Non-slipping JKR model for transversely isotropic materials

A generalized plane strain JKR model is established for non-slipping adhesive contact between an elastic transversely isotropic cylinder and a dissimilar elastic transversely isotropic half plane, in which a pulling force acts on the cylinder with the pulling direction at an angle inclined to the contact interface. Full-coupled solutions are obtained through the Griffith energy balance between elastic and surface energies. The analysis shows that, for a special case, i.e., the direction of pulling normal to the contact interface, the full-coupled solution can be approximated by a non-oscillatory one, in which the critical pull-off force, pull-off contact half-width and adhesion strength can be expressed explicitly. For the other cases, i.e., the direction of pulling inclined to the contact interface, tangential tractions have significant effects on the pull-off process, it should be described by an exact full-coupled solution. The elastic anisotropy leads to an orientation-dependent pull-off force and adhesion strength. This study could not only supply an exact solution to the generalized JKR model of transversely isotropic materials, but also suggest a reversible adhesion sensor designed by transversely isotropic materials, such as PZT or fiber-reinforced materials with parallel fibers.     

Mechanics of adhesive contact at the nanoscale: The effect of surface stress

At small length scales, the adhesion and surface effect are of great significance, both of which play important roles in the contact between two elastic solids. In this study, the classical Johnson–Kendall–Roberts (JKR) adhesive contact theory is generalized to the nanoscale at which the surface effect is considered. The influence of the surface stress on the JKR adhesive contact is investigated by employing the non-classical Boussinesq fundamental solutions. It is found that, compared with the classical theory, the pull-off force increases while the critical contact radius decreases as a result of the surface effect. Numerical results show that a relative error of 10% can be introduced in the pull-off force when the indenter radius is less than 20 nm. A detailed theoretical analysis of this interesting phenomenon is presented based on dimensional analysis, and two scaling laws for the adhesive contact at the nanoscale are constructed. These two new scaling laws reveal that the pull-off force is relevant to the elastic properties of the bulk materials, which is different from the classical adhesive contact theory. The present work is promising for the engineering applications in micro-electro-mechanical systems (MEMS) and nano-intelligent devices.     

Non-slipping adhesive contact of a rigid cylinder on an elastic power-law graded half-space

In this paper, adhesive contact of a rigid cylinder on an elastic power-law graded half-space is studied analytically with the theory of weakly singular integral equation and orthogonal polynomial method. Emphasis is placed on the coupling effect between tangential and normal directions which was often neglected in previous works. Our analysis shows that the coupling effect tends to reduce the contact area in the compressive regime. The effect of bending moment on the adhesion behavior is also examined. Like a pull-off force, there also exists a critical bending moment at which the cylinder can be bended apart from the substrate. However, unlike pull-off force, the critical bending moment is insensitive to the gradient exponent of the graded material.     

Bio-inspired mechanics of reversible adhesion: Orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials

Geckos and many insects have evolved elastically anisotropic adhesive tissues with hierarchical structures that allow these animals not only to adhere robustly to rough surfaces but also to detach easily upon movement. In order to improve our understanding of the role of elastic anisotropy in reversible adhesion, here we extend the classical JKR model of adhesive contact mechanics to anisotropic materials. In particular, we consider the plane strain problem of a rigid cylinder in non-slipping adhesive contact with a transversely isotropic elastic half space with the axis of symmetry oriented at an angle inclined to the surface. The cylinder is then subjected to an arbitrarily oriented pulling force. The critical force and contact width at pull-off are calculated as a function of the pulling angle. The analysis shows that elastic anisotropy leads to an orientation-dependent adhesion strength which can vary strongly with the direction of pulling. This study may suggest possible mechanisms by which reversible adhesion devices can be designed for engineering applications.     

Non-slipping adhesive contact between mismatched elastic cylinders

We have recently proposed a generalized JKR model for non-slipping adhesive contact between two elastic spheres subjected to a pair of pulling forces and a mismatch strain (Chen, S., Gao, H., 2006c. Non-slipping adhesive contact between mismatched elastic spheres: a model of adhesion mediated deformation sensor. J. Mech. Phys. Solids 54, 1548–1567). Here we extend this model to adhesion between two mismatched elastic cylinders. The attention is focused on how the mismatch strain affects the contact area and the pull-off force. It is found that there exists a critical mismatch strain at which the contact spontaneously dissociates. The analysis suggests possible mechanisms by which mechanical deformation can affect binding between cells and molecules in biology.     

Complex variable formulation for non-slipping plane strain contact of two elastic solids in the presence of interface mismatch eigenstrain

In this paper, the problems of non-slipping contact, non-slipping adhesive contact, and non-slipping adhesive contact with a stretched substrate are sequentially studied under the plane strain theory. The main results are obtained as follows:(i) The explicit solutions for a kind of singular integrals frequently encountered in contact mechanics (and fracture mechanics) are derived, which enables a comprehensive analysis of non-slipping contacts. (ii) The non-slipping contact problems are formulated in terms of the Kolosov–Muskhelishvili complex potential formulae and their exact solutions are obtained in closed or explicit forms. The relative tangential displacement within a non-slipping contact is found in a compact form. (iii) The spatial derivative of this relative displacement will be referred to in this study as the interface mismatch eigenstrain. Taking into account the interface mismatch eigenstrain, a new non-slipping adhesive contact model is proposed and its solution is obtained. It is shown that the pull-off force and the half-width of the non-slipping adhesive contact are smaller than the corresponding solutions of the JKR model (Johnson et al., 1971). The maximum difference can reach 9% for pull-off force and 17% for pull-off width, respectively. In contrast, the new model may be more accurate in modeling the non-slipping adhesion. (iv) The non-slipping adhesions with a stretch strain (S-strain) imposed to one of contact counterparts are re-examined and the analytical solutions are obtained. The accurate analysis shows that under small values of the S-strain both the natural adhesive contact half-width and the pull-off force may be augmented, but for the larger S-strain values they are always reduced. It is also found that Dundurs’ parameter β may exert a considerable effect on the solution of the pull-off problem under the S-strain.These solutions may be used to study contacts at macro-, micro-, and nano-scales.     

Non-slipping adhesive contact between mismatched elastic spheres: A model of adhesion mediated deformation sensor

A generalized JKR model is established for non-slipping adhesive contact between two dissimilar elastic spheres subjected to a pair of pulling forces and a mismatch strain. We discuss the full elastic solution to the problem as well as the so-called non-oscillatory solution in which tension and shear tractions along the contact interface is decoupled from each other. The model indicates that the mismatch strain has significant effect on the contact area and the pull-off process. Under a finite pulling force, a pair of adhering spheres is predicted to break apart spontaneously at a critical mismatch strain. This study suggests an adhesion mediated deformation sensing mechanism by which cells and molecules can detect mechanical signals in the environment via adhesive interactions.     

Adhesion model of side contact for an extensible elastic fiber

For accurately predicted adhesion laws of fibrillar structures contribute to the rational design of high-performance biomimetic adhesives, an adhesion model is proposed to study the directional adhesion behavior of an extensible elastic fiber that contacts a rigid smooth surface with its side surface under the coupling effect of normal and shear forces, based on the extensible Euler Bernoulli beam theory and the surface energy concept. The deformed configuration of the fiber is obtained analytically, and on the basis of this result, the detachment mode and the normal pull-off force of the fiber for a given shear force are predicted directly. It is also found that, due to the extensibility of the fiber, there exists a maximum normal pull-off force (MNPF) when an optimal shear force is applied. The MNPF will be enhanced by increasing the axial stiffness, and reduced by increasing the bending stiffness. In addition, generating an optimal pre-tension in the adhered part of the fiber will maximize the MNPF. The derived adhesion law is expected to contribute to the optimal design and applications of single-level fibrillar adhesives.     

MEASUREMENT OF ADHESION FORCES IN AIR WITH THE VIBRATION METHOD

The vibration method represents a practical method for the measurement of adhesion forces and adhesion force distributions. This method causes sinusoidally altemating stresses and yields detachment and contact forces between particles and substrate of the same order of magnitude. Alternating contact forces of the vibration method can cause an adhesion force intensification through flattening of asperities. The measuring principle of the vibration method and the analysis of experimental results are described in the article. Normal adhesion forces (pull-off forces) are measured using the vibration method and the colloidal probe technique. The results of both methods show good agreement for small particle sizes. The influence of the detachment force direction is shown by comparing tangential and normal adhesion forces measured using particle reentrainment in a turbulent air flow and the vibration method, respectively. The surface roughness of the substrate and the relative humidity are shown to significantly influence the measured adhesion forces. For the calculation of the adhesion forces, an approach by Rabinovich was combined with approximations of plastic micro asperity flattening. The Rabinovich approach accounts for roughness effects on the van der Waals force by incorporating the rms roughness of the interacting surfaces. rms-values of the particles and substrates were measured with atomic force microscopy at different scanning areas.     

Snap transitions in adhesion

Equilibrium adhesion states are analyzed for nonlinear spherical caps adhered to a rigid substrate under the influence of adhesive tractions that depend on the local separation between the shell and substrate. Transitions between bistable snapped-in and snapped-out configurations are predicted as a function of four nondimensional parameters representing the adhesive energy, the undeformed shell curvature, the range of the adhesive interactions, and the magnitude of an externally applied load. Nonuniform energy and traction fields associated with free-edge boundary conditions are calculated to better understand localized phenomena such as the diffusion of impurities into a bonded interface and the diffusion of receptors in the cell membrane. The linear Griffith approximations commonly used in the literature are shown to be limited to shells with a small height to thickness ratio and short-range adhesive interactions. External loading is found to alter the adhered configurations and the spatial distributions of both adhesive and elastic energies. An important implication of the latter analysis is the theoretical prediction of the pull-off force, which is shown to depend not only on the interface properties, but also on the geometric and material parameters of the shell and on both the magnitude and type of external loading.     

Detachment of a rigid solid from an elastic wavy surface: Theory

The mechanics of detachment between a wavy elastic half space and a rigid solid is considered. Solutions for the axisymmetric problem of a rigid sphere and the plane strain problem of a rigid cylinder detaching from a wavy surface are developed. The interacting solids are taken to be in complete contact over a finite area initially. It is shown that the surface waviness makes the detachment process unstable, with the interface separating in alternating stable and unstable segments. Each unstable segment dissipates mechanical energy, leading to an increase in the total work of separation compared to that of a flat surface. Further, waviness causes the maximum separation force or the pull-off force to increase during detachment, resulting in an apparent toughening of the interface. This mechanism provides an alternative explanation to the experimental observations in the literature that roughness can sometimes lead to increase in pull-off force. It also illustrates the role of roughness in the attachment capability of several insect feet possessing soft pads. The basic solution presented here can be used to analyze the detachment of surfaces with multiple scale roughness as well. The solution also suggests strategies to improve reversible adhesion of a soft material by designing optimal surface topographies.     

Mechanics of robust and releasable adhesion in biology: Bottom-up designed hierarchical structures of gecko

Gecko and many insects have evolved specialized adhesive tissues with bottom-up designed (from nanoscale and up) hierarchical structures that allow them to maneuver on vertical walls and ceilings. The adhesion mechanisms of gecko must be robust enough to function on unknown rough surfaces and also easily releasable upon animal movement. How does nature design such macroscopic sized robust and releasable adhesion devices? How can an adhesion system designed for robust attachment simultaneously allow easy detachment? These questions have motivated the present investigation on mechanics of robust and releasable adhesion in biology. On the question of robust adhesion, we introduce a fractal gecko hairs model, which assumes self-similar fibrillar structures at multiple hierarchical levels mimicking gecko's spatula ultrastructure, to show that structural hierarchy plays a key role in robust adhesion: it allows the work of adhesion to be exponentially enhanced with each added level of hierarchy. We demonstrate that, barring fiber fracture, the fractal gecko hairs can be designed from nanoscale and up to achieve flaw tolerant adhesion at any length scales. However, consideration of crack-like flaws in the hairs themselves results in an upper size limit for flaw tolerant design. On the question of releasable adhesion, we hypothesize that the asymmetrically aligned seta hairs of gecko form a strongly anisotropic material with adhesion strength strongly varying with the direction of pulling. We use analytical solutions to show that a strongly anisotropic elastic solid indeed exhibits a strongly anisotropic adhesion strength when sticking on a rough surface. Furthermore, we perform finite element calculations to show that the adhesion strength of a strongly anisotropic attachment pad exhibits essentially two levels of adhesion strength depending on the direction of pulling, resulting in an orientation-controlled switch between attachment and detachment. These findings not only provide a theoretical foundation to understand adhesion mechanisms in biology but also suggest possible strategies to develop novel adhesive materials for engineering applications.     

Analytical and experimental study of a circular membrane in adhesive contact with a rigid substrate

The problem that is addressed here is that of a pressurized circular membrane in adhesive contact with a rigid substrate. A closed-form membrane analysis is developed for the JKR, DMT and Maugis regimes, which describes the relationships between adhesion energy, pressure, contact radius and contact force. The JKR–DMT transition is studied for this case of membrane contact by introducing an appropriate dimensionless parameter. Experiments are conducted with smooth and structured acrylate layers on a PET carrier film contacting a glass substrate using an apparatus based on moiré deflectometry to measure the contact radius and slope of these thin transparent films. They demonstrate that this analysis predicts the contact radius well. The adhesion energy extracted from the analysis of the measured pressure-contact radius response is constant during unloading but appears to increase during pressurization.     

仿生柔性表面的结构设计及吸附力试验分析

模仿昆虫脚上光滑型吸附垫表面的结构设计,选用具有黏弹性的硅胶板,分别测试了光滑、带凹槽、带凹坑试样在干的和湿的玻璃表面上的水平摩擦力和垂直吸附力.结构表明在干玻璃表面非光滑结构的接触面积比光滑的要小,具有减粘降阻的作用;而在有一层厚液体膜作媒介时,摩擦力比光滑的要大.有液体时,水平摩擦力是凹槽型的最大,垂直吸附力是凹坑型的最大.有一薄层液体时的湿吸附能力比干吸附大,且液体粘性越大吸附能力越强.这些研究为仿生爬壁机器人的足掌设计提供了有价值的参考.     

Adhesion of heterogeneous thin films II: Adhesive heterogeneity

This paper continues the study of the effective adhesion of thin films on rigid substrates in the presence of spatial heterogeneities started in Xia et al. (2013). In this paper, we focus on thin adhesive tape with spatial heterogeneity in the adhesive strength. This heterogeneity leads to a wavy peel front and consequently a complex corrugated shape in the tape. We develop a theory for the evolution of the peel front that accounts for this complex interaction, and an experimental method that is able to examine this in detail. We show through theory and experimentation that spatial patterning of the adhesive strength can lead to a very rich range of behaviors in the effective adhesive strength. In particular we show that adhesive heterogeneity can be used to create asymmetry in that the force required to peel the tape in one direction can be different from that in the other.     

Preload-responsive adhesion of microfibre arrays to rough surfaces

Adhesion of bio-inspired microfibre arrays to a rough surface is studied theoretically. The array consists of vertical elastic rods fixed on a rigid backing layer,and the surface is modeled by rigid steps with a normally distributed height. Analytical expressions are obtained for the adhesion forces in both the approach and retraction processes. It is shown that, with the increasing preload, the pull-off force increases at first and then attains a plateau value. The results agree with the previous experiments and are expected helpful in adhesion control of the array in practical applications.     

Hard-material Adhesion: Which Scales of Roughness Matter?

Background

Surface topography strongly modifies adhesion of hard-material contacts, yet roughness of real surfaces typically exists over many length scales, and it is not clear which of these scales has the strongest effect. Objective: This investigation aims to determine which scales of topography have the strongest effect on macroscopic adhesion.

Methods

Adhesion measurements were performed on technology-relevant diamond coatings of varying roughness using spherical ruby probes that are large enough (0.5-mm-diameter) to sample all length scales of topography. For each material, more than 2000 measurements of pull-off force were performed in order to investigate the magnitude and statistical distribution of adhesion. Using sphere-contact models, the roughness-dependent effective values of work of adhesion were measured, ranging from 0.08 to 7.15 mJ/m² across the four surfaces. The data was more accurately fit using numerical analysis, where an interaction potential was integrated over the AFM-measured topography of all contacting surfaces.

Results

These calculations revealed that consideration of nanometer-scale plasticity in the materials was crucial for a good quantitative fit of the measurements, and the presence of such plasticity was confirmed with AFM measurements of the probe after testing. This analysis enabled the extraction of geometry-independent material parameters; the intrinsic work of adhesion between ruby and diamond was determined to be 46.3 mJ/m². The range of adhesion was 5.6 nm, which is longer than is typically assumed for atomic interactions, but is in agreement with other recent investigations. Finally, the numerical analysis was repeated for the same surfaces but this time with different length-scales of roughness included or filtered out.

Conclusions

The results demonstrate a critical band of length-scales—between 43 nm and 1.8 µm in lateral size—that has the strongest effect on the total adhesive force for these hard, rough contacts.

     

硅表面电沉积MoS2薄膜及其微观摩擦性能研究

以单晶硅片为基片,采用电化学沉积工艺通过阴极还原硫代钼酸根制备MoS2薄膜,利用光学显微镜、扫描电子显微镜、X射线衍射仪、俄歇电子能谱仪以及原子力显微镜表征薄膜结构,并研究其微观摩擦磨损性能.结果表明:所制备的薄膜为纳米/亚微米厚度,表面光滑致密,结构为非晶态,由钼、硫和氧元素构成;微米厚度的薄膜表面粗糙度增加,薄膜易开裂,结合性差;沉积MoS2薄膜的硅表面的最小摩擦力约为原始硅表面的1/2;沉积MoS2可以使硅表面的粘着能减少50%左右,从而使其微观摩擦力降低.     

A review of adhesion mechanisms of mushroom-shaped microstructured adhesives

Very recently, both experimental and theoretical investigations have shown that micro-structured surfaces covered with mushroom shaped micropillars present strongly enhanced adhesive properties if compared to standard flat surfaces made of the same material. However, different geometries lead to different adhesive performance, and finding the optimal solution has become of utmost importance. In this review we summarize the main detachment mechanisms of flat-topped and mushroom-topped soft micro pillars and show how the geometry of the pillars should be designed in order to obtain the best adhesive performances. We also discuss the effect of air entrapment at the interface between the pillar and the substrate and investigate the influence of the non uniform pillar height and thermal fluctuations on pull-off force.