Different approaches to superhard coatings and nanocomposites

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 indentation size effect is one of several size effects on strength for which “smaller is stronger.” Through use of geometrically self-similar indenters such as cones and pyramids, the size effect is manifested as an increase in hardness with decreasing depth of penetration and becomes important at depths of less than approximately 1 μm. For spherical indenters, the diameter of the sphere is the most important length scale; spheres with diameters of less than approximately 100 μm produce measurably higher hardnesses. We critically review experimental observations of the size effect, focusing on the behavior of crystalline metals, and examine prevailing ideas on the mechanisms responsible for the effect in light of recent experimental observations and computer simulations.

The Indentation Size Effect: A Critical Examination of Experimental Observations and Mechanistic Interpretations

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

On the reverse indentation size effect and microhardness measurement of solids

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.

E. H. Yoffe

Papers

An explanation of the indentation size effect in ceramics