Experimental results are presented which show that the indentation size effect for pyramidal and spherical indenters can be correlated. For a pyramidal indenter, the hardness measured in crystalline materials usually increases with decreasing depth of penetration, which is known as the indentation size effect. Spherical indentation also shows an indentation size effect. However, for a spherical indenter, hardness is not affected by depth, but increases with decreasing sphere radius. The correlation for pyramidal and spherical indenter shapes is based on geometrically necessary dislocations and work-hardening. The Nix and Gao indentation size effect model (J. Mech. Phys. Solids 46 (1998) 411) for conical indenters is extended to indenters of various shapes and compared to the experimental results.

The correlation of the indentation size effect measured with indenters of various shapes

Nanotwinned diamond synthesized with onion carbon nanoparticles as precursors has much higher hardness and thermal stability than natural diamond; its enhanced hardness is due to the reduced size of its twin structures. Even diamond has its limitations when used in tools to cut and shape the hardest of materials. Materials scientists have therefore sought to synthesize materials that are harder than natural diamond, preferably with increased thermal stability. In air, natural diamond starts to oxidize at about 800 °C, leading to severe wear at high temperatures. Attempts to increase the hardness of diamond by decreasing its grain size have succeeded, but at the cost of even poorer thermal stability. Yongjun Tian and colleagues report the synthesis of synthetic diamond that is both ultrahard and has a dramatically enhanced thermal stability with an oxidization temperature of more than 1,000 °C. The material is synthesized using onion carbon nanoparticles as precursors and owes its enhanced hardness to a nanoscale structure consisting not of tiny grains, but of crystal 'twins' — domains of the crystal lattice related by symmetry. This result, which follows similar success with nanotwinned cubic boron nitride, suggests a general approach to making new, advanced carbon-based materials with exceptional properties. Although diamond is the hardest material for cutting tools, poor thermal stability has limited its applications, especially at high temperatures. Simultaneous improvement of the hardness and thermal stability of diamond has long been desirable. According to the Hall−Petch effect1,2, the hardness of diamond can be enhanced by nanostructuring (by means of nanograined and nanotwinned microstructures), as shown in previous studies3,4,5,6,7. However, for well-sintered nanograined diamonds, the grain sizes are technically limited to 10−30 nm (ref. 3), with degraded thermal stability4 compared with that of natural diamond. Recent success in synthesizing nanotwinned cubic boron nitride (nt-cBN) with a twin thickness down to ∼3.8 nm makes it feasible to simultaneously achieve smaller nanosize, ultrahardness and superior thermal stability5. At present, nanotwinned diamond (nt-diamond) has not been fabricated successfully through direct conversions of various carbon precursors3,6,7 (such as graphite, amorphous carbon, glassy carbon and C60). Here we report the direct synthesis of nt-diamond with an average twin thickness of ∼5 nm, using a precursor of onion carbon nanoparticles at high pressure and high temperature, and the observation of a new monoclinic crystalline form of diamond coexisting with nt-diamond. The pure synthetic bulk nt-diamond material shows unprecedented hardness and thermal stability, with Vickers hardness up to ∼200 GPa and an in-air oxidization temperature more than 200 °C higher than that of natural diamond. The creation of nanotwinned microstructures offers a general pathway for manufacturing new advanced carbon-based materials with exceptional thermal stability and mechanical properties.

Nanotwinned diamond with unprecedented hardness and stability

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

Reversible control of adhesion is an important feature of many desired, existing, and potential systems, including climbing robots, medical tapes, and stamps for transfer printing. We present experimental and theoretical studies of pressure modulated adhesion between flat, stiff objects and elastomeric surfaces with sharp features of surface relief in optimized geometries. Here, the strength of nonspecific adhesion can be switched by more than three orders of magnitude, from strong to weak, in a reversible fashion. Implementing these concepts in advanced stamps for transfer printing enables versatile modes for deterministic assembly of solid materials in micro/nanostructured forms. Demonstrations in printed two- and three-dimensional collections of silicon platelets and membranes illustrate some capabilities. An unusual type of transistor that incorporates a printed gate electrode, an air gap dielectric, and an aligned array of single walled carbon nanotubes provides a device example.

https://www.pnas.org/content/pnas/107/40/17095.full.pdf

Microstructured elastomeric surfaces with reversible adhesion and examples of their use in deterministic assembly by transfer printing

The indentation hardness–depth relation established by Nix and Gao [1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411–425] agrees well with the micro-indentation but not nano-indentation hardness data. We establish an analytic model for nano-indentation hardness based on the maximum allowable density of geometrically necessary dislocations. The model gives a simple relation between indentation hardness and depth, which degenerates to Nix and Gao [1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411–425] for micro-indentation. The model agrees well with both micro- and nano-indentation hardness data of MgO and iridium.

A model of size effects in nano-indentation

An experimental investigation of the nanohardness of polycrystalline work-hardened and annealed oxygen-free copper (OFC) for different indenter loads is described. Nanoindentations were made using a Berkovich diamond indenter and the indenter loads used were in the range 1–100 mN. It is shown that by accurately measuring the projected contact areas of nanoindentations with an atomic force microscope the overall nanohardness behaviour of the work-hardened OFC was quite different from that of the annealed OFC. The nanohardness of the former behaved non-monotonically with increasing indenter penetration depth, whereas the nanohardness of the latter decreased monotonically with increasing indenter penetration depth. A three-stage qualitative model has been proposed to explain the nanohardness results. In the first stage, it is argued that, at low penetration depths of less than 150nm (our lowest measured depth), dislocation loops are nucleated at relatively high shear stress values of about G/75, whe...

The effect of the indenter load on the nanohardness of ductile metals : an experimental study on polycrystalline work-hardened and annealed oxygen-free copper

Quasistatic microindentation hardness studies of specimens of high-purity polycrystals and single crystals of copper and aluminium have been made at room temperature using a Vickers diamond and a t...

The influence of grain size on the indentation hardness of high-purity copper and aluminium

Indentation of elastic solids with a rigid Vickers pyramidal indenter

Indentation studies of polycrystalline heavily work-hardened and annealed oxygen-free copper have been made using spherical indenters of radii 7, 35, 60, 200 and 500 μm. In the case of the 200 and 500 μm radii indenters an instron mechanical testing machine was used for applying the load, whereas for the smaller indenters a UMIS 2000 machine was used. It is shown that the relationship between the mean indentation pressure, Pm and a/R (i.e. indentation stress-strain), where a and R are the radii of the circle of contact and indenter, respectively, is independent of indenter radius, provided the indentation radius, a, is correctly measured. It is also shown that in the case of the work-hardened copper, the departure from the elastic behaviour occurs at Pm ≈ 1.1 Y, where Y is the uni-axial yield stress of the copper. In the case of the annealed copper, although the Pm vs a/R curve for the smallest indenter has the same form as for the 200 and 500 7mu;m radii indenters, the values of Pm, are higher by 50% over the enitre range of a/R. It is discussed that the spherical indentation hardness measurements, using micron-sized spherical indenters, provide a suitable method for estimating the yield stress of thin coatings and surfaces.

Nano and Macro Indentation Studies of Polycrystalline Copper Using Spherical Indenters

Results obtained from a series of experimental investigations are described in which an elastic polyisoprene hemisphere and elastic rubber cones of included angles 60°, 90°, 120° and 150° were loaded normally on to smooth blocks of soda–lime glass and polydimethylsiloxane (PDMS) containing 10% and 20% by volume of the curing agent. The load versus displacement data were continuously recorded with an instrumented indentation machine. It is shown that, whereas the loading behaviour of the hemisphere on to the blocks of the soda–lime glass and PDMS closely follows the theory of Hertz (see equation (1)), the load versus displacement behaviour of the rubber cones of included angles 60°, 90° and 120° could not be fitted by the Sneddon equation (see equation (5)) for rigid conical indenters loading on to an elastic half-space or by the modified Sneddon equation (see equation (6)) employing the combined moduli of the indenter and the half-space. The discrepancy between the predictions of the modified Sneddon equa...

Yong Yee Lim

Papers

The effect of the indenter load on the nanohardness of ductile metals : an experimental study on polycrystalline work-hardened and annealed oxygen-free copper

The influence of grain size on the indentation hardness of high-purity copper and aluminium

Indentation of elastic solids with a rigid Vickers pyramidal indenter

Nano and Macro Indentation Studies of Polycrystalline Copper Using Spherical Indenters

Experimental investigations of the normal loading of elastic spherical and conical indenters on to elastic flats