The method we introduced in 1992 for measuring hardness and elastic modulus by instrumented indentation techniques has widely been adopted and used in the characterization of small-scale mechanical behavior. Since its original development, the method has undergone numerous refinements and changes brought about by improvements to testing equipment and techniques as well as from advances in our understanding of the mechanics of elastic–plastic contact. Here, we review our current understanding of the mechanics governing elastic–plastic indentation as they pertain to load and depth-sensing indentation testing of monolithic materials and provide an update of how we now implement the method to make the most accurate mechanical property measurements. The limitations of the method are also discussed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0884291400085800

Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology

Effects of the substrate on the determination of thin film mechanical properties by nanoindentation

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

This paper reviews commonly used methods of analysing and interpreting nanoindentation test data, with a particular emphasis on the testing of thin films. The popularity of nanoindentation testing is evidenced by the large number of papers that report such measurements in recent years. Unfortunately, there appear to be several issues that are emerging as common sources of error in using this technique. The present paper is aimed at highlighting these errors for the benefit of those practitioners who wish to use the technique but are not fully conversant with the field.

Critical review of analysis and interpretation of nanoindentation test data

http://www.eng.usf.edu/~volinsky/VolinskyActaMatReview2002.pdf

Interfacial toughness measurements for thin films on substrates

The hardness of a number of coated systems has been measured using a variety of experimental techniques ranging from traditional macro-Vickers indentation to ultra-low-load depth-sensing nanoindentation. This has allowed the hardness response to be measured over scales ranging from those less than the coating thickness, where a coating-dominated response is expected, to much more macroscopic scales where system behaviour is dominated by the substrate. The objective has been to construct a mathematical description of the hardness performance of coated systems which well describes the behaviour over this wide range of scales. Previous attempts at such quantitative descriptions have usually involved models focusing on some particular deformation mechanism (e.g. plasticity, elastic response or fracture). In contrast, this paper presents a new approach to analysing hardness data essentially using dimensionless parameters containing descriptors equally applicable to either plasticity- or fracture-dominated behaviour with all scales measured relative to the coating thickness. The model shows an excellent fit to a wide range of experimental data. Furthermore, once the fit has been made, not only can some deductions be made regarding dominant deformation mechanisms, but the model allows predictions of the contact response of other coated systems to be made.

On the hardness of coated systems

The effect of coating cracking during depth-sensing indentation testing (e.g. nanoindentation testing) on systems comprising thin hard coatings (e.g. TiN) on a less stiff, hard substrate (e.g. steel) has been investigated in order to establish whether, at such small scales, the occurrence of annular through-thickness cracks around indentation sites can be detected from load–displacement plots and whether any accompanying localized debonding of the coating from the substrate can also be identified. Experiments were performed on thin TiN and NbN monolayers, and compositionally modulated TiN/NbN and TiN/ZrN deposited onto hard steel or stainless steel substrates. Above a critical load ( P crit ) in the range 80–500 mN, all systems exhibited annular through-thickness cracks around indentation sites. The cracking was found to be accompanied by a discrete change in gradient of the loading portion of the load–displacement curve. Also, analysis of the unloading curves beyond this point showed that elastic recovery was controlled by the elastic modulus of the underlying substrate material alone. The cracking mechanism has been characterized using scanning electron microscopy, coupled with optical profilometry to map the detailed z -displacement of the surface — a procedure critical to understanding whether coating–substrate debonding had occurred. Some cracks were found to show a spiral morphology and the effect of indentation loading rate was investigated to see if appearance of these cracks was loading-rate sensitive. Our results highlight the problems inherent in assessing both the interfacial failure and the interfacial fracture toughness of thin film coated systems at the small contact scales (⩽1 μm) associated with crack genesis where it is difficult to confirm the extent of sub-surface cracks by conventional means. We have also demonstrated that both load–displacement and load–displacement squared plots are necessary if a more complete understanding of system behaviour is to be gained. Also, a simple fracture mechanics model for the annular cracking behaviour seen in such systems has been derived and used to estimate a value of G i c (the interfacial work of fracture) as 180 J m −2 for the TiN/ZrN-stainless steel system.

The effect of coating cracking on the indentation response of thin hard-coated systems

The continuously recording indentation responses of a number of coated systems, mainly thin (<10 μm) hard nitride coatings on stainless steels and a powder metallurgy tool steel, have been explored using nanoindentation with indenter displacements increasing progressively to values greater than the coating thickness. The resultant load-displacement data have been analyzed not only to produce conventional load-displacement (P-δ) plots but also to examine the relationship between P and δ2. Recent models have proposed that there should be a linear P-δ2 relationship for homogeneous systems and that such plots have the potential to reveal the load/displacement regimes in which either the coating or the substrate, or both, are dominant in controlling the overall behavior of the coated system. By utilizing point-to-point differentiation of the P-δ2 relationship, this paper extends this approach to confirm not only that these different regimes of behavior may be readily experimentally identified in this way, but also that further details, such as the propagation of cracks, may be recognized. Our analysis also provides a valuable experimental link to models describing the near-surface deformation behavior of coated systems.

Using the P-δ 2 analysis to deconvolute the nanoindentation response of hard-coated systems

In order to design the hard coating best suited to engineer the surface of a given substrate for a particular application, it is important that we have a clear picture of the mechanisms by which thin hard coated systems work. In this paper we describe a quantitative model designed to explore the increase in systems' hardness attributable to stresses created on the coating by the upthrust of substrate. material flowing plastically in response to indentation. Thus the model considers how the upwelling of displaced substrate material creates an upward pressure on the coating inducing elastic flexure which, in turn, resists the substrate deformation. The influence of this flexure has been investigated using a combination of existing analytical solutions (e.g. plate theory) to determine the overall effect on the indentation response of coated systems. The resulting model is critically compared with previous work. Experimental verification is provided by diverse experimental data from indentation tests on thin (1–24 μm) coatings of TiN and Cr on various metal substrates, sugar on chocolate substrates and other results drawn from the literature. The model helps to identify Eh 3 / d 3 H 0 as a dimensionless parameter which provides a means of condensing all available data onto a single “master” curve. Further developments are discussed.

Modelling the hardness response of coated systems: the plate bending approach

In a previous paper, we described a new approach to understanding the hardness enhancements provided to ductile substrates by the application of thin hard coatings. The model, based on plate theory, examined the constraining effect of the coating (after cracking) on the “up-welling” movement of plastically displaced material (“pile-up”) in the substrate. The key concepts are that, this upthrust is resisted and constrained by elastic flexure of the coating around the periphery of the contact damage site (e.g. a hardness indentation) and this impedance to deformation appears as an increase in the system hardness. The model led to a plot which can also be used to predict the mechanical properties of coatings necessary to withstand any given scale of contact damage. In this paper the detailed appearance of the plot is further examined with respect to the effects of cracks of differing morphologies. Stronger experimental evidence is also presented to confirm this “master curve” or “design curve” which can be used in coating selection over a wide range of coated systems and contact scales. Our new data also shows how deviations from the master curve can be used to identify regimes in which differing mechanisms are playing some significant role. Thus our current refinements serve to map out the dominant mechanisms in the deformation response of hard coatings and shed light on exactly how the detailed indentation response of coatings can add significant resistance to contact damage of components, even after cracking of the coating has occurred.

M.R. McGurk

Papers

On the hardness of coated systems

The effect of coating cracking on the indentation response of thin hard-coated systems

Using the P-δ 2 analysis to deconvolute the nanoindentation response of hard-coated systems

Modelling the hardness response of coated systems: the plate bending approach

Exploration of the plate bending model for predicting the hardness response of coated systems