Adhesive Contact Behavior Research Articles

Axisymmetric Indentations of an Elastic Half-Space With Tensed Surface/Membrane in the Johnson–Kendall–Roberts Adhesive Approximation

Abstract Owing to the significant effects of adhesive force and surface/membrane tension, the classical contact models often fail to describe the indentation responses of soft materials and biological systems. This work addresses the axisymmetric indentation of an elastic substrate with constant surface/membrane tension by a spherical, conical, or cylindrical flat indenter in the Johnson–Kendall–Roberts adhesive approximation. On the basis of non-adhesive contact solutions accounting for the surface/membrane tension effect, explicit expressions for the external load and depth with respect to the contact radius are derived for the adhesive contact cases, which act as the theoretical fundamental for the accurate analysis of indentation tests. Despite using different correction functions, the results for spherical indentation are consistent with the solution of previous studies. It is found that the role of surface/membrane tension in the adhesive contact behavior is controlled by a dimensionless parameter. As the parameter gets larger, the pull-off force and the contact size at zero-external load for spherical and conical indentations are smaller, whereas the pull-off force for cylindrical flat indentation is higher.

Viscoelastic adhesive contact between a sphere and a two-dimensional nano-wavy surface

For contact involving viscoelastic materials with nanoscale roughness surfaces, both the viscoelasticity and the adhesive interaction play significant roles, and an in-depth understanding of this viscoelastic adhesive contact behavior is essential. This paper establishes a numerical viscoelastic adhesive contact model between a smooth sphere and a two-dimensional nano-wavy surface based on the Derjaguin approximation and elastic–viscoelastic correspondence principle, and the wavy surface is considered by introducing the height distribution into the surface gap equation. Influences of approach speed, contact position and wavy surface parameters on the viscoelastic adhesive contact behavior are quantitatively analyzed. It is shown that the viscoelasticity can be ignored at large approach speed, while when the speed is small, viscoelasticity significantly increases the maximum contact area and pull-off force. Variations of maximum contact area and pull-off force with contact position or wavy surface parameters are not completely consistent, where the contact positions with relatively large maximum contact area may exhibit small pull-off force. The pull-off force changes monotonically with increasing wavy parameter, while the maximum contact area changes nonmonotonically. This study can offer guidance for the application of wavy surface in viscoelastic adhesion regulation, and provide basis for the surface design and parameter determination of viscoelastic materials.

Adhesive contact behavior between piezoelectric and elastic materials with a mismatch strain

Adhesive contact behavior between piezoelectric and elastic materials with a mismatch strain

Adhesive behavior of transversely isotropic piezoelectric bimaterials

The adhesive contact behavior between two dissimilar transversely isotropic piezoelectric cylinders is investigated in this paper. The effect of adhesion on the contact behavior between piezoelectric bimaterials is considered within the framework of the non-slipping JKR model, which takes the coupling effect between the tangential and normal tractions inside the contact region into account. The explicit analytical solutions of stress and electric displacement fields within the contact region are obtained by solving the resulting coupling singular integral equations with the analytical function theory. The relationship between the contact size and external loadings are established by adopting the Griffith energy balance criterion at the edges of the contact zone. It is found that different types of piezoelectric bimaterials show the same adhesive contact behaviors, which is different from the case of a single layer piezoelectric material. The result obtained from the present paper should be helpful for the design of micro-electro-mechanical systems (MEMS) devices involving multi-layered smart structures.

Tuning nanoscale adhesive contact behavior to a near ideal Hertzian state via graphene coverage

We carry out molecular statics (MS) simulations to study the indentation process of Pt (111) surfaces using an indenter with the radius of 5–20 nm. The substrate and indenter surfaces are either bare or graphene-covered. Our simulations show that the influence of the adhesion between the bare substrate and indenter tip can be significantly reduced by decreasing the adhesion strength and adhesion range between the atoms on the substrate and indenter, or by enhancing the substrate stiffness. Our results suggest that the elastic response of the substrate exhibits weaker adhesion after the coating of graphene layers on either side of the contacting interface, which is attributed to the weak interaction between the graphene layers. Based on these principles obtained for the bare substrate, the nanoscale contact behavior of the substrate can be tuned into a near-ideal Hertzian state by increasing the number of graphene layers, applying pre-strains to graphene on substrate, or using large indenters. Therefore, even for strong adhesion between tip, graphene, and substrate, mechanical properties of substrate can be determined by nanoindentation using graphene coverage. Our research provides theoretical guidance for designing adhesion-less coatings for AFM probes and MEMS/NEMS systems.

Effect of surface tension on the behavior of adhesive contact based on Maugis‒Dugdale model

This present study reconsiders the effect of surface tension on the behavior of adhesive contact between a rigid sphere and an elastic half-plane, in which the adhesive interactions are supposed to follow the Dugdale laws. The adhesive contact issue is transformed into two inter coupled non-linear integral equations which are governed by two parameters: λ (Maugis adhesion parameter) and S (elastocapillary number). By means of iteration method, numeric results are obtained. Analogous to the traditional Maugis-Dugdale (M-D) model, the results provide transition of the pull-off force between JKR and DMT type contact models through the Maugis adhesion parameter λ with a fixed parameter S. On the other hand, with a fixed adhesion parameter λ, we also present the transitions of the pull-off force between four extreme models, named M-D, JKR, Bradley models and Young–Dupre equation, through adjustment of the parameter S. Finally, we find the uniformity and discontinuity of the pressure distribution are affected by the combination of three factors: applied load P, adhesion parameter λ and elastocapillary number S.

The two-dimensional adhesive contact problem in the theory of couple stress elasticity

The adhesive contact problem of a half-space indented by a rigid cylindrical punch in the theory of couple-stress elasticity is investigated. Both the size effect and adhesion are considered to analyze the two-dimensional frictionless contact problem. The method of Mindlin’s stress function and the technology of Fourier transform are applied to reduce the mixed boundary value problem to the singular integral equations. Efficient computational techniques is used to obtain the influence of the size effect and adhesion parameter on the adhesive contact behavior. Results indicated that the size effect play an important role in contact with adhesion and can help understanding the mechanism of adhesion.

Surface effect in nanoscale adhesive contact

ABSTRACT Using the well-known Lennard–Jones potential and a recently proposed surface energy density-based elastic theory, we analyze the adhesive contact behavior between a rigid spherical nano-indenter and an elastic half-space in this paper. With the help of Newton’s method of iterations and arc-length continuation algorithm, both contact pressure and normal displacement at the indented surface are obtained numerically, based on which the load–approach curves are further achieved. It is found that the surface effect could be characterized by only one intrinsic length, i.e., the ratio of bulk surface energy density to shear modulus of the indented material. Comparison of the results with or without surface effect shows that the surface effect leads to a smaller pull-off force. Moreover, for the case of a zero-external loading, the corresponding approaches become smaller than the classical predictions, which qualitatively agree with the existing experimental findings. This indicates the elastic substrate becomes hardened due to the surface effect. All the study should have contributions to the deep understanding of surface effect on nanoscale adhesive contact behaviors.

An investigation on the behavior of anisothermal adhesive contact based on Maugis–Dugdale model

The present study considers the effect of heat conduction on the behavior of adhesive contact between two elastic spheres of different temperatures, where the adhesion forces are supposed to follow the Dugdale model. The thermal adhesive contact issue is transformed into two intercoupled nonlinear integral equations which are governed by two parameters: λ (adhesion parameter) and M. By means of iteration method, numeric results are obtained. Analogous to the traditional Maugis-Dugdale (M-D) model, the results provide transition of the pull-off force between JKR and DMT type contact models through the adjustment of the adhesion parameter λ with fixed parameter M. On the other hand, with a fixed adhesion parameter λ, it is indicated that the shape of the force-contact radius curve and the pull-off force are dependent on the parameter M. Finally, we find the uniformity of the pressure distribution is affected by the applied load F and adhesion parameter λ.

Investigations of the Adhesive Contact Behavior of Elastic Layered Media With Surface Roughness

A deterministic adhesive model for the contact between an elastic layered medium with surface roughness and a smooth elastic microsphere was developed on the basis of the Lennard–Jones surface force law. Through numerical simulations, the adhesive contact behavior of the layered medium with the measured three-dimensional (3D) surface topography was comparatively analyzed with that of the homogeneous medium. Furthermore, the contact characteristics of the layered medium with pre-assigned roughness parameters were investigated with the aid of a computer-generated technique for simulating surface roughness. Results showed that the pull-off force for the contact problem involving rough surfaces was influenced by the contact location, and the average value for the contact between an alumina (SiO2) microsphere and a diamond-like carbon/silicon (DLC/Si)-layered medium was smaller than that for the contact between a SiO2 microsphere and a Si homogeneous half-space. In addition, the effect of the diamond-like carbon (DLC) layer on reducing adhesion was smaller than that of the surface roughness. Finally, the average pull-off force for a DLC/Si-layered medium with computer-generated surface roughness rapidly decreased; however, it eventually became almost unchangeable with the increase in the root-mean-square (RMS) deviation.

The Investigation on Adhesive Contact Problem of Gradient Piezoelectric Coating under Insulating Punch

This paper considers the two-dimensional adhesive contact problem for a rigid insulating cylindrical punch acting on a gradient piezoelectric coating bonded to half-space.It is assumed that the material parameters of functionally gradient piezoelectric materials vary exponentially along the thickness direction.The adhesion between the punch and the contact surface of the coating is described according to the adhesion Model given by Maugis. By using the Fourier integral transform, the adhesive contact problem of gradient piezoelectric coatings is reduced to singular integral equations. the numerical method is applied to solve the singular integral equations with Cauthy kernel.The numerical results show that both non-homogeneous parameters of gradient piezoelectric material and adhesion effect have significiant impact on the adhesive contact behavior of gradient piezoelectric coating.

Two-Dimensional Adhesive Contact Problem for Graded Coating Based on a New Multi-Layer Model

In this paper, the contact problem with adhesion for graded coating indented by a cylindrical indenter is considered. A multi-layered model is developed to model functionally graded material (FGM) coating with arbitrarily varying elastic modulus. By using the transfer matrix method and Fourier integral transform technique, the problem is reduced to a Cauchy singular integral equation. The numerical calculation is conducted to achieve the effect of the gradient index of the FGM coating and the adhesive parameter on the pull-off force and the relation between the normal load and the maximum indentation depth. The results show that the gradient index of coating can effectively change the behavior of adhesive contact.

Effect of surface tension on the behavior of adhesive contact based on Lennard–Jones potential law

The present study explores the effect of surface tension on adhesive contact behavior where the adhesion is interpreted by long-range intermolecular forces. The adhesive contact is analyzed using the equivalent system of a rigid sphere and an elastic half space covered by a membrane with surface tension. The long-range intermolecular forces are modeled with the Lennard‒Jones (L‒J) potential law. The current adhesive contact issue can be represented by a nonlinear integral equation, which can be solved by Newton‒Raphson method. In contrast to previous studies which consider intermolecular forces as short-range, the present study reveals more details of the features of adhesive contact with surface tension, in terms of jump instabilities, pull-off forces, pressure distribution within the contact area, etc. The transition of the pull-off force is not only consistent with previous studies, but also presents some new interesting characteristics in the current situation.

The effect of bottom boundary condition type on the behavior of adhesive contact of spherical probe on an elastic film

This study presents an investigation on the behavior of adhesive contact between a rigid sphere and an elastic film which is either perfectly bonded (case I) or in frictionless contact (case II) with a rigid substrate. By using linear fracture mechanics, we formulate an convenient semi-analytical approach to develop relations between the applied force, penetration depth and contact radius. Finite element analysis (FEA) is used to verify the relationships. Our results reveal that the interfacial boundary conditions between the film and substrate have distinct effects on the adhesive contact behavior between the sphere and the film. The aim of the present study is to provide an instructive inspiration for controlling adhesion strength of the thin film subject to adhesive contact.

The Influence of Velocity Variation on the Adhesive Contact Behavior and the Deformation of Substrate Based on Molecular Dynamics Method

The contact behavior between indenter and single crystal copper substrate is performed to investigate based on EAM and Morse potentials and Verlet algorithm. Effects of different velocities on the contact behavior and substrate deformation are compared and analyzed. The results show that the single crystal copper material’s resist deformation level is limited by low velocity, and more dislocated atoms were accumulated under the direction of indenter moving in higher indenting velocity. During sliding process, lager chip volume is produced in front of the indenter as the sliding speed or sliding distance increases. The dislocated band in basis lies at the angle of 45 degrees with the direction of indenter moving in indenting and sliding process. Furthermore, the contact force, friction force and normal force increase with the rising of speed. On the contrary, the friction coefficient decrease gradually with higher sliding speed.

The study of anisotropic behavior of nano-adhesive contact by multiscale simulation

Quasi-continuum method is applied to investigate the anisotropic behavior of nanoscale adhesive contact when a Ni tip indents into and then pulls out of single crystal Cu substrates. For 1¯10 substrate, the Ni tip exhibits excellent brittle behavior. Interface fracture is mainly characterized by atomic rearrangement since few slip planes are available. For (001) substrate, Shockley partials and deformation twins are both observed during the indentation process. Interface fracture is dominated by atomic slip which leads to the ductile fracture of the interface. As for (111) substrate, the nanocontact leads to significant plastic deformation of the substrate and the piling up of Cu atoms as well as the wetting of the Ni tip. This is because the Ni tip and Cu substrate share the same crystal orientations and the misfit effect between them is less evident. These anisotropic adhesive behaviors illustrate the importance of choosing a proper crystal contact surface to prevent wearing in micro-electro-mechanical systems. Distinctive nanocontact-induced deformation mechanisms and fracture mechanisms are revealed and analyzed. We found that available slip systems should be paid enough attention to for adhesive contact at nanoscale. It is recommended that adhesive contact between the Ni tip and Cu substrate with the same orientations should be avoided in order to reduce wearing. Some of the results found in our work are also validated by similar or related experiments by other researchers.

Effective macroscopic adhesive contact behavior induced by small surface roughness

In this paper we study a model contact problem involving adhesive elastic frictionless contact between rough surfaces. The problem's most notable feature is that it captures the phenomenon of depth-dependent-hysteresis (DDH) (e.g., see Kesari et al., 2010), which refers to the observation of different contact forces during the loading and unloading stages of a contact experiment. We specifically study contact between a rigid axi-symmetric punch and an elastic half-space. The roughness is represented as arbitrary periodic undulations in the punch's radial profile. These undulations induce multiple equilibrium contact regions between the bodies at each indentation-depth. Assuming that the system evolves so as to minimize its potential energy, we show that different equilibrium contact regions are selected during the loading and unloading stages at each indentation-depth, giving rise to DDH. When the period and amplitude of our model's roughness is reduced, we show that the evolution of the contact force and radius with the indentation-depth can be approximated with simpler curves, the effective macroscopic behavior, which we compute. Remarkably, the effective behavior depends solely on the amplitude and period of the model's roughness. The effective behavior is useful for estimating material properties from contact experiments displaying DDH. We show one such example here. Using the effective behavior for a particular roughness model (sinusoidal) we analyze the energy loss during a loading/unloading cycle, finding that roughness can toughen the interface. We also estimate the energy barriers between the different equilibrium contact regions at a fixed indentation-depth, which can be used to assess the importance of ambient energy fluctuations on DDH.

A generalized JKR-model for two-dimensional adhesive contact of transversely isotropic piezoelectric half-space

The aim of the present paper is to investigate the adhesive behavior between a transversely isotropic piezoelectric half-space and a cylinder punch subjected to combined mechanical and electric loads under plane-strain condition. The effect of adhesion is described by using a generalized JKR-model which can account for the non-slip condition in the contact regions. Analytical function theory is employed to find the solution of the resulting singular integral equations. Our analysis shows that the adhesive contact behavior for different types of piezoelectric materials may be quite different. The results obtained in this paper may be helpful to understand the contact mechanics of piezoelectric materials at micro-scale.

Micro-scale adhesive contact of a spherical rigid punch on a piezoelectric half-space

The micro-scale adhesive contact behavior of a spherical rigid punch on a piezoelectric half-space was investigated in this paper. The governing equations describing the piezoelectric adhesive contact behavior were obtained by using the Maugis-Dugdale (M-D) elastic adhesive contact theory [Maugis D. Adhesion of spheres: the JKR-DMT transition using a Dugdale model. J Colloid Interf Sci 1992;150(1):243–69]. The solutions for indentation of piezoelectric materials and for elastic adhesive contact can be reduced from the present results in the absence of adhesion effect and piezoelectric effect, respectively. The effect of the electric load on the adhesive contact behavior was analyzed in detail. It was shown that the piezoelectric effect has a significant effect on the adhesive contact behavior of piezoelectric materials. The obtained results will be helpful to understand the micro-indentation properties of piezoelectric materials and piezoelectric composites.

Adhesive contact based on the Lennard-Jones potential: a correction to the value of the equilibrium distance as used in the potential.

A Lennard-Jones type surface law is commonly used in adhesive contact modeling; however, one of its parameters, namely the equilibrium distance z0, is not well defined. In this paper, a self-consistent method is used to derive the Lennard-Jones surface law from the interatomic Lennard-Jones potential. The parameters of the surface law are directly related to the material lattice parameter and surface energy, and the equilibrium distance z0 values are obtained for various materials. The effect of using the z0 proposed in the present work is demonstrated via the study of adhesive contact behavior for a single sphere and a flat surface, as well as the contact between planar rough surfaces. For pull-off force prediction of the contact between a single sphere and a flat surface, the error of using the z0 suggested in previous studies could be as large as 10% at intermediate ranges of a dimensionless adhesion parameter. For the contact between planar rough surfaces, the error of using the previously proposed z0 is larger for smoother cases, and the prediction of pull-off force could be different by as much as a factor of 5.