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

Mechanical models for living cells--a review

Nanoindentation of biological materials

Instrumented indentation, also known as depth-sensing indentation or nanoindentation, is increasingly being used to probe the mechanical response of materials from metals and ceramics to polymeric and biological materials. The additional levels of control, sensitivity, and data acquisition offered by instrumented indentation systems have resulted in numerous advances in materials science, particularly regarding fundamental mechanisms of mechanical behavior at micrometer and even sub-micrometer length scales. Continued improvements of instrumented indentation testing towards absolute quantification of a wide range of material properties and behavior will require advances in instrument calibration, measurement protocols, and analysis tools and techniques. In this paper, an overview of instrumented indentation is given with regard to current instrument technology and analysis methods. Research efforts at the National Institute of Standards and Technology (NIST) aimed at improving the related measurement science are discussed.

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Review of Instrumented Indentation

Nanoindentation in polymer nanocomposites

The indentation of standard viscoelastic solids, that is, the three-element viscoelastic material, by an axisymmetric, flat-ended indenter has been investigated theoretically. Under the boundary conditions of flat-punch indentation of a viscoelastic half-space, the solutions of the equations of viscoelastic deformation are derived for the standard viscoelastic material. Their generality resides in their inclusion of compressible as well as incompressible solids. They cover the two transient situations: flat-punch creep test and load-relaxation test. In experimental tests of their applicability, nanoindentation and microindentation probes under creep and relaxation conditions yielded a modulus from 0.1 to 1.1 GPa and viscosity from 1 to 37 Gpa · s for a crosslinked glassy polyurethane coatings. For bulk polystyrene, the values vary from 1 to 2 GPa and from 20 to 40 Gpa · s, respectively. The analysis here provides a fundamental basis for probing elastic and viscous properties of coatings with nanoindentation or microindentation tests. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 10–22, 2000

https://onlinelibrary.wiley.com/doi/pdf/10.1002/%28SICI%291099-0488%2820000101%2938%3A1%3C10%3A%3AAID-POLB2%3E3.0.CO%3B2-6

Flat-punch indentation of viscoelastic material

A new method for evaluating modulus and hardness from nanoindentation load/ displacement curves is presented. As a spherical indenter penetrates an elastoplastic half-space, the elastic displacement above the contact line is presumed to diminish in proportion to the total elastic displacement under the indenter. Applying boundary conditions on the elastic and plastic displacements for elastic and rigid plastic contacts leads to an expression that can be best fit to the entire unloading curve to determine E*, the reduced modulus. Justification of the formulation is presented, followed by the results of a preliminary survey conducted on three predominantly isotropic materials: fused quartz, polycrystalline Al, and single crystal W. Diamond tips with radii ranging from 130 nm to 5 μm were used in combination with three different nanoindentation devices. Results indicate that the method gives property values consistent with accepted values for modulus and hardness. The importance of surface roughness and indentation depth are also considered.

Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations

Effect of Low Temperature on Apparent Fatigue Threshold Stress Intensity Factors

FATIGUE THRESHOLD STUDIES IN Fe, Fe-Si, AND HSLA STEEL

It was found that crack opening stress intensities are not constant after holding for various times in the unloaded state for iron and a sequence of Fe-Si binary alloys. The crack opening level decreased with time first because of asperity creep and substructure relaxation, and then increased again with time due to reverse plastic zone relaxation allowing a new set of asperities to come into contact. It is demonstrated that the crack closure phenomenon is not only a result of residual plasticity, oxidation and asperities, but also is due to asperity creep and reverse plastic zone relaxation at the crack tip for low strength materials.

W. Yu

Papers

Flat-punch indentation of viscoelastic material

Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations

Effect of Low Temperature on Apparent Fatigue Threshold Stress Intensity Factors

FATIGUE THRESHOLD STUDIES IN Fe, Fe-Si, AND HSLA STEEL

The variation of crack opening stress intensity with time