Adhesion and wear of diamond: formation of nanocracks and adhesive craters of torn out material.

Mechanical transformation of rough diamonds into brilliant ones is usually achieved by polishing using microsized abrasive diamond particles. It is shown that in addition to formation of periodic pattern of 'partial' Hertzian cone cracks on the diamond surface, nano-sized domains (50-150 nm in diameter) of crumbled material are observed. Because these domains are located in the centres of the regions (250-500 nm in diameter) partially surrounded by the Hertzian cone cracks, where the stresses are close to the stress field of hydrostatic compression, the material removal cannot be explained by creation of tensile or shear cracks. It is argued that the creation of these domains of crumbled material is due to adhesive interactions between sliding diamond particles and the diamond surface. Employing a two-term law of friction, the scheme of ultimate equilibrium between the particle and the surface is presented. The distributions of contact stresses are calculated for two approaches: (i) the extended Johnson-Kendall-Roberts model and (ii) the 'soft' model of adhesive contact. Thus, adhesion between the sliding diamond particle and the surface leads to creation of periodic pattern of the crumbling domains with the steps 500-1000 nm and adhesive tearing out of the material from the domains. This article is part of the theme issue 'Nanocracks in nature and industry'.

Explicit transformation between non-adhesive and adhesive contact problems by means of the classical Johnson-Kendall-Roberts formalism.

The classic Johnson-Kendall-Roberts (JKR) contact theory was developed for frictionless adhesive contact between two isotropic elastic spheres. The advantage of the classical JKR formalism is the use of the principle of superposition of solutions to non-adhesive axisymmetric contact problems. In the recent years, the JKR formalism has been extended to other cases, including problems of contact between an arbitrary-shaped blunt axisymmetric indenter and a linear elastic half-space obeying rotational symmetry of its elastic properties. Here the most general form of the JKR formalism using the minimal number of a priori conditions is studied. The corresponding condition of energy balance is developed. For the axisymmetric case and a convex indenter, the condition is reduced to a set of expressions allowing explicit transformation of force-displacement curves from non-adhesive to corresponding adhesive cases. The implementation of the developed theory is demonstrated by presentation of a two-term asymptotic adhesive solution of the contact between a thin elastic layer and a rigid punch of arbitrary axisymmetric shape. Some aspects of numerical implementation of the theory by means of Finite-Element Method are also discussed. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

Contact probing of prestressed adhesive membranes of living cells.

Atomic force microscopy (AFM) studies of living biological cells is one of main experimental tools that enable quantitative measurements of deformation of the cells and extraction of information about their structural and mechanical properties. However, proper modelling of AFM probing and related adhesive contact problems are of crucial importance for interpretation of experimental data. The Johnson-Kendall-Roberts (JKR) theory of adhesive contact has often been used as a basis for modelling of various phenomena including cell-cell interactions. However, strictly speaking the original JKR theory is valid only for contact of isotropic linearly elastic spheres, while the cell membranes are often prestressed. For the first time, effects caused by molecular adhesion for living cells are analytically studied taking into account the mechanical properties of cell membranes whose stiffness depends on the level of the tensile prestress. Another important question is how one can extract the work of adhesion between the probe and the cell. An extended version of the Borodich-Galanov method for non-direct extraction of elastic and adhesive properties of contacted materials is proposed to apply to experiments of cell probing. Evidently, the proposed models of adhesive contact for cells with prestressed membranes do not cover all types of biological cells because the structure and properties of the cells may vary considerably. However, the obtained results can be applied to many types of smooth cells and can be used to describe initial stages of contact and various other processes when effects of adhesion are of crucial importance. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

A Review of the Mechanical Properties of Graphene Aerogel Materials: Experimental Measurements and Computer Simulations.

Graphene aerogels (GAs) combine the unique properties of two-dimensional graphene with the structural characteristics of microscale porous materials, exhibiting ultralight, ultra-strength, and ultra-tough properties. GAs are a type of promising carbon-based metamaterials suitable for harsh environments in aerospace, military, and energy-related fields. However, there are still some challenges in the application of graphene aerogel (GA) materials, which requires an in-depth understanding of the mechanical properties of GAs and the associated enhancement mechanisms. This review first presents experimental research works related to the mechanical properties of GAs in recent years and identifies the key parameters that dominate the mechanical properties of GAs in different situations. Then, simulation works on the mechanical properties of GAs are reviewed, the deformation mechanisms are discussed, and the advantages and limitations are summarized. Finally, an outlook on the potential directions and main challenges is provided for future studies in the mechanical properties of GA materials.

A Macro Model for Electroadhesive Contact of a Soft Finger With a Touchscreen.

A contact problem of electroadhesion for a conductive elastic body pressed against a rigid plane surface of a dielectric coating covering a conductive substrate is formulated applying the Johnsen-Rahbek approximation for the attractive surface stresses and the Derjaguin-Muller-Toporov (DMT) hypothesis about the influence of the adhesive stresses on the deformable shape of the elastic body. An approximate solution is obtained using the Winkler-Fuss deformation model with the equivalent (contact load dependent) stiffness coefficient evaluated according to the Xydas-Kao soft finger model. The friction force under applied voltage is evaluated as the product of the coefficient of friction and the integral of the macro contact pressure over the apparent contact area. The upper and lower estimates for the friction force are discussed in the case of absence of any external normal load.

Depth-Sensing Indentation as a Micro- and Nanomechanical Approach to Characterisation of Mechanical Properties of Soft, Biological, and Biomimetic Materials.

Classical methods of material testing become extremely complicated or impossible at micro-/nanoscale. At the same time, depth-sensing indentation (DSI) can be applied without much change at various length scales. However, interpretation of the DSI data needs to be done carefully, as length-scale dependent effects, such as adhesion, should be taken into account. This review paper is focused on different DSI approaches and factors that can lead to erroneous results, if conventional DSI methods are used for micro-/nanomechanical testing, or testing soft materials. We also review our recent advances in the development of a method that intrinsically takes adhesion effects in DSI into account: the Borodich-Galanov (BG) method, and its extended variant (eBG). The BG/eBG methods can be considered a framework made of the experimental part (DSI by means of spherical indenters), and the data processing part (data fitting based on the mathematical model of the experiment), with such distinctive features as intrinsic model-based account of adhesion, the ability to simultaneously estimate elastic and adhesive properties of materials, and non-destructive nature.

Contact probing of stretched membranes and adhesive interactions: graphene and other two-dimensional materials.

Contact probing is the preferable method for studying mechanical properties of thin two-dimensional (2D) materials. These studies are based on analysis of experimental force-displacement curves obtained by loading of a stretched membrane by a probe of an atomic force microscope or a nanoindenter. Both non-adhesive and adhesive contact interactions between such a probe and a 2D membrane are studied. As an example of the 2D materials, we consider a graphene crystal monolayer whose discrete structure is modelled as a 2D isotropic elastic membrane. Initially, for contact between a punch and the stretched circular membrane, we formulate and solve problems that are analogies to the Hertz-type and Boussinesq frictionless contact problems. A general statement for the slope of the force-displacement curve is formulated and proved. Then analogies to the JKR (Johnson, Kendall and Roberts) and the Boussinesq-Kendall contact problems in the presence of adhesive interactions are formulated. General nonlinear relations among the actual force, displacements and contact radius between a sticky membrane and an arbitrary axisymmetric indenter are derived. The dimensionless form of the equations for power-law shaped indenters has been analysed, and the explicit expressions are derived for the values of the pull-off force and corresponding critical contact radius.