Johnson , Kendall And Roberts Research Articles

Deep Learning Regressors of Surface Properties from Atomic Force Microscopy Nanoindentations

Atomic force microscopy (AFM) is a powerful technique to study the nanomechanical properties of a wide range of materials at the piconewton level. AFM force–indentation curves can be fitted with appropriate contact models, enabling the determination of material properties for a given sample. However, the analysis of large datasets comprising thousands of curves using conventional methods presents a time-intensive challenge. As a result, there is an increasing interest in exploring alternative methodologies, such as integrating machine learning (ML) models to streamline and improve the efficiency of this process. In this work, two data-driven regressors were tuned to predict the Young’s modulus and adhesion energy from force–indentation curves of soft samples (Young’s modulus up to 10 kPa). Both models were trained exclusively on synthetic data derived from the contact theories developed by Hertz as well as Johnson, Kendall and Roberts (JKR). The PyTorch library was employed to build and train the models; then, the key hyperparameters were refined by implementing the optimization framework Optuna. The first model was successfully tested with synthetic and experimental curves from AFM nanoindentations, and the second presented promising results on the synthetic data. Our work suggests that experimental data may not be essential for training data-driven models to predict surface properties from AFM nanoindentations. By delivering accurate predictions in a computationally efficient way, our regressors validate the potential of a deep learning approach in exploring AFM nanoindentations and motivate further development of similar strategies to overcome current limitations in AFM postprocessing.

Colloidal interactions for a polystyrene particle and a smooth silicon surface: Atomic force microscopy, XDLVO theory, and Surface Element Integration

In this study Liftshitz van der Waals, electrostatic and acid base interaction forces of a 4 µm polystyrene particle with flat silicon surfaces were experimentally determined using interfacial interaction energy measurements and atomic force microscopy (AFM). Interfacial forces computed using analytical expressions based on the Surface Element Integration (SEI) technique were compared with the standard Derjaguin Approximation (DA) and Continuum Mechanics Adhesion approaches, namely: Derjaguin, Muller and Toporov (DMT), Johnson, Kendall and Roberts (JKR) and Maugis and Pollock (MP) theories in order to assess the effect of curvature on a sphere-plate geometry. For acid base interactions, the SEI was found to deviate from the DA at small particles radii (less than 100 nm) and over a wide ratio of decay length, λ, to particle size, R. Accounting for curvature for acid base interaction requires geometric factors that are functions of λ/R. For van der Waals force of interaction, the SEI and DA showed large variation at large ratios of interparticle separation, D, to particle radius, R. For Double layer interaction force large variation between SEI and DA was observed for small κa values, and good agreement observed at large κa values. The AFM forces of adhesion of polystyrene in 0.01 mM and 100 mM KCl electrolyte solutions were found to be 2.38 ± 2.15 nN and 9.29 ± 6.89 nN, respectively. These results were found to be consistent with the SEI technique that gave adhesion forces of 4.8 and 10.2 nN at the low and high electrolyte concentrations, respectively. These data are also aligned with Maugis and Pollock (MP) theory that accounts for elasto-plastic deformation, Pe.

Effect of X-ray exposure on nano-mechanical properties of multi-walled carbon nanotube incorporated silicone polymer nanocomposites: An AFM-based study

Nano-mechanical properties of silicone polymer-based nanocomposites loaded with multi-walled carbon nanotube (MWCNT) as nanofillers are probed here using the atomic force microscopy (AFM) technique. Further, the effects of MWCNT concentration and X-ray exposure on the nano-mechanical and topographic properties of the polymer nanocomposites are systematically studied. The root mean square surface roughness is found to increase by ∼123% when the neat polymer matrix is loaded with 2.5 wt.% of MWCNT, whereas, for a fixed MWCNT concentration, the surface roughness is found to increase by ∼171% after X-ray irradiation. This is attributed to the X-ray induced polymer degradation, polymer pull-out and poor filler-matrix interaction leading to the aggregation of MWCNT. Adhesion force and adhesion energy are estimated from the AFM-based force-displacement curves. Both quantities are found to increase with MWCNT concentration. After an exposure to diagnostic X-rays (30–70 keV), the adhesion force is found to increase by ∼4 times, which is attributed to the increased tip-surface contact area due to the higher surface roughness of the X-ray exposed samples. Further, the variation of adhesion energy with filler concentration is found to be in agreement with the theoretical values obtained from the Johnson, Kendall and Roberts (JKR) model. The elastic modulus is found to increase with the filler concentration due to an increase in adhesion force. The obtained results are beneficial for the optimal design of nanofiller loaded polymer nanocomposites for various applications, including the fabrication of lead-free radio-opaque nanocomposites.

Nanocracks in nature and industry.

Nanocracks in nature and industry.

A mathematical model for evaluating adhesion contact of an elastomeric seal-on-seal structure

For low impact docking systems (LIDS) developing for rendezvous and docking of spacecraft, the main interface docking seal (MID seal) is one of the key components, and its seal and adhesion performances are crucial for mating LIDS-adapted spacecrafts. An elastomeric seal-on-seal structure is one of the mainstream designs of the MID seal and is generally made of silicone rubbers that can adapt to complex space environments. For the MID seal of seal-on-seal structure, the adhesion performance has been confirmed to have significant effects on the separation reliability of mating spacecrafts. By analyzing the sealing and adhesive mechanisms of the MID seal that is an elastomeric seal-on-seal structure, an adhesive contact model of single rough peak is derived on the grounds of Johnson, Kendall and Roberts (JKR) theory. Utilizing the asperities model and the adhesive contact model of single rough peak, an adhesive contact model of the elastomeric seal-on-seal structure is further proposed. The experiments were performed to verify the adhesion model, and the satisfied consistencies were presented in the comparative studies of the experimental data and the calculated data. Based on the proposed mathematical model, the simulation analyses were performed to disclosure adhesive performances of the MID seal. The influence rules of some parameters on adhesive performances were presented, including material parameters, geometric parameters, and parameters of surface morphology. The research findings are proven to be favorable for the design, machining, assemblage and actual service of the MID seal, and can be also used for other elastomeric seals.

Adhesion and heat build-up of rubber for energy-saved tyre

The objective of this study was to investigate the effect of crosslinking systems (conventional and efficient systems) on the contact mechanics and heat build-up of natural rubber (NR) tyre mimicking samples. The JKR (Johnson, Kendall and Roberts) experiment has been established to measure the contact mechanics in NR samples at different vulcanization systems. Work of adhesion obtained from JKR model is in good agreement with that calculated from contact angle measurement. From the contact mechanics point of view, the adsorption of the rubber to the glass slide surface plays a major role in the strain energy release rate. Higher rubber free chain samples (unvulcanized rubber) represent higher adhesion hysteresis and higher heat build-up compared to vulcanized rubbers whichever was the vulcanization system. Finally, rubber sample obtained using efficient vulcanization has the lowest adhesion hysteresis and heat build-up. These results suggest that the rubber with efficient vulcanization is preferable for the application of energy-saving tyres.

Indentation of thin elastic films glued to rigid substrate: Asymptotic solutions and effects of adhesion

Indentation of a thin elastic film attached through an interlayer to a rigid support is studied. Because the common interpretations of depth-sensing indentation tests are not applicable to such structured coatings, usually various approximating functions are employed to take into account influence of the interlayer. Contrary to the common approaches, a strict mathematical approach is applied here to study the problems under consideration assuming that the thickness of the two-layer structure is much less than characteristic dimension of the region of contact between the indenter and the coating. A simple derivation of asymptotic relations for displacements and stresses is presented. It is shown that often the leading term approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler-Fuss elastic foundation with an effective elastic constant. Because the contact between the indenter and the film at nanoscale may be greatly affected by adhesion, the adhesive problem for these bilayer coatings is studied in the framework of the JKR (Johnson, Kendall, and Roberts) theory of adhesion. Assuming the indenter shape near the tip has some deviation from its nominal shape and using the leading term approximation of the layered coatings, the explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius of adhesive contact region.

Developing viscoelastic contact models and selecting suitable creep function for spherical biological cells.

In most contact theories, the most popular of which are the three models of Hertz, Derjaguin, Muller and Toporov (DMT) and Johnson, Kendall and Roberts (JKR), biological cells were considered as an elastic material which is not a proper assumption. The elastic assumption in the case of biological cells could lead to neglecting the loading history as a result of which the stresses and strains applied to the material would not be studied accurately. In this paper, developing the three mentioned elastic models into viscoelastic models, simulating and comparing them with empirical data obtained through the indentation test of the MCF-7 cancer cell showed that the viscoelastic state presents a better prediction of biological cell behavior compared to that of an elastic state. The selection of the suitable creep function for objects in contact is another issue that has a significant importance in the viscoelastic case and this was investigated. Different mechanical models of a cell were studied and simulated for all three named theories among which the creep function obtained from the Kelvin model, a parallel combination of spring-damper, simplified the simulation and gave more precise results for modeling due to the fact that the obtained results from this model are closer to experimental ones and simpler than other models. On the other hand, for a more exact prediction of cell behavior, this model was modified by an equivalent elasticity module which considered cell components instead of the cell cortex only. The results of the simulation confirmed that a new elasticity module can improve the accuracy of cell models. After choosing the suitable mechanical model for the cell, we scrutinized the capability of the developed theories in predicting the results for biological liquid environments. Although the results of the Hertz and DMT viscoelastic models are closer to experimental ones in comparison with viscoelastic JKR, neglecting adhesion makes their prediction in biological liquid environments weak and erroneous. Therefore, it can be concluded that the developed viscoelastic model of JKR is more accurate and has a better performance in different environments than the other mentioned models.

The role of adhesion in contact mechanics.

Adhesive (e.g. van der Waals) forces were not generally taken into account in contact mechanics until 1971, when Johnson, Kendall and Roberts (JKR) generalized Hertz' solution for an elastic sphere using an energetic argument which we now recognize to be analogous to that used in linear elastic fracture mechanics. A significant result is that the load-displacement relation exhibits instabilities in which approaching bodies 'jump in' to contact, whereas separated bodies 'jump out' at a tensile 'pull-off force'. The JKR approach has since been widely used in other geometries, but at small length scales or for stiffer materials it is found to be less accurate. In conformal contact problems, other instabilities can occur, characterized by the development of regular patterns of regions of large and small traction. All these instabilities result in differences between loading and unloading curves and consequent hysteretic energy losses. Adhesive contact mechanics has become increasingly important in recent years with the focus on soft materials (which generally permit larger areas of the interacting surfaces to come within the range of adhesive forces), nano-devices and the analysis of bio-systems. Applications are found in nature, such as insect attachment forces, in nano-manufacturing, and more generally in industrial systems involving rubber or polymer contacts. In this paper, we review the strengths and limitations of various methods for analysing contact problems involving adhesive tractions, with particular reference to the effect of the inevitable roughness of the contacting surfaces.

Comparison of Hertzian and JKR theories with a finite element model in boundary lubrication conditions between a compression ring and a cylinder

This study focuses on the creation of an isothermal elastic model to highlight, through stresses, the occurrence of plastic deformation in certain crank angles under extreme dry conditions inside an internal combustion engine. The stresses that are exported from this analysis are pointing out not only the necessity for an elastoplastic model to be created, but also the importance of predicting the correct friction coefficient, as pointed out by both the contact surface stress and those in depth of the two bodies in contact. A comparison between two coefficients of frictions and one frictionless case is conducted. The comparison between the finite element model and the adhesion mathematical model of Johnson, Kendall and Roberts (JKR), seals the importance of the interaction forces, acting on the common solid surface, in the pursuit of defining a propriate contact patch. Furthermore, a three-dimensional model is proposed for further investigation, highlighting the importance of modelling surface’s micro asperities for a solid stress analysis.

Contact probing of stretched membranes and adhesive interactions: graphene and other two-dimensional materials.

Contact probing is the preferable method for studying mechanical properties of thin two-dimensional (2D) materials. These studies are based on analysis of experimental force–displacement curves obtained by loading of a stretched membrane by a probe of an atomic force microscope or a nanoindenter. Both non-adhesive and adhesive contact interactions between such a probe and a 2D membrane are studied. As an example of the 2D materials, we consider a graphene crystal monolayer whose discrete structure is modelled as a 2D isotropic elastic membrane. Initially, for contact between a punch and the stretched circular membrane, we formulate and solve problems that are analogies to the Hertz-type and Boussinesq frictionless contact problems. A general statement for the slope of the force–displacement curve is formulated and proved. Then analogies to the JKR (Johnson, Kendall and Roberts) and the Boussinesq–Kendall contact problems in the presence of adhesive interactions are formulated. General nonlinear relations among the actual force, displacements and contact radius between a sticky membrane and an arbitrary axisymmetric indenter are derived. The dimensionless form of the equations for power-law shaped indenters has been analysed, and the explicit expressions are derived for the values of the pull-off force and corresponding critical contact radius.

On roughness-induced adhesion enhancement

While adhesion reduction due to roughness is not surprising, roughness induced adhesion remained a puzzle until recently. Guduru and coworkers have shown a very convincing mechanism to explain both the increase of strength and of toughness in a sphere with a concentric single scale of waviness. Kesari and coworkers later showed some very elegant convenient asymptotic expansions of Guduru’s solution. This enhancement is very high and indeed, using Kesari’s solution, it is here shown to depend uniquely on a Johnson parameter for adhesion of a sinusoidal contact. However, counterintuitively, it leads to unbounded enhancement for conditions of large roughness for which the Johnson parameter is very low. Guduru postulated that this enhancement should occur after sufficiently large pressure has been applied to any spherical contact. Also, although the enhancement is limited to the Johnson, Kendall and Roberts (JKR) regime of large soft materials with high adhesion, the DMT limit for the smooth sphere is found otherwise. However, for hard materials, even the Derjaguin, Muller and Toporov (DMT) limit for the smooth solids is very hard to observe, which suggests that adhesion reduction is also not yet well understood. The limitations of the assumption of simply connected area are here further discussed, and a well-known model for hard particles in contact with rough planes due to Rumpf is used to show that, in the range where an unbounded increase is predicted, orders of magnitude reduction is instead expected for rigid solids. We suggest that Guduru’s model may be close to an upper bound for adhesion of rough bodies, while the Rumpf–Rabinovich model may be close to a lower bound.

JKR adhesive contact for a transversely isotropic layer of finite thickness

A frictionless contact interaction with a circular area of contact between an arbitrary axisymmetric rigid probe and a transversely isotopic elastic layer deposited on a substrate is studied in the framework of the JKR (Johnson, Kendall, and Roberts) adhesion theory. Under the assumption that the diameter of the contact area is less than the thickness of the elastic layer, the forth-order asymptotic model is explicitly written out. The effect of the layer thickness and the material anisotropy is taken into account via the asymptotic coefficients, which are integral characteristics of the elastic layer and also depend on the boundary conditions at the layer/substrate interface. A special case of an isotropic elastic layer bonded to an isotropic elastic half-space is considered in detail.

Adhesive contact of the Weierstrass profile

The Weierstrass series was considered in Ciavarellaet al.(Ciavarellaet al.2000Proc. R. Soc. Lond. A456, 387–405. (doi:10.1098/rspa.2000.0522)) to describe a linear contact problem between a rigid fractally rough surface and an elastic half-plane. In such cases, no applied mean pressure is sufficiently large to ensure full contact, and specifically there are not even any contact areas of finite dimension. Later, Gao & Bower (Gao & Bower 2006Proc. R. Soc. A462, 319–348. (doi:10.1098/rspa.2005.1563)) introduced plasticity in the Weierstrass model, but concluded that the fractal limit continued to lead to what they considered unphysical predictions of the true contact size and number of contact spots, similar to the elastic case. In this paper, we deal with the contact problem between rough surfaces in the presence of adhesion with the assumption of a Johnson, Kendall and Roberts (JKR) regime. We find that, for fractal dimensionD>1.5, the presence of adhesion does not qualitatively modify the contact behaviour. However, for fractal dimensionD<1.5, a regularization of the contact area can be observed at a large magnification where the contact area consists of segments of finite size. Moreover, full contact can occur at all scales forD<1.5 provided the mean contact pressure is larger than a certain value. We discuss, however, the implication of our assumption of a JKR regime.

Adhesive contact mechanics: From deterministic to stochastic description

The theoretical models in adhesive contact mechanics have been successfully applied in fields such as colloidal assembly, drug delivery as well as virus-cell interaction. This report briefly reviews the classical models in describing particle-substrate adhesion. Johnson, Kendall and Roberts (JKR) first obtained the critical tensile load leading to ballistic particle pull off from a substrate. Derjaguin, Muller and Toporov (DMT) proposed an alternate theory with a different prediction on the critical load. Maugis was able to show the JKR-DMT transition using a Dugdale cohesive description of surface interaction. More extensions of adhesive contact models have involved material anisotropy, elasticity gradation, viscoelasticity, and large deformation in nonlinear elastomers. All of these existing results are inherently deterministic, sharing the viewpoint that a critical level of pulling force, commonly referred to as the pull-off force, is needed for particles to detach from substrates. Below the critical pull-off force, particle detachment never occurs.

Determining the adhesion force between particles and rough surfaces

Adhesion between powders and surfaces plays an important role in various industrial applications such as food and pharmaceutical industries. The Centrifugal Technique was used to measure the adhesion force distribution of several hundred particles simultaneously. The powder particles were initially forced onto the substrate surface by centrifuging them at a particular speed, and immediately after this stage, the adhesion profile was determined. The powder used was microcrystalline cellulose (ρ=1.620kgm−3). The materials used as substrates were a membrane of cellulose ester 0.2μm in porosity, brand Shleicher & Shuell Filtration Life Science, used in process monitoring particulate material and a compressed particulate (tablets) microcrystalline cellulose (MCC). A microcentrifuge that reached a maximum rotation speed of 14,000rpm and which contained specially designed centrifuge tubes was used in the adhesion force measurements. An image analysis program (Image-Pro Plus 7.0) was used to monitor the number of particles that remained adhered on the surface of the substratum after each angular speed increase. The geometric median force of adhesion for the substrates was found to increase linearly with the preliminary applied force. The slope of each regression line indicated quantitatively the change of the median adhesion force per unit increase of the applied force. Finally, the adhesion force experimental results and the adhesion force theoretical values using the models proposed by Derjaguin, Muller and Toporov (DMT) and Johnson, Kendall and Roberts (JKR) were compared. Although the JKR Model was the closest one to the experimental results, the adhesion force theoretical values were far higher than the experimental values.

Numerical modelling of breakage and adhesion of loose fine-particle agglomerates

In this study, discrete element method (DEM) simulations are used to examine the breakage and capturing behaviour of loose fine-particle agglomerates on impact with a target particle. The model system is an agglomerate composed of 5µm fine particles and a 200µm target particle. The cohesion between fine particles was modelled using the Johnson, Kendall and Roberts (JKR) theory. In contrast to the breakage of hard agglomerates which break in large fragments, as commonly investigated, loose agglomerates break in finer fragments. Impact velocity was found to be a significant parameter not only for the adhesion strength but also for the structure of the particles captured on the target. The capture ratio of the agglomerate as well as the thickness of the particle layer covering the target decreases with increasing impact velocity. High impact velocity results in finer fragments attached to the target with greater tensile strength due to the re-structuring mechanism that occurs during impact. Accordingly, impact velocity is one of the critical parameters governing the structure resulting after collision. However, the effect of material properties, e.g. surface energy, material hardness and plasticity, on adhesion behaviour should be investigated to obtain a full picture of the breakage-adhesion regime map.

The JKR-type adhesive contact problems for transversely isotropic elastic solids

The JKR (Johnson, Kendall, and Roberts) and Boussinesq–Kendall models describe adhesive frictionless contact between two isotropic elastic spheres or between a flat end punch and an elastic isotropic half-space. Here adhesive contact is studied for transversely isotropic materials in the framework of the JKR theory. The theory is extended to much more general shapes of contacting axisymmetric solids, namely the distance between the solids is described by a monomial (power-law) function of an arbitrary degree d⩾1. The classic JKR and Boussinesq–Kendall models can be considered as two particular cases of these problems, when the degree of the punch d is equal to two or it goes to infinity, respectively. It is shown that the formulae for extended JKR contact model for transversely isotropic materials have the same mathematical form as the corresponding formulae for isotropic materials; however the effective elastic contact moduli have different expression for different materials. The dimensionless relations between the actual force, displacements and contact radius are given in explicit form. Connections of the problems to nanoindentation of transversely isotropic materials are discussed.

The JKR-type adhesive contact problems for power-law shaped axisymmetric punches

The JKR (Johnson, Kendall, and Roberts) and Boussinesq–Kendall models describe adhesive frictionless contact between two isotropic elastic spheres, and between a flat-ended axisymmetric punch and an elastic half-space respectively. However, the shapes of contacting solids may be more general than spherical or flat ones. In addition, the derivation of the main formulae of these models is based on the assumption that the material points within the contact region can move along the punch surface without any friction. However, it is more natural to assume that a material point that came to contact with the punch sticks to its surface, i.e. to assume that the non-slipping boundary conditions are valid. It is shown that the frictionless JKR model may be generalized to arbitrary convex, blunt axisymmetric body, in particular to the case of the punch shape being described by monomial (power-law) punches of an arbitrary degree d≥1. The JKR and Boussinesq–Kendall models are particular cases of the problems for monomial punches, when the degree of the punch d is equal to two or it goes to infinity respectively. The generalized problems for monomial punches are studied under both frictionless and non-slipping (or no-slip) boundary conditions. It is shown that regardless of the boundary conditions, the solution to the problems is reduced to the same dimensionless relations among the actual force, displacements and contact radius. The explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius. Connections of the results obtained for problems of nanoindentation in the case of the indenter shape near the tip has some deviation from its nominal shape and the shape function can be approximated by a monomial function of radius, are discussed.

Contact interactions of aorta against PVC catheters

Catheters are common medical devices routinely employed to deliver or drain fluids and medicines. The insertion of such devices generates friction forces that can lead to patient discomfort and tissue damage. In the development of new materials the evaluation of the friction characteristics is a very important step. However, in the development stage only the raw sheet material can be available but not catheters made of it; consequently in vitro test are often carried out.The multi-asperity adhesion model based on the JKR (Johnson, Kendall and Roberts) theory proposed by Prokopovich and Perni. Langmuir. 26 (2010). p. 17028–17036 has been extended taking into consideration that asperities summits are not perfectly hemispherical; therefore, it is now applicable also to ellipsoidal or paraboloidal asperities. The adhesion between aorta tissue and Polyvinyl chloride (PVC) catheters has been modeled considering also the presence of blood as a lubricant as the capillary forces resulting from a liquid film between surfaces have been also implemented.Aorta surface properties, such as asperity heights and radii of curvature, were obtained and used in the calculations. Through the model the adhesion force and real area of contact were calculated; these were used to predict the static friction coefficient in both dry and lubricated case. A good agreement was found between experimental and simulated values of adhesion force and of friction coefficient.