We provide an overview of the basic concepts of scaling and dimensional analysis, followed by a review of some of the recent work on applying these concepts to modeling instrumented indentation measurements. Specifically, we examine conical and pyramidal indentation in elastic-plastic solids with power-law work-hardening, in power-law creep solids, and in linear viscoelastic materials. We show that the scaling approach to indentation modeling provides new insights into several basic questions in instrumented indentation, including, what information is contained in the indentation load-displacement curves? How does hardness depend on the mechanical properties and indenter geometry? What are the factors determining piling-up and sinking-in of surface profiles around indents? Can stress-strain relationships be obtained from indentation load-displacement curves? How to measure time dependent mechanical properties from indentation? How to detect or confirm indentation size effects? The scaling approach also helps organize knowledge and provides a framework for bridging micro- and macroscales. We hope that this review will accomplish two purposes: (1) introducing the basic concepts of scaling and dimensional analysis to materials scientists and engineers, and (2) providing a better understanding of instrumented indentation measurements.

Scaling, dimensional analysis, and indentation measurements

An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented. The evolution of the elastic-plastic contact with increasing interference is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. The model provides dimensionless expressions for the contact load, contact area, and mean contact pressure, covering a large range of interference values from yielding inception to fully plastic regime of the spherical contact zone. Comparison with previous elastic-plastic models that were based on some arbitrary assumptions is made showing large differences. ©2002 ASME

Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat

This paper presents an elastic-plastic asperity microcontact model for contact between two nominally flat surfaces. The transition from elastic deformation to fully plastic flow of the contacting asperity is modeled based on contact-mechanics theories in conjunction with the continuity and smoothness of variables across different modes of deformation. The relations of the mean contact pressure and contact area of the asperity to its contact interference in the elastoplastic regime of deformation are respectively modeled by logarithmic and fourth-order polynomial functions. These asperity-scale equations are then used to develop the elastic-plastic contact model between two rough surfaces, allowing the mean surface separation and the real area of contact to be calculated as functions of the contact load and surface plasticity index. Results are presented for a wide range of contact load and plasticity index, showing the importance of accurately modeling the deformation in the elastoplastic transitional regime of the asperity contacts. The results are also compared with those calculated by the GW and CEB models, showing that the present model is more complete in describing the contact of rough surfaces.

An Asperity Microcontact Model Incorporating the Transition From Elastic Deformation to Fully Plastic Flow

http://ece.uprm.edu/~msuarez/4001/doc/read_assign3_2ndSem0910.pdf

Nanoindentation studies of materials

The Climate Near the Ground

Finite-elements model for the contact of rough surfaces

Using the two-parameter power hardening rule σ=kepm, the parameters k and m are identified from spherical indentation loading–unloading tests which account for the variation of the indentation profile during elastic unloading and sphere deformation. The predicted and measured stress–strain curves are compared for several materials. Both experimental and actual data for 18G2A low-alloy steel are used to assess the accuracy of the identification procedure. Finally, identification of the stress–strain curve of an aluminium alloy is demonstrated.

Identification of plastic hardening parameters of metals from spherical indentation tests

Identification of yield stress and plastic hardening parameters from a spherical indentation test

The ablation of graphite is studied as a function of laser fluence for 355, 532 and 1,064 nm wavelength generated by a nanosecond Nd:YAG laser. It has been found that in the case of lower wavelengths, the transition from the thermal ablation to the phase explosion takes place at lower laser fluences. The change of crater shape due to the effect of deep drilling in the proximity of the phase explosion threshold was observed. The calculations of plasma radiation flux to the target surface were made, and the considerable increase of absorbed energy density was found in the case of 355 nm wavelength.

/pdf/the-effect-of-laser-wavelength-on-the-ablation-rate-of-4skgzavpgk.pdf

S. Kucharski

Papers

Finite-elements model for the contact of rough surfaces

Identification of plastic hardening parameters of metals from spherical indentation tests

Identification of yield stress and plastic hardening parameters from a spherical indentation test

The effect of laser wavelength on the ablation rate of carbon

Study of contact of rough surfaces: Modeling and experiment