Self-Similar Law of Energy Release before Materials Fracture

A general law of energy release is derived for stressed heterogeneous materials, being valid from the starting moment of loading till the moment of materials fracture. This law is obtained by employing the extrapolation technique of the self-similar approximation theory. Experiments are accomplished measuring the energy release for industrial composite samples. The derived analytical law is confronted with these experimental data as well as with the known experimental data for other materials.Comment: Latex, 15 pages, no figure

Simulations of sliding adhesive contact between microgear teeth in silicon-based MEMS work in a vacuum environment

Sliding friction and adhesive contact interactions between microgear silicon-based MEMS teeth working in a clean and vacuum environment have been modelled using a multiscale hierarchical elastic structure. Here the results of numerical simulations based on the use of multiscale block model are presented. The tooth is modelled as a bulk silicon-based MEMS surface covered by roughness having two subscales specified by the character of interactions: atomic subscale level and adhesive subscale. Friction over completely meshing teeth surfaces is estimated by calculation of the total energy dissipated during sliding. The dissipation is caused by the different physical and chemical mechanisms. Due to the vacuum environment, these mechanisms reduced to the energy lost by the dissociation of chemical and van der Waals bonds, and by the elastic interlocking between the asperities located on the meshing micro-tooth surfaces. It is argued that due to the Polonsky-Keer effect, there is no plastic deformation of the MEMS tooth surface asperities because the asperity sizes are within the validity of this effect. The adhesion layer is defined employing ideas of the Maugis approximation. The adhesion force of each nanoasperity has assumed to be equal to the pull-off force in the Boussinesq-Kendall model corrected by the Borodich no-slip coefficient. The simulations show that MEMS with the clean silicon surfaces of teeth cannot work due to stiction between surfaces, while friction between tooth surfaces functionalised by carbon-based layer is much smaller. If the functionalised coating is worn away then stiction may occur

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

The JKR-type adhesive contact problems for transversely isotropic elastic solids

The JKR (Johnson, Kendall, and Roberts) and Boussinesq–Kendall models describe adhesive frictionless contact between two isotropic elastic spheres or between a flat end punch and an elastic isotropic half-space. Here adhesive contact is studied for transversely isotropic materials in the framework of the JKR theory. The theory is extended to much more general shapes of contacting axisymmetric solids, namely the distance between the solids is described by a monomial (power-law) function of an arbitrary degree d⩾1d⩾1. The classic JKR and Boussinesq–Kendall models can be considered as two particular cases of these problems, when the degree of the punch d is equal to two or it goes to infinity, respectively. It is shown that the formulae for extended JKR contact model for transversely isotropic materials have the same mathematical form as the corresponding formulae for isotropic materials; however the effective elastic contact moduli have different expression for different materials. The dimensionless relations between the actual force, displacements and contact radius are given in explicit form. Connections of the problems to nanoindentation of transversely isotropic materials are discussed

Insight into mechanics of AFM tip-based nanomachining: bending of cantilevers and machined grooves

Atomic force microscope (AFM) tip-based nanomachining is currently the object of intense research investigations. Values of the load applied to the tip at the free end of the AFM cantilever probe used for nanomachining are always large enough to induce plastic deformation on the specimen surface contrary to the small load values used for the conventional contact mode AFM imaging. This study describes an important phenomenon specific for AFM nanomachining in the forward direction: under certain processing conditions, the deformed shape of the cantilever probe may change from a convex to a concave orientation. The phenomenon can principally change the depth and width of grooves machined, e.g. the grooves machined on a single crystal copper specimen may increase by 50% on average following such a change in the deformed shape of the cantilever. It is argued that this phenomenon can take place even when the AFM-based tool is operated in the so-called force-controlled mode. The study involves the refined theoretical analysis of cantilever probe bending, the analysis of experimental signals monitored during the backward and forward AFM tip-based machining and the inspection of the topography of produced grooves