Showing papers on "Contact area published in 2020"

FFT-Based Methods for Computational Contact Mechanics

Abstract: Computational contact mechanics seeks for numerical solutions to contact area, pressure, deformation, and stresses, as well as flash temperature, in response to the interaction of two bodies. The materials of the bodies may be homogeneous or inhomogeneous, isotropic or anisotropic, layered or functionally graded, elastic, elastoplastic, or viscoelastic, and the physical interactions may be subjected to a single field or multiple fields. The contact geometry can be cylindrical, point (circular or elliptical), or nominally flat-to-flat. With reasonable simplifications, the mathematical nature of the relationship between a surface excitation and a body response for an elastic contact problem is either in the form of convolution or correlation, making it possible to formulate and solve the contact problem by means of an efficient Fourier-transform algorithm. The Green function inside such a convolution or correlation form is the fundamental solution to an elementary problem, and if explicitly available, it can be integrated over a region, or an element, to obtain influence coefficients (ICs). Either the problem itself or Green’s functions/ICs can be transformed to a space-related frequency domain, via a Fourier transform algorithm, to a formulate frequency-domain solution for contact problems. This approach converts the original tedious integration operation to multiplication accompanied by Fourier and inverse Fourier transforms, and a great computation efficiency is thus achieved. The conversion between ICs and frequency-response functions facilitate the solutions to problems with no explicit space-domain Green’s function. This paper summarizes different algorithms involving the fast Fourier transform (FFT), developed for different contact problems, error control, as well as solutions to the problems with different contact geometries, different types of materials, and different physical issues. The related works suggest that i) a proper FFT algorithm should be used for each of the cylindrical, point, and nominally flat-flat contact problems, and then ii) the FFT-based algorithms are accurate and efficient. In most cases, the ICs from the 0-order shape function can be applied to achieve satisfactory accuracy and efficiency if i) is guaranteed.

Origin of Friction in Superlubric Graphite Contacts.

Abstract: More than thirty years ago, it was theoretically predicted that friction for incommensurate contacts between atomically smooth, infinite, crystalline materials (e.g., graphite, ${\mathrm{MoS}}_{2}$) is vanishing in the low speed limit, and this corresponding state was called structural superlubricity (SSL). However, experimental validation of this prediction has met challenges, since real contacts always have a finite size, and the overall friction arises not only from the atoms located within the contact area, but also from those at the contact edges which can contribute a finite amount of friction even when the incommensurate area does not. Here, we report, using a novel method, the decoupling of these contributions for the first time. The results obtained from nanoscale to microscale incommensurate contacts of graphite under ambient conditions verify that the average frictional contribution of an inner atom is no more than ${10}^{\ensuremath{-}4}$ that of an atom at the edge. Correspondingly, the total friction force is dominated by friction between the contact edges for contacts up to $10\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ in lateral size. We discuss the physical mechanisms of friction observed in SSL contacts, and provide guidelines for the rational design of large-scale SSL contacts.

Deformation Behaviors of Flat Rolled Wire in Twinning-Induced Plasticity Steel

Abstract: The influence of room temperature flat rolling on microstructure, mechanical properties, and shape change in twinning-induced plasticity (TWIP) steel wire has been investigated to understand the deformation behaviors of flat rolled wire in TWIP steel and to apply TWIP steels to flat rolled wire products. Numerical simulation, hardness test, and EBSD techniques were used to analyze the distribution of strain, mechanical properties, and microstructure of flat rolled TWIP steel wire. The shape of flat rolled TWIP steel wire was also evaluated and compared with plain carbon steels having low strain hardening rate. A very different behavior of hardness, strain, twinning, and KAM value was observed with area of flat rolled wire due to the different stress state and strain with area of wire. The center area had the maximum twin density, KAM value, effective strain, and hardness; whereas free surface area had the minimum values. The hardness inhomogeneity factor (HIF) along the horizontal direction was much higher in comparison with that of the vertical direction. The maximum HIF value occurred at the specific reduction in height, i.e., 27%. This means HIF value gradually increased and then decreased with reduction in height, which is inconsistent with the results of plain carbon steel and Cu wire. The lateral spread and width of contact area of flat rolled TWIP steel wire were lower than those of plain carbon steels, indicating that material properties such as strain hardening exponent are crucial parameters that influence the shape of flat rolled wire products.

Dynamic wetting and heat transfer during droplet impact on bi-phobic wettability-patterned surfaces

Abstract: This paper reports the dynamic wetting behavior and heat transfer characteristics for impinging droplets on heated bi-phobic surfaces (superhydrophobic matrix with hydrophobic spots). A non-patterned superhydrophobic and a sticky hydrophobic surface acted as control wettability surfaces. As expected, differences in wetting and heat transfer dynamics were noticeable for all surfaces with the most pronounced variation during the receding phase. During spreading, inertia from the impact dominated the droplet dynamics, and heat transfer was dominated by convection at the contact line and internal flow. As contact line velocities decreased over time, evaporative cooling at the contact line gained importance, especially for the bi-phobic surfaces, where liquid remained trapped on the hydrophobic spots during receding. These satellite droplets increased the contact area and contact line length and assisted heat transfer and substrate cooling after lift-off of the main droplet. Compared with the hydrophobic surface, the contribution of the contact line heat transfer increased by 17%–27% on the bi-phobic surfaces depending on the location of impact relative to the hydrophobic spots. Nonetheless, the bi-phobic surfaces had a lower total thermal energy transfer. However, compared with the plain superhydrophobic surface, heat transfer was enhanced by 33%–46% by patterning the surface. Depending on the application, a trade-off exists between the different surfaces: the sticky hydrophobic surface provides the best cooling efficiency yet is prone to flooding, whereas the superhydrophobic surface repels the liquid but has poor cooling efficiency. The bi-phobic surfaces provide a middle path with reasonable cooling effectiveness and low flooding probability.

Study on contact fatigue of a wind turbine gear pair considering surface roughness

Abstract: Contact fatigue issues become more and more crucial in gear industry as they significantly affect the reliability and service life of associated mechanical systems such as wind turbine gearboxes. The contact fatigue behavior is mostly determined by the mechanical properties of materials and stress fields near the contact area, which is further influenced by the lubrication and surface roughness due to pressure fluctuations. In this study, a numerical model incorporating the lubrication state, tooth surface roughness, residual stress, and mechanical properties of the material is developed to determine the contact fatigue behavior of a megawatt level wind turbine carburized gear. The variations of the hardness and residual stress along the depth were characterized by the Vickers hardness measurement and X-ray diffraction test, respectively. The elastohydrodynamic lubrication theory was applied to predict the contact pressure distribution, highlighting the influence of the surface roughness that stemed from the original measurement through an optical profiler. The stress histories of the studied material points during a complete contact loading cycle were fast calculated using the discreteconcrete fast Fourier transformation (DC-FFT) method. Modified Dang Van diagrams under different working conditions were determined to estimate the contact fatigue failure risk. The effect of the root mean square (RMS) value of the surface roughness on the failure risk at critical material points were discussed in detail. Results revealed that the surface roughness significantly increases the contact fatigue failure risk within a shallow area, and the maximum risk appears near the surface.

Finite deformations govern the anisotropic shear-induced area reduction of soft elastic contacts

Abstract: Solid contacts involving soft materials are important in mechanical engineering or biomechanics. Experimentally, such contacts have been shown to shrink significantly under shear, an effect which is usually explained using adhesion models. Here we show that quantitative agreement with recent high-load experiments can be obtained, with no adjustable parameter, using a non-adhesive model, provided that finite deformations are taken into account. Analysis of the model uncovers the basic mechanisms underlying anisotropic shear-induced area reduction, local contact lifting being the dominant one. We confirm experimentally the relevance of all those mechanisms, by tracking the shear-induced evolution of tracers inserted close to the surface of a smooth elastomer sphere in contact with a smooth glass plate. Our results suggest that finite deformations are an alternative to adhesion, when interpreting a variety of sheared contact experiments involving soft materials.

Dynamic wetting and heat transfer during droplet impact on heated bi-phobic wettability-patterned surfaces

Abstract: This paper reports the dynamic wetting behavior and heat transfer characteristics for impinging droplets on heated bi-phobic surfaces (superhydrophobic matrix with hydrophobic spots). A non-patterned superhydrophobic and a sticky hydrophobic surface acted as control wettability surfaces. As expected, differences in wetting and heat transfer dynamics were noticeable for all surfaces, with the most pronounced variation during the receding phase. During spreading, inertia from the impact dominated the droplet dynamics and heat transfer was dominated by convection at the contact line and internal flow. As contact line velocities decreased over time, evaporative cooling at the contact line gained importance, especially for the bi-phobic surfaces, where liquid remained trapped on the hydrophobic spots during receding. These satellite droplets increased the contact area and contact line length, and assisted heat transfer and substrate cooling after lift-off of the main droplet. Compared with the hydrophobic surface, the contribution of the contact line heat transfer increased by 17 to 27% on the bi-phobic surfaces, depending on the location of impact relative to the hydrophobic spots. Nonetheless, the bi-phobic surfaces had a lower total thermal energy transfer. However, compared with the plain superhydrophobic surface, heat transfer was enhanced by 33% to 46% by patterning the surface. Depending on the application, a trade-off exists between the different surfaces: the sticky hydrophobic surface provides the best cooling efficiency, yet is prone to flooding, whereas the superhydrophobic surface repels the liquid, but has poor cooling efficiency. The bi-phobic surfaces provide a middle path with reasonable cooling effectiveness and low flooding probability.

Adhesion paradox: Why adhesion is usually not observed for macroscopic solids.

Abstract: The adhesion paradox refers to the observation that for most solid objects no adhesion can be detected when they are separated from a state of molecular contact The adhesion paradox results from surface roughness, and we present experimental and theoretical results that show that adhesion in most cases is "killed" by the longest-wavelength roughness In addition, adhesion experiments between a human finger and a clean glass plate were carried out, and for a dry finger no macroscopic adhesion occurred We suggest that the observed decrease in the contact area with increasing shear force results from nonadhesive finger-glass contact mechanics, involving large deformations of complex layered material

Dynamic fields at the tip of sub-Rayleigh and supershear frictional rupture fronts

Abstract: The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact area in the tip vicinity of supershear ruptures are well described by analytical fracture-mechanics solutions. Fracture-mechanics theory further allows us to determine long sought-after interface properties, such as local fracture energy and frictional peak strength. Both properties are observed to be roughly independent of rupture speed and mode of propagation. However, our study also reveals discrepancies between measurements and analytical solutions that appear as the rupture speed approaches the longitudinal wave speed. Further comparison with dynamic simulations illustrates that, in the supershear propagation regime, transient and geometrical (finite sample thickness) effects cause smaller near-tip strain amplitudes than expected from the fracture-mechanics theory. By showing good quantitative agreement between experiments, simulations and theory over the entire range of possible rupture speeds, we demonstrate that frictional rupture fronts are classic dynamic cracks despite residual friction.

Distributed-Spring Edge-to-Edge Contact Model for Two-Dimensional Discontinuous Deformation Analysis

Abstract: Edge-to-edge contact is a fundamental contact type in blocky systems. In two-dimensional discontinuous deformation analysis (2D DDA, and hereinafter DDA for short), an edge-to-edge contact is transformed into two separated vertex-to-edge contacts by applying two pairs of concentrated springs. Although this simplification facilitates the DDA algorithm, it is not always sufficiently accurate and can even yield irregular results. To solve this problem, a distributed-spring contact model (DSCM) that exerts distributed instead of concentrated forces on contact edges is proposed in this paper for the edge-to-edge contact in DDA. Submatrices for the force matrix and stiffness matrix are obtained by minimizing the potential energy of the distributed contact forces and are incorporated into an improved DDA (I-DDA) code. Four examples are evaluated to illustrate the validations and advantages of the I-DDA. The first example is a single square impacting on a base block. Deformation of the contact area is evaluated by comparison with the theoretical deformation solution, and the results calculated by the I-DDA show better agreement with the analytical solution than the original DDA (O-DDA). The second example is an impact validation, proving that the I-DDA is more adaptable to discrete systems containing blocks of different sizes. Then an example and an experiment about block rebounding are provided, demonstrating that the errors in rotation and rebounding exhibited in the O-DDA results are avoided when using the I-DDA, indicating that the I-DDA provides more realistic solutions. The results of this study suggest that the proposed I-DDA incorporating the DSCM is quite accurate and capable of improving calculation accuracy compared to the O-DDA.

Sliding of adhesive nanoscale polymer contacts

Abstract: The interaction between friction and adhesion is a defining factor of the macroscopic behavior of natural and synthetic soft materials. In this work, the interfacial normal and shear adhesion strength of contacts between nanoscale polymeric fibers were studied using novel experiments aided by micromachined devices by which the critical normal and tangential pull-off forces between individual polyacrylonitrile (PAN) nanofibers with diameters in the range 400 nm – 4 µm were measured in real-time. The work of adhesion under normal detachment, as computed using the Johnson-Kendall-Roberts (JKR) and the Maugis-Dugdale (M-D) models for elastic adhesive contact, was shown to be independent of the nanofiber diameter and comparable to twice the surface energy of bulk PAN. Under shear detachment, peeling of the contact area was calculated using the JKR and the M-D models combined with linear elastic fracture mechanics (LEFM). The M-D model combined with LEFM could predict the experimentally obtained tangential pull-off force instabilities. The interfacial shear adhesion strength is shown to be constant for a broad range of contact radii (25–140 nm) and approximately equal to the material shear stress at yielding. Thus, shear yielding is shown to be the controlling mechanism during shear detachment of individual polymer nanofibers interacting with strong van der Waals adhesion.

The Interaction of Frictional Slip and Adhesion for a Stiff Sphere on a Compliant Substrate

Abstract: How friction affects adhesion is addressed. The problem is considered in the context of a very stiff sphere adhering to a compliant, isotropic, linear elastic substrate, and experiencing adhesion and frictional slip relative to each other. The adhesion is considered to be driven by very large attractive tractions between the sphere and the substrate that can act only at very small distances between them. As a consequence, the adhesion behavior can be represented by the Johnson-Kendall-Roberts model, and this is assumed to prevail also when frictional slip is occurring. Frictional slip is considered to be resisted by a uniform, constant shear traction at the slipping interface, a model that is considered to be valid for small asperities and for compliant elastomers in contact with stiff material. A model for the interaction of friction and adhesion, known to agree with some experimental data, is utilized. This model is due to Johnson, and its adhesion-friction interaction is assumed to stem, upon shrinkage of the contact area, from a postulated reversible energy release associated with frictional slip. This behavior is considered to arise from surface microstructures generated or eliminated by frictional slip, where these microstructures store some elastic strain energy in a reversible manner. The associated reversible energy release rate is derived from the energy exchanges that occur in the system. The Johnson model, and an asymptotic analysis of it for small amounts of frictional slip, is shown to be consistent with the reversible energy release rate that we identify.