High-Precision Tribometer for Studies of Adhesive Contacts.

Herein, we describe the design of a laboratory setup operating as a high-precision tribometer. The whole design procedure is presented, starting with a concept, followed by the creation of an exact 3D model and final assembly of all functional parts. The functional idea of the setup is based on a previously designed device that was used to perform more simple tasks. A series of experiments revealed certain disadvantages of the initial setup, for which pertinent solutions were found and implemented. Processing and correction of the data obtained from the device are demonstrated with an example involving backlash and signal drift errors. Correction of both linear and non-linear signal drift errors is considered. We also show that, depending on the research interests, the developed equipment can be further modified by alternating its peripheral parts without changing the main frame of the device.

Johnson-Kendall-Roberts adhesive contact for a toroidal indenter.

The unilateral axisymmetric frictionless adhesive contact problem for a toroidal indenter and an elastic half-space is considered in the framework of the Johnson-Kendall-Roberts theory. In the case of a semi-fixed annular contact area, when one of the contact radii is fixed, while the other varies during indentation, we obtain the asymptotic solution of the adhesive contact problem based on the solution of the corresponding unilateral non-adhesive contact problem. In particular, the adhesive contact problem for Barber's concave indenter is considered in detail. In the case when both contact radii are variable, we construct the leading-order asymptotic solution for a narrow annular contact area. It is found that for a v-shaped generalized toroidal indenter, the pull-off force is independent of the elastic properties of the indented solid.

Partial-slip frictional response of rough surfaces.

If two elastic bodies with rough surfaces are first pressed against each other and then loaded tangentially, sliding will occur at the boundary of the contact area while the inner parts may still stick. With increasing tangential force, the sliding parts will expand while the sticking parts shrink and finally vanish. In this paper, we study the fractions of the contact area, tangential force and tangential stiffness, associated with the sticking portion of the contact area, as a function of the total applied tangential force up to the onset of full sliding. For the numerical analysis randomly rough, fractal surfaces are used, with the Hurst exponent H ranging from 0.1 to 0.9. Numerical simulations by boundary element method are compared with an analytical analysis in the framework of the Greenwood and Williamson (GW) model. In both cases, a universal linear dependency between the real contact area fraction in stick condition and the applied tangential force is found, regardless of the Hurst exponent of the rough surfaces. Regarding the dependence of the differential tangential stiffness on the tangential force, a linear relation is found in the GW case. For randomly rough surfaces, a nonlinear relation depending on H is derived.

Contact stiffness of randomly rough surfaces.

We investigate the contact stiffness of an elastic half-space and a rigid indenter with randomly rough surface having a power spectrum C2D(q)proportional q(-2H-2), where q is the wave vector. The range of H[symbol: see text] is studied covering a wide range of roughness types from white noise to smooth single asperities. At low forces, the contact stiffness is in all cases a power law function of the normal force with an exponent α. For H > 2, the simple Hertzian behavior is observed . In the range of 0 < H < 2, the Pohrt-Popov behavior is valid (). For H < 0, a power law with a constant power of approximately 0.9 is observed, while the exact value depends on the number of modes used to produce the rough surface. Interpretation of the three regions is given both in the frame of the three dimensional contact mechanics and the method of dimensionality reduction (MDR). The influence of the long wavelength roll-off is investigated and discussed.

Normal contact stiffness of elastic solids with fractal rough surfaces for one- and three-dimensional systems.

It was shown earlier that some classes of three-dimensional contact problems can be mapped onto one-dimensional systems without loss of essential macroscopic information, thus allowing for immense acceleration of numerical simulations. The validity of this method of reduction of dimensionality has been strictly proven for contact of any axisymmetric bodies, both with and without adhesion. In [T. Geike and V. L. Popov, Phys. Rev. E 76, 036710 (2007)], it was shown that this method is valid "with empirical accuracy" for the simulation of contacts between randomly rough surfaces. In the present paper, we compare exact calculations of contact stiffness between elastic bodies with fractal rough surfaces (carried out by means of the boundary element method) with results of the corresponding one-dimensional model. Both calculations independently predict the contact stiffness as a function of the applied normal force to be a power law, with the exponent varying from 0.50 to 0.85, depending on the fractal dimension. The results strongly support the application of the method of reduction of dimensionality to a general class of randomly rough surfaces. The mapping onto a one-dimensional system drastically decreases the computation time.

Normal contact stiffness of elastic solids with fractal rough surfaces.

Using the boundary element method, we calculate the normal interfacial stiffness and constriction resistance of two elastic bodies with randomly rough surfaces and varying fractal dimensions. The contact stiffness as a function of the applied normal force can be approximated by a power law, with an exponent varying from 0.51 to 0.77 for fractal dimensions varying from 2 to 3.