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

Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients

A Review of Nanoindentation Continuous Stiffness Measurement Technique and Its Applications

The recent development in the field of superhard materials with Vickers hardness of ⩾40 GPa is reviewed. Two basic approaches are outlined including the intrinsic superhard materials, such as diamond, cubic boron nitride, C3N4, carbonitrides, etc. and extrinsic, nanostructured materials for which superhardness is achieved by an appropriate design of their microstructure. The theoretically predicted high hardness of C3N4 has not been experimentally documented so far. Ceramics made of cubic boron nitride prepared at high pressure and temperature find many applications whereas thin films prepared by activated deposition from the gas phase are still in the stage of fundamental development. The greatest progress has been achieved in the field of nanostructured materials including superlattices and nanocomposites where superhardness of ⩾50 GPa was reported for several systems. More recently, nc-TiN/SiNx nanocomposites with hardness of 105 GPa were prepared, reaching the hardness of diamond. The principles of de...

https://mediatum.ub.tum.de/doc/958917/file.pdf

The search for novel, superhard materials

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 ultra-low load indentation response of ceramic single crystal surfaces (Al2O3, SiC, Si) has been studied with a software-controlled hardness tester (Nanoindenter) operating in the load range 2–60 mN. In all cases, scanning and transmission electron microscopy have been used to characterize the deformation structures associated with these very small-scale hardness impressions. Emphasis has been placed on correlating the deformation behavior observed for particular indentations with irregularities in recorded load-displacement curves. For carefully annealed sapphire, a threshold load (for a given indenter) was observed below which the only surface response was elastic flexure and beyond which dislocation loop nucleation occurred at, or near, the theoretical shear strength to create the indentation. This onset of plasticity was seen as a sudden displacement discontinuity in the load-displacement response. At higher loads, indentations appeared to be accommodated predominantly by dislocation activity, though microcracks were observed to form at contact loads of only tens of milliNewtons. Possibly such cracks are the incipient slip-induced nuclei for the much larger, indentation-induced cracks usually apparent only on the surface at much higher loads and often used for estimating indentation toughness. By contrast, silicon did not show this behavior but exhibited unusually large amounts of depth recovery within indentations, resulting in a characteristic reverse thrust on the indenter during unloading. TEM studies of indentations in silicon revealed less evidence of obvious dislocation activity than in sapphire (particularly at the lowest loads used) but did show residual highly imperfect–and often amorphous–structures within the indentations, consistent with a densification transformation occurring at the very high hydrostatic stresses produced under the indenter. The reverse thrust is caused by the relaxation of densified material during unloading. Thus, it appears that the low-load hardness response of silicon is controlled by a pressure-sensitive phase transformation. Though SiC has been predicted to undergo a densification transformation similar to silicon, its load-displacement behavior was found to be similar to Al2O3 suggesting that, for these contact experiments at least, the critical resolved shear stress for dislocation nucleation is exceeded before the critical hydrostatic pressure for densification is reached. In all cases, residual, plastically formed indentations were measured to be smaller than the fully loaded indentation depths would suggest, confirming that a significant portion of the deformation is elastic surface flexure. However, there is some doubt as to whether silicon displays elastic-only deformation even at very small penetration depths. The use of microstructural studies to complement nanoindentation experiments is shown to be a key route not only to interpreting the recorded load-displacement responses, but also to examining the deformation mechanisms controlling the mechanical behavior of ceramics to surface contacts at these small spatial scales.

The deformation behavior of ceramic crystals subjected to very low load (nano)indentations

A quantitative model is proposed to explain the indentation size effect (ISE) often observed in the hardness response of hard brittle materials, namely that hardness is observed to increase with decreasing indentation size. The model is based on a mixed elastic/plastic materials deformation response whereby plastic deformation occurs in a discrete manner progressively to relieve stresses created by elastic flexure of the surface at the edges of the indentation. During unloading of the indenter, recovery of the elastic increment of deformation, which precedes each new band of plastic deformation, results in the indentation appearing smaller than expected, particularly as the indentation sizes decrease to approach the scale of the plastic deformation band spacing. The model fits observed experimental data well and analysis of hardness/size data in this way is shown to allow both a bulk hardness value and a characteristic deformation band scale to be calculated for a given sample.

An explanation of the indentation size effect in ceramics

Nanoindentation load-displacement curves provide a “mechanical fingerprint” of a materials response to contact deformation. Over the last few years, much attention has been focused on understanding the factors controlling the detailed shape of unloading curves so that parameters such as true contact area, Young's modulus, and an indentation hardness number can be derived. When the unloading curve is well behaved (by which we mean approximating to linear behavior, or alternatively, fitting a power-law relationship), then this approach can be very successful. However, when the test volume displays considerable elastic recovery as the load is removed [e.g., for many stiff hard materials and many inhomogeneous systems (e.g., those employing thin hard coatings)], then the unloading curve fits no existing model particularly well. This results in considerable difficulty in obtaining valid mechanical property data for these types of materials. An alternative approach, described here, is to attempt to understand the shapes of nanoindentation loading curve and thus quantitatively model the relationship between Young's modulus, indentation hardness, indenter geometry, and the resultant maximum displacement for a given load. This paper describes the development and refinement of a previous approach by Loubet et al1 originally suggested for a Vickers indenter, but applied here to understand the factors that control the shape of the loading curve during nanoindentation experiments with a pointed, trigonal (Berkovich) indenter. For a range of materials, the relationship P = Kmδ2 was found to describe the indenter displacement, δ, in terms of the applied load P. For each material, Km can be predicted from the Young's modulus (E) and the hardness (H). The result is that if either E or H is known, then the other may be calculated from the experimental loading curve. This approach provides an attractive alternative to finite element modeling and is a tractable approach for those cases where analysis of unloading curves is infeasible.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0884291400024432

Analysis of nanoindentation load-displacement loading curves

A detailed microstructural investigation of reaction-bonded silicon carbide has been performed using both fully-bonded and quenched samples and other specially prepared specimens containing large original single crystals of known crystallographic habit. The development of the epitaxial SiC overgrowth on the original SiC particles has been followed and found to proceed by the progressive growth and coalescence of identically-oriented nuclei. This epitaxial layer grows with a habit characteristic ofβ (cubic) SiC and then transforms toα-SiC in the high temperature region behind the reaction front. The formation of faceted grain boundaries is explained by this growth morphology. Furthermore, SiC:SiC grain boundaries, SiC:SiC epitaxial boundaries and SiC:Si interfaces have all been characterized by TEM techniques. The grain boundaries are of particular interest since they usually comprise a thin (∼1 nm) layer of amorphous SiC with occasional suicide and graphite inclusions. The general cleanliness of the vast majority of interfacial area is a result of the removal of the impurities insoluble in SiC by liquid silicon moving through the sample. The overall distribution of impurities is discussed. Other microstructural features have been characterized and texturing due to original particle alignment during fabrication of the green compact investigated. The control of the mechanical properties of reaction-bonded silicon carbide by these various microstructural features is discussed. A basis for an explanation of the interesting trace-impurity-controlled contrast seen in secondary electron images of these materials is also established.

Trevor F. Page

Papers

On the hardness of coated systems

The deformation behavior of ceramic crystals subjected to very low load (nano)indentations

An explanation of the indentation size effect in ceramics

Analysis of nanoindentation load-displacement loading curves

Microstructural evolution in reaction-bonded silicon carbide