On a recent stickiness criterion using a very simple generalization of DMT theory of adhesion

In the contact of rough surfaces, contact occurs on smaller and smaller scales, the well-known Tabor adhesion parameter decreases and the so-called Derjaguin–Muller–Toporov (DMT) theory is the appropriate limit. Fuller and Tabor developed 40 years ago a model based on asperities and JKR theory, and more recently the author developed an asperity theory using asperities and DMT theory in the form given by Maugis. Both lead to adhesion parameters which do not depend on the range of attractive forces, in contrast to the parameter recently suggested by Pastewka and Robbins (PNAS, 111(9), 3298–3303, 2014). As it is well known from random process theory that contact of rough surfaces can be described reasonably well by asperity summits at least for low bandwidths, the Pastewka–Robbins DMT model and stickiness criterion should correspond in the limit case of a spherical contact. We therefore consider this limit case, and show that Pastewka–Robbins DMT model introduces a dependence on range of attractive forces, or on Tabor parameter, which is not correct for the sphere, and therefore may be incorrect also in general.     

Numerical investigation of indentation tests on a transversely isotropic elastic material by power-law shaped axisymmetric indenters

Nowadays, there exist many well-known classical models of frictionless adhesive contact including the Johnson–Kendall–Roberts (JKR) model, the Derjaguin–Muller–Toporov (DMT) model, and the Maugis solution for the JKR-type-to-DMT-type transition regimes. These models are very helpful for studying molecular adhesion between two contacting linearly elastic isotropic spherical bodies. However, in experimental studies, such as nanoindentation tests, the shapes of the indenters are often more general than the spherical or flat ones. Moreover, very often, the materials to be tested are anisotropic. A special case of anisotropy is transverse isotropy, which contains a plane of isotropy, implying that the material can be rotated with respect to the loading direction about one axis without measurable effect on the material’s response. In this paper, numerical studies on JKR-type frictionless adhesive contact between power-law shaped indenters and transversely isotropic materials are presented. It shows that the formulae for numerical simulations of JKR-type frictionless adhesive contact for transversely isotropic materials have the same mathematical form as the corresponding formulae for isotropic materials, except that the effective elastic contact modulus has different expression for different materials. The DMT-type and JKR-type-to-DMT-type transition regimes have been explored by conducting the simulations using smaller values of Tabor parameters. The good agreement between numerical simulation results and existing analytical solutions shows that this numerical simulation method can be extended to simulate indentation tests using indenters of arbitrary shapes.     

A Novel Test for the Appraisal of Solid/Solid Interfacial Interactions

The Johnson, Kendall and Roberts (JKR) technique has been used with considerable success for assessing solid/solid interfacial interactions over the past 25 years or so. Nevertheless, the contact zone between the two spherical solids is often small and the energy of adhesion scales with the cube of the contact radius (at low load), thus potentially magnifying errors in adhesion assessment. The theoretical aspects of a novel technique are presented here, in which a hollow, slightly inflated, spherical membrane replaces a full sphere, and is placed in contact with a flat rigid solid. A judicious choice of experimental conditions should lead to increased contact radius and the energy of adhesion scales with its square (at low load), thus reducing possible errors. An added advantage is that the effective elasticity of the sphere depends on internal gas pressure. Thus surface and bulk effects are decoupled.     

Effect of surface cavities on static and dynamic adhesion to an elastomer

The analysis of contact between two spherical surfaces introduced in the 19th century by Hertz was modified some 30 years ago by Johnson, Kendall and Roberts (JKR) to allow for adhesion between the two solids. Since then, the technique has been much used with various systems employing sphere/sphere and sphere/flat solid (sphere of infinite radius) geometry. We consider here the geometry in which one solid has a negative radius of curvature: a spherical solid contacts the second solid in a shallow spherical cavity. It is thus shown that the contact area of a rigid sphere on the smooth surface of an elastomer depends markedly on the flatness of the latter. Any neglect of cavities of large radius of curvature leads to an overestimate of the value of the intrinsic adhesion of Dupré, W₀, and falsifies interpretation of separation kinetics under (variable) applied load. By allowing for the negaive radius of curvature of the cavities in the rubber, correction can be made leading to coherent values of W₀ and debonding kinetics. The analysis may be of use for the assessment of flatness of surfaces and the increase in contact radius may prove beneficial for improving the precision of static adhesion tests.     

A Novel Test for the Appraisal of Solid/Solid Interfacial Interactions

The Johnson, Kendall and Roberts (JKR) technique has been used with considerable success for assessing solid/solid interfacial interactions over the past 25 years or so. Nevertheless, the contact zone between the two spherical solids is often small and the energy of adhesion scales with the cube of the contact radius (at low load), thus potentially magnifying errors in adhesion assessment. The theoretical aspects of a novel technique are presented here, in which a hollow, slightly inflated, spherical membrane replaces a full sphere, and is placed in contact with a flat rigid solid. A judicious choice of experimental conditions should lead to increased contact radius and the energy of adhesion scales with its square (at low load), thus reducing possible errors. An added advantage is that the effective elasticity of the sphere depends on internal gas pressure. Thus surface and bulk effects are decoupled.     

Numerical Analyses on the Adhesive Contact between a Sphere and a Longitudinal Wavy Surface

The adhesive contact between a sphere and a longitudinal wavy surface is simulated numerically. A modified simulation method is proposed using the Newton BI-CGSTAB method in a rectangular coordinate. The effective Tabor parameter is proposed. It is found that when the amplitude of the wavy surface is larger, the contact area is smaller and the pull-off force is smaller. Jump-in from noncontact phenomena occurs when the Tabor parameter is large. Jumping from one ridge to the next ridge occurs when the effect of the Tabor parameter is large and the amplitude of the wavy surface is not too small. Jumping from noncontact to full contact is affected by the amplitude and the wave number of the wavy surface and is also affected by the Tabor parameter.     

Adhesive contact and kinetics of adherence between a rigid sphere and an elastomeric solid

The adhesive contact of rigid spherical punches on viscoelastic solids is studied using a solution of the axisymmetric Boussinesq problem, assuming an integral constant to be non-zero. The JKR theory, based on the energy balance, is then found. The stress tensor is computed by superposition of the Hertzian stress tensor and the flat punch stress tensor, and is plotted for two particular cases: zero and minimum negative applied loads. It is shown that, whatever the load, the existence of molecular attraction forces provokes infinite stresses at the edge of the contact area.Fracture mechanics concepts are used to study the kinetics of adherence. It is shown that the general equation used allows the kinetics of interfacial crack propagation to be predicted in all types of test: fixed load; displacement; loading velocity; and crosshead velocity. Finally, the problem of the tackiness of elastomers and the dwell time effect on adherence are examined.The experimental results collected in this review have been obtained for the contact surface glass ball/polyurethane. All the theoretical predictions are verified with a reproducibility of better than 2%.     

The Jump-to-Contact Distance in Atomic Force Microscopy Measurement

The jump-to-contact phenomenon of atomic force microscopy measurement is investigated. The force-approach relation for the adhesive contact based on the Lennard-Jones potential with the Derjaguin approximation is analyzed. For a small Tabor parameter, the force-approach relation is similar to that with the van der Waals force between two rigid spheres. For a large Tabor parameter, the force-approach relation is similar to that with the van der Waals force between two deformable spheres. Empirical formulas for the approaching part of the force-approach curve are proposed. The jump-to-contact distance can be obtained by using the semi-empirical formulas. The jump-to-contact distance for a fixed grips device and for large Tabor parameter is also obtained.     

Adhesion Map of Spheres: Effects of Curved Contact Interface and Surface Interaction Outside Contact Region

In this work three dimensionless parameters are introduced in the debate concerning hard contact models. These parameters are related to the overall adhesive contact area, curved surface contribution and surface interaction forces outside the contact region. With the variations of these three parameters, the relations and transitions between the different hard contact models such as Hertz, Bradley, Johnson–Kendall–Roberts (JKR), Derjaguin–Muller–Toporov (DMT) and Maugis–Dugdale (MD) models are presented in a systematic way. The combination of the three parameters provides a new hybrid model. The influence of these three parameters on the contact between spheres has been studied. By analyzing the pressure profiles of contact region, two new instability jumps are proposed. The instability jumps together with the three parameters are used to explain some recent experimental and numerical observations which deviate more or less from those predicated by the classical hard contact models.     

Model of inertial spreading and imbibition of a liquid drop on a capillary plate

We outline a low‐order Lagrangian model for the inertial dynamics of spreading and imbibition of a spherical liquid cap on a plane featuring independent cylindrical capillaries without gravity. The analysis predicts the relative roles of radial and axial kinetic energy, reveals the critical Laplace number beyond which the drop oscillates, and attributes the exponent of the initial power‐law for contact patch radius vs. time to the form of capillary potential energy just after the liquid sphere touches the plate. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5474–5481, 2017     

Underwater Adhesion Measurements using the JKR Technique

The JKR (Johnson–Kendall–Roberts) method of contact mechanics has been widely utilized for measuring adhesion properties between a deformable elastomeric lens and various materials. Such measurements are normally performed in air. We attempted to verify whether the JKR technique could be practical for evaluating adhesion properties under water. After modifying the common JKR apparatus to be suitable for underwater studies, two types of hydrophobic coating systems, silicone/silicone and silicone/silanized silicon wafer, were used. The work of adhesion (W _A ) values obtained from loading measurements and under zero load were found to be slightly smaller than the values estimated using surface energies and contact angles of water formed on the surfaces of these coatings. One possible cause for the slightly smaller values could be contamination/alteration of the coating surface properties upon immersion in water. The results suggested that, with proper control of experimental conditions, the JKR technique could be extended to evaluate adhesion properties under water.     

A random process asperity model for adhesion between rough surfaces

A simple asperity model using random process theory is developed in the presence of adhesion, using the Derjaguin, Muller and Toporov model for each individual asperity. A new adhesion parameter is found, which perhaps improves the previous parameter proposed by Fuller and Tabor which assumed identical asperities – the model in all his variants for the radius always gives a finite pull-off force, as in Fuller and Tabor, and contrary to the exponential asperity height distribution, where the force is either always compressive, or always tensile. It is shown that a model with spheres having a radius only dependent on height is a reasonable approximation with respect to models having also a distribution of radius curvatures – the three models differ considerably, as opposed to the adhesionless case where these details did not matter. The important surface parameters in the theory determining the pull-off force are the three moments m₀, m₂, m₄. The asymptotic form of the model at large separation is solved in closed form. As the theoretical pull-off of aligned asperities having the same radius (the average value) increases with the square root of the Nayak bandwidth of the roughness, and as asperity models are known to describe less well the surface at large bandwidth parameters, the limit behavior at large bandwidths remains uncertain.     

An atomic interaction-based adhesive contact model for shallow nanoindentation and nanoscratch

The size effects and physical mechanisms governing small-scale mechanical behavior have important influences on the atomic force microscopy (AFM) measurement. Typically, high surface to volume ratio associated with the small-scale system leads to an appreciable surface force; such that the adhesion of AFM indenter to specimen should be taken into consideration for the nanoindentation and nanoscratch testing. In this work, a finite element method (FEM) model was developed to simulate the adhesive contact between spherical indenter and half-space, in which the adhesive stress is obtained based on the Lennard–Jones potential. Shallow indentation and scratching under different contact conditions were investigated with the proposed FEM model. For adhesion-included cases, the load drop events were found during the indent process, which is demonstrated as a manifestation of local plastic yielding caused by the adhesive stress in contact edge. Adhesion-included scratch load was found sharply increased in the beginning, and rapidly decreased once the scratch displacement reaches to a critical value. Such a predicted stick-slip behavior was interpreted as the rupture of adhesive bond with increasing of scratching distance.     

Study of adhesion forces and mechanical properties of human skin in vivo

In this work we have studied the effect of adhesion forces on the mechanical parameters between a spherical indenter and human skin surface with an indentation test. To take into account the effect of adhesion on Hertzian contact radius, pressure and strain, a theory of adhesion contact, like that of Johnson, Kendall and Roberts (JKR) or Derjaguin, Muller and Toporov (DMT) must be used. These theories correct the errors induced by the adhesion forces on contact parameters. The change in skin surface lipid film during hydration by water is assessed by analyzing the evolution of the adhesion energy and skin stiffness.     

A cohesive zone model for the adhesion of cylinders

A cohesive zone model is developed to describe the adhesion between long cylinders in contact, thus extending the work of Maugis, who considered the adhesion of spheres. A parameter λ is shown to govern the range of applicability of the different contact theories, and an explicit condition is given for the use of the Johnson-Kendall-Roberts (JKR) approach. An interesting result is that unlike the situation in the three-dimensional problem, the Derjaguin-Muller-Toporov (DMT) solution is not approached as λ → 0. Instead, it is when λ is of order 1 that an approximation similar to the DMT theory can be used.     

Numerical Simulation of the Adhesive Contact between a Slightly Wavy Surface and a Half-Space

In this work, the adhesive contact between a slightly wavy surface and a half-space has been investigated numerically. The surface traction was described by the Lennard–Jones potential with the Derjaguin's approximation. The deformation was first obtained by using the formula for the line contact and then, using the arc-length continuation algorithm, the relation between the contact half-width and the total force per asperity was obtained. The pull-off forces were then determined. The numerical simulation presented in this paper can be used to simulate all adhesive contacts ranging from the JKR contact to a rigid contact.     

Effect of work of adhesion on contact of an elastica with a flat surface

The JKR technique has enjoyed widespread usage in recent years for measuring the work of adhesion between an elastomeric cap and substrates of interest. Although some success has been seen in coating the cap with other materials, the requirement that one of the contacting members be elastomeric remains an important feature of the test. The use of a soft structure instead of a soft material for the flexible contact element is proposed here. A flexible strip is bent and then pushed onto a rigid horizontal surface. First a JKR type of analysis is carried out, in which the surface energy is assumed to be proportional to the contact area, and the effects of adhesion are represented by a bending couple at the two separation points of the strip with the surface. For a given work of adhesion, the magnitude of the unknown couple is varied until the total energy is minimized. Then a DMT type of model is considered, with forces acting in the cohesive zone outside of each separation point. The forces are either constant or are linear functions of the gap. For both analyses, the effect of adhesion on the contact length, displacements, and forces is investigated. The results can be applied to determine the work of adhesion, based on measurements taken from such a contact problem.     

Underwater Adhesion Measurements using the JKR Technique

The JKR (Johnson-Kendall-Roberts) method of contact mechanics has been widely utilized for measuring adhesion properties between a deformable elastomeric lens and various materials. Such measurements are normally performed in air. We attempted to verify whether the JKR technique could be practical for evaluating adhesion properties under water. After modifying the common JKR apparatus to be suitable for underwater studies, two types of hydrophobic coating systems, silicone/silicone and silicone/silanized silicon wafer, were used. The work of adhesion (W_A) values obtained from loading measurements and under zero load were found to be slightly smaller than the values estimated using surface energies and contact angles of water formed on the surfaces of these coatings. One possible cause for the slightly smaller values could be contamination/alteration of the coating surface properties upon immersion in water. The results suggested that, with proper control of experimental conditions, the JKR technique could be extended to evaluate adhesion properties under water.     

The Interactions between Spheres and between a Sphere and a Half-Space,Based on the Lennard–Jones Potential

This paper investigates the interaction between two rigid spheres and between a rigid sphere and a rigid half-space, based on the Lennard–Jones potential. By using the divergence theorem and integrating the Lennard–Jones potential over the surfaces, the analytical forms of the surface tractions were obtained, and by integrating the Lennard–Jones potential over the volumes, the analytical form of the total force between two rigid spheres was obtained. The results are compared to those with the Derjaguin approximations and with the parabolic approximation for the sphere profile. The accuracy of the Derjaguin approximation and the parabolic approximation were estimated. The analytical surface traction can be used for the adhesive contact between an elastic body and a rigid one.     

Measurement of nanoindentation properties of polymers considering adhesion effects between AFM sharp indenter and material

Abstract

Nanomechanical properties of polymer samples were calculated using an adhesive contact model appropriate for AFM indentation problems. A series of Polydimethylsiloxane (PDMS) samples were indented by the sharp indenter in the air by using an AFM, and dozens of the force–displacement curves of each sample were obtained. An adhesive contact model suitable for sharp indentation with adhesion was established based on the same assumptions of the JKR model which is only suitable for spherical indentation at small penetration depth. Differences between sharp indentation problems with and without adhesion were discussed, and the limitations of the traditional adhesion model were given. The elastic modulus was obtained by fitting experimental force–displacement curves with theoretical ones, and results were compared to those macroscopic values in literature. The adhesion energy between the indenter and the sample surface was accurately calculated using the adhesion model based on the calculated elastic modulus. The influence of the indenter tip angle on the calculation results of the elastic modulus was also discussed theoretically. In this study, the mechanical properties of polymer samples were calculated at the nanoscale considering the adhesion effect.