Mater. Struct.

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The constitutive differential equations governing the time-dependent indentation response for axisymetric indenters into a fractional viscoelastic half-space are derived, together with indentation creep and relaxation functions suitable for the backanalysis of fractional viscoelastic properties from indentation data. These novel fractional viscoelastic indentation relations include, as a subset, classical integer-type viscoelastic models such as the Maxwell model or Zener model. Using the correspondence principle of viscoelasticty, it is found that the differential order of the governing equations of the indentation response is higher than the one governing the material level. This difference in differential order between the material scale and indentation scale is more pronounced for the viscoelastic shear response than for the viscoelastic bulk response, which translates, into fractional derivatives, the well-known fact that an indentation test is rather a shear test than a hydrostatic test. By way of example, an original method for the inverse analysis of fractional viscoelastic properties is proposed and applied to experimental indentation creep data of polystyrene. The method is based on fitting the time-dependent indentation data (in the Laplace domain) to the fractional viscoelastic model response. Applied to polysterene, it is shown that the particular time-dependent response of this material is best captured by a bulk-and-deviator fractional viscoelastic model of the Zener type.

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“…Indeed, one has w Z 2P c 3pR ; This approach can be used as an alternative to the currently used BASh formula (Borodich & Keer 2004b) for the estimation of the elastic modulus of the material. After the determination of the values P c and d c , one can substitute them into (2.2), with l defined from (2.4), and calculate the pull-off force P adh as the modulus of the minimum force of the PKd diagram and the minimum displacement min d of the diagram.…”

Section: Estimations Of Elastic and Molecular Adhesion Characteristicsmentioning

confidence: 99%

“…Elastic characteristics are estimated using either the unloading branch of the PKd diagram, assuming that the material deforms elastically at unloading and by employing the so-called BASh formula (Bulychev et al 1975) and its modification (Borodich & Keer 2004a), or from the initial elastic stage of the diagram when the material is loaded by spherical indenters (for details see Chaudhri & Lim 2007). These estimations are usually obtained by neglecting the effects of molecular adhesion and using the formulae of the Hertz contact theory or their modifications (see discussion in Borodich & Keer (2004b), Fischer-Cripps (2006), Chaudhri & Lim (2007) and references therein).…”

Section: Introductionmentioning

confidence: 99%

Non-direct estimations of adhesive and elastic properties of materials by depth-sensing indentation

Borodich

Galanov

2008

Proc. R. Soc. A.

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Using the connection between depth-sensing indentation by spherical indenters and mechanics of adhesive contact, a new method for non-direct determination of adhesive and elastic properties of contacting materials is proposed. At low loads, the forcedisplacement curves reflect not only elastic properties but also adhesive properties of the contact, and therefore one can try to extract from experiments both the elastic characteristics of contacting materials (such as the reduced elastic modulus) and characteristics of molecular adhesion (such as the work of adhesion and the pull-off force) using a non-direct approach. The direct methods of estimations of the adhesive characteristics of materials currently used in experiments are rather complicated due to the instability of the experimental force-displacement diagrams for ultra-low tensile forces. The proposed method is based on the use of the stable experimental data for the elastic stage of the force-displacement curve and the mechanics of adhesive contact for spherical indenters. Since the experimental data always have some measurement errors, mathematical techniques for solving ill-posed problems are employed.

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Contact problems and depth-sensing nanoindentation for frictionless and frictional boundary conditions

Cited by 101 publications

References 38 publications

Evaluation of adhesive and elastic properties of materials by depth-sensing indentation of spheres

Evaluation of adhesive and elastic properties of materials by depth-sensing indentation of spheres

Indentation analysis of fractional viscoelastic solids

Non-direct estimations of adhesive and elastic properties of materials by depth-sensing indentation

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