Solutions of a singular integro-differential equation related to the adhesive contact problems of elasticity theory

Exact and approximate solutions of a some type singular integro-differential equation related to problems of adhesive interaction between elastic thin half-infinite or finite homogeneous patch and elastic plate are investigated. For the patch loaded with vertical forces, there holds a standard model in which vertical elastic displacements are assumed to be constant. Using the theory of analytic functions, integral transforms and orthogonal polynomials, the singular integro-differential equation is reduced to a different boundary value problem of the theory of analytic functions or to an infinite system of linear algebraic equations. Exact or approximate solutions of such problems and asymptotic estimates of normal contact stresses are obtained.

On the stability of spinning asteroids

Most asteroids with a diameter larger than ∼ 300 m are rubble piles i.e. consisting of more than one solid object. All asteroids are rotating but almost all asteroids larger than ∼ 300 m rotate with a period longer than 2.3 hours, which is the critical period where the centrifugal force equals the gravitational force. This indicates that there are nearly no adhesive interaction forces between the asteroid fragments. We show that this is due to the surface roughness of the asteroid particles which reduces the van der Waals interaction between the particles by a factor of 100 for micrometer sized particles and even more for larger particles. We show that surface roughness results in an interaction force which is independent of the size of the particles, in contrast to the linear size dependency expected for particles with smooth surfaces. Thus, two stone fragments of size 100 nm attract each other with the same non-gravitational force as two fragments of size 10 m.

Increasing the Adherence of Metallic Copper to the Surface of Titanium Hydride

Studies have been carried out to increase the adhesive interaction between a titanium hydride substrate and a copper coating. An additional layer containing chemically active groups was created on the surface of the spherical titanium hydride by chemisorption modification. This paper discusses the results of scanning electron microscopy (SEM) using energy-dispersive X-ray spectroscopic mapping of coatings obtained on spherical granules of titanium hydride before and after adsorption modification. The mechanism of interaction of the surface of spherical granules of titanium hydride and titanium sulfate salt is proposed. It is shown that the creation of a chemisorbed layer of hydroxotitanyl and the subsequent electrodeposition of metallic copper contribute to the formation of a multilayer shell of a titanium–copper coating on the surface of spherical titanium hydride granules (≡Ti-O-Cu-) with a high adhesive interaction. Results have been given for an experimental study of the thermal stability of the initial spherical granules of titanium hydride and granules coated with a multilayer titanium-copper shell.

Waves in Flexural Beams with Nonlinear Adhesive Interaction

The paper studies the initial boundary value problem related to the dynamic evolution of an elastic beam interacting with a substrate through an elastic-breakable forcing term. This discontinuous interaction is aimed to model the phenomenon of attachment-detachment of the beam occurring in adhesion phenomena. We prove existence of solutions in energy space and exhibit various counterexamples to uniqueness. Furthermore we characterize some relevant features of the solutions, ruling the main effects of the nonlinearity due to the elastic-breakable term on the dynamical evolution, by proving the linearization property according to Gérard (J Funct Anal 141(1):60–98, 1996) and an asymptotic result pertaining the long time behavior.

Investigations on the Adhesive Contact Behaviors between a Viscoelastic Stamp and a Transferred Element in Microtransfer Printing

Microtransfer printing is a sophisticated technique for the heterogeneous integration of separately fabricated micro/nano-elements into functional systems by virtue of an elastomeric stamp. One important factor influencing the capability of this technique depends on the adhesion between the viscoelastic stamp and the transferred element. To provide theoretical guidance for the control of adhesion in the transfer printing process, a finite element model for the viscoelastic adhesive contact between a polydimethylsiloxane (PDMS) stamp and a spherical transferred element was established, in which the adhesive interaction was modeled by the Lennard-Jones surface force law. Effects of the unloading velocity, preload, and thermodynamic work of adhesion on the adhesion strength, characterized by the pull-off force, were examined for a loading-dwelling-unloading history. Simulation results showed that the unloading path deviated from the loading path due to the viscoelastic property of the PDMS stamp. The pull-off force increased with the unloading velocity, and the increasing ratio was large at first and then became low. Furthermore, the influence of the preload on increasing the pull-off force was more significant under larger unloading velocity than that under smaller unloading velocity. In addition, the pull-off force increased remarkably with the thermodynamic work of adhesion at a fixed maximum approach.

Molecular Dynamics Calculation on the Adhesive Interaction Between the Polytetrafluoroethylene Transfer Film and Iron Surface

During the friction process, the polytetrafluoroethylene (PTFE) adhered on the counterpart surface was known as the PTFE transfer film, which was fundamental to the lubricating performance of the PTFE. However, the adhesive interaction between the iron surface and the adhered PTFE transfer film is still unclear. In present study, molecular dynamics simulations were used to reveal the adhesive interaction between the iron surface and PTFE transfer film. Based on the atomic trajectories obtained through the molecular dynamics, the interaction energy, concentration profile, radial distribution function, and mean square displacement were calculated to analyze the structure of the interface. The negative values of the interaction energy demonstrated the adhesive interaction between the PTFE transfer film and Fe surfaces, resulting in the accumulation of the PTFE transfer film on the Fe surface. Among the (100) (110), and (111) surfaces of α-Fe (110) surface owns the strongest adhesive interaction with the PTFE transfer film. Compared with the original PTFE molecule, the chain broken PTFE, hydroxyl substituted PTFE, and carbonyl substituted PTFE exhibited stronger adhesive interaction with Fe surface. The adhesive interaction between the PTFE transfer film and Fe surfaces was mainly originated from the Fe atoms and the F atoms of the adsorbate PTFE transfer film, which was governed by the van der Waals force. The bonding distance between the Fe atom and the F atom of the adsorbate PTFE transfer film is around 2.8 Å. Moreover, the chain broken of PTFE molecule and the rise of temperature can remarkably increase the mobility of polymer chains in the interface system.

On the problem of tool destruction when obtaining fixed joints of thick-walled aluminum alloy blanks by friction welding with mixing

Introduction. Among the technologies for manufacturing rocket and aircraft bodies, marine vessels, and vehicles, currently, more and more attention is paid to the technology of friction stir welding (FSW). First of all, the use of this technology is necessary where it is required to produce fixed joints of high-strength aluminum alloys. In this case, special attention should be paid to welding thick-walled blanks, as fixed joints with a thickness of 30.0 mm or more are the target products in the rocket-space and aviation industries. At the same time, it is most prone to the formation of defects due to uneven heat distribution throughout the height of the blank. It can lead to a violation of the adhesive interaction between the weld metal and the tool and can even lead to a destruction of the welding tool. The purpose of this work is to reveal regularities of welding tool destruction depending on parameters of friction stir welding process of aluminum alloy AA5056 fixed joints with a thickness of 35.0 mm. Following research methods were used in the work: the obtaining of fixed joints was carried out by friction welding with mixing, the production of samples for research was carried out by electric erosion cutting, the study of samples was carried out using optical metallography methods. Results and discussion. As a result of performed studies, it is revealed that samples of aluminum alloy with a thickness of 35.0 mm have a heterogeneous structure through the height of weld. There are the tool shoulder effect zone and the pin effect zone, in which certain whirling of weld material caused by the presence of grooves on tool surface is distinctly distinguished. It is shown that the zone of shoulders effect is the most exposed to the formation of tunnel-type defects because of low loading force and high welding speeds. It is revealed that tool destruction occurs tangentially to the surface of the tool grooves due to the high tool load and high welding speeds.

Experimental Studies of the Physical and Mechanical Properties of Glued Building Materials Based on Modified Veneer

Today, glued timber products occupy a significant place in the volume of finished products of modern construction and woodworking enterprises. Plywood is one such product. The durability and structural characteristics of plywood depend on the quality of binder, the type of wood and the quality of veneer. The paper explores the technology of ultraviolet treatment of thermally modified birch veneer with subsequent production of waterproof plywood. The results of a study on the influence of the operating parameters of veneer modification on the complex of sorption and strength characteristics of plywood materials are presented. It is established that the combination of thermal modification of wood throughout the entire volume with surface treatment with ultraviolet radiation allows creating glued wood material with increased water resistance and high-quality adhesive interaction.