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

Determination of plastic properties of metals by instrumented indentation using different sharp indenters

The development of instrumented nanoindentation equipment has occurred concurrently with the discovery of many new families of bulk metallic glass during the past decade. While indentation testing has long been used to assess the mechanical properties of metallic glasses, depth-sensing capabilities offer a new approach to study the fundamental physics behind glass deformation. This article is a succinct review of the research to date on the indentation of metallic glasses. In addition to standard hardness measurements, the onset of plasticity in metallic glasses is reviewed as well as the role of shear banding in indentation, structural changes beneath the indenter, and rate-dependent effects measured by nanoindentation. The article concludes with perspectives about the future directions for nanocontact studies on metallic glasses.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0884291400085836

A survey of instrumented indentation studies on metallic glasses

Indentation is widely used to extract material elastoplastic properties from the measured force–displacement curves. One of the most well-established indentation techniques utilizes dual (or plural) sharp indenters (which have different apex angles) to deduce key parameters such as the elastic modulus, yield stress, and work-hardening exponent for materials that obey the power-law constitutive relationship. However, the uniqueness of such analysis is not yet systematically studied or challenged. Here we show the existence of “mystical materials”, which have distinct elastoplastic properties yet they yield almost identical indentation behaviors, even when the indenter angle is varied in a large range. These mystical materials are, therefore, indistinguishable by many existing indentation analyses unless extreme (and often impractical) indenter angles are used. Explicit procedures of deriving these mystical materials are established, and the general characteristics of the mystical materials are discussed. In many cases, for a given indenter angle range, a material would have infinite numbers of mystical siblings, and the existence maps of the mystical materials are also obtained. Furthermore, we propose two alternative techniques to effectively distinguish these mystical materials. The study in this paper addresses the important question of the uniqueness of indentation test, as well as providing useful guidelines to properly use the indentation technique to measure material elastoplastic properties.

On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials

An empirical relationship for estimating the pile-up contact area from the contact stiffness, S and the contact depth, hc, has been developed. This was achieved first by using the atomic force microscope to image nanoindents made with the Berkovich indenter in soda-lime glass and approximating the pile-up contact perimeter as a semi-ellipse. Then, by determining the pile-up contact area for several peak indentation loads, a correlation was found between the pile-up contact area and the load used to generate it. The importance of this new method of determining the pile-up contact area is that the need for indent imaging is made completely redundant, since the contact stiffness is a quantity that is routinely obtained during nanoindentation data analysis. Elastic modulus of soda-lime glass of 70 ± 1.5 GPa is measured with loads ranging from 20 to 500 mN. The hardness measured also falls within the range of values, 5.2–5.9 GPa, normally quoted in the literature for the glass.

C.-h Chiu

Papers

An analysis of load–penetration curves from instrumented indentation