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

Estimation of the elastic modulus and the work of adhesion of soft materials using the extended Borodich–Galanov (BG) method and depth sensing indentation

© 2018 Elsevier Ltd The depth-sensing indentation (DSI) is currently one of the main experimental techniques for studying elastic properties of materials of small volumes. Usually DSI tests are performed using sharp pyramidal indenters and the load-displacement curves obtained are used for estimations of elastic moduli of materials, while the curve analysis for these estimations is based on the assumptions of the Hertz contact theory of non-adhesive contact. The Borodich–Galanov (BG) method provides an alternative methodology for estimations of the elastic moduli along with estimations of the work of adhesion of the contacting pair in a single experiment using the experimental DSI data for spherical indenters. The method assumes fitting the experimental points of the load-displacement curves using a dimensionless expression of an appropriate theory of adhesive contact. Earlier numerical simulations showed that the BG method was robust. Here first the original BG method is modified and then its accuracy in the estimation of the reduced elastic modulus is directly tested by comparison with the results of conventional tensile tests. The method modification is twofold: (i) a two-stage fitting of the theoretical DSI dependency to the experimental data is used and (ii) a new objective functional is introduced which minimizes the squared norm of difference between the theoretical curve and the one used in preliminary data fitting. The direct experimental validation of accuracy and robustness of the BG method has two independent steps. First the material properties of polyvinyl siloxane (PVS) are determined from a DSI data by means of the modified BG method; and then the obtained results for the reduced elastic modulus are compared with the results of tensile tests on dumbbell specimens made of the same charge of PVS. Comparison of the results of the two experiments showed that the absolute minimum in relative difference between individual identified values of the reduced elastic modulus in the two experiments was 3.80%; the absolute maximum of the same quantity was 27.38%; the relative difference in averaged values of the reduced elastic modulus varied in the range 16.20.. 17.09% depending on particular settings used during preliminary fitting. Hence, the comparison of the results shows that the experimental values of the elastic modulus obtained by the tensile tests are in good agreement with the results of the extended BG method. Our analysis shows that unaccounted factors and phenomena tend to decrease the difference in the results of the two experiments. Thus, the robustness and accuracy of the proposed extension of the BG method has been directly validated

The 3D nature of a real un-dismantled electrical contact interface

AbstractA 3D contact analysis and modeling suite of tools are developed and introduced in this work. The “3D Contact Map” of an electrical contact interface is presented demonstrating the 3D nature of the contact. It gives information on where the electrical contact spots in a 3D surface profile are located. An X-ray Computer Tomography (CT) technique is used to collect the 3D data to a resolution of around 5μm of a real un-dismantled contact interface for analysis. Previous work by Lalechos and Swingler presented “2D Contact Map” on a 2D contact profile from collected 3D data to a resolution of around 8μm. The main advantages of both 3D and 2D mapping techniques focus on the fact that they are non-destructive and there is no need to dismantle the component of interest. This current work focuses on the 3D mapping technique showing its advantages over the 2D mapping technique. For test purposes, a 16A rated AC single pole switch is scanned after two different current loading tests (0A and 16A). A comparison for the total mechanical area of contact, the number of contact spots and the total contact resistance is conducted using both the 2D and 3D mapping techniques to a resolution of around 5μm

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

Probabilistic, fractal, and related techniques for analysis of engineering surfaces

n many engineering fields surface topography is of crucial importance solving problems offriction and other problems of tribology. A review of mathematical approaches for descriptionof topography of engineering surfaces is presented. Firstly, we give a brief introduction to someof statistical parameters used for description of surface roughness. It is argued that althoughsome of these parameters may be quite useful for specific engineering problems, a set of finitenumbers of parameters cannot describe contact properties of rough surfaces. Then we discussvarious models of surface roughness based on Gaussian models of the asperity heights.The results of application of various modern tests of normality for checking whether thedistribution of the asperity heights is Gaussian, are presented. Further fractal models of rough-ness are discussed. Using fractal parametric-homogeneous (PH) surfaces, it is demonstratedthat tribological properties of a rough surface cannot be characterized just by the fractaldimension of the surface. It is also shown that models based solely on the power-spectraldensity function (PSDF) are quite similar to fractal models and these models do not reflecttribological properties of surfaces. In particular, it is demonstrated that different profiles mayhave the same PSDF

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

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