Explicit transformation between non-adhesive and adhesive contact problems by means of the classical Johnson–Kendall–Roberts formalism

The classic Johnson–Kendall–Roberts (JKR) contact theory was developed for frictionless adhesive contact between two isotropic elastic spheres. The advantage of the classical JKR formalism is the use of the principle of superposition of solutions to non-adhesive axisymmetric contact problems. In the recent years, the JKR formalism has been extended to other cases, including problems of contact between an arbitrary-shaped blunt axisymmetric indenter and a linear elastic half-space obeying rotational symmetry of its elastic properties. Here the most general form of the JKR formalism using the minimal number of conditions is studied. The corresponding condition of energy balance is developed. For the axisymmetric case and a convex indenter, the condition is reduced to a set of expressions allowing explicit transformation of force–displacement curves from non-adhesive to corresponding adhesive cases. The implementation of the developed theory is demonstrated by presentation of a two-term asymptotic adhesive solution of the contact between a thin elastic layer and a rigid punch of arbitrary axisymmetric shape. Some aspects of numerical implementation of the theory by means of Finite-Element Method are also discussed. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’

Adhesive contact problems for a thin elastic layer : Asymptotic analysis and the JKR theory

Contact problems for a thin compressible elastic layer attached to a rigid support are studied. Assuming that the thickness of the layer is much less than the characteristic dimension of the contact area, a direct derivation of asymptotic relations for displacements and stress is presented. The proposed approach is compared with other published approaches. The cases are established when the leading-order approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler–Fuss elastic foundation. For this elastic foundation, the axisymmetric adhesive contact is studied in the framework of the Johnson–Kendall–Roberts (JKR) theory. The JKR approach has been generalized to the case of the punch shape being described by an arbitrary blunt axisymmetric indenter. Connections of the results obtained to problems of nanoindentation in the case that the indenter shape near the tip has some deviation from its nominal shape are discussed. For indenters whose shape is described by power-law functions, the explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius

Experimental testing of self-healing ability of soft polymer materials

Bioinspired materials that act like living tissues and can repair internal damage by themselves, i.e. self-healing materials, are an active field of research. Here a methodology for experimental testing of self-healing ability of soft polymer materials is described. The methodology is applied to a recently synthesized polyurethane material Smartpol (ADHTECH Smart Polymers & Adhesives S.L., Alicante, Spain). Series of tests showed that the material demonstrated self-healing ability. The tests included the following steps: each Smartpol specimen was cut in halves, then it was put together under compression, and after specified amount of time, it was pulled apart while monitoring the force in contact. The test conditions were intentionally chosen to be non-ideal. These non-idealities simultaneously included: (1) separation time was rather long (minutes and dozens of minutes), (2) there was misalignment of specimen parts when they were put together, (3) contacting surfaces were non-flat, and (4) repeated testing of the same specimens was performed and, therefore, repeated damage was simulated. Despite the above, the recovery of structural integrity (self-healing) of the material was observed which demonstrated the remarkable features of Smartpol. Analysis of the experimental results showed clear correlation between adhesion forces (observed through the values of maximum pull-off force) and the time in contact which is a clear indicator of self-healing ability of material. It is argued that the factors contributing to self-healing of the tested material at macro-scale were high adhesion and strong viscoelasticity. The results of fitting the force relaxation data by means of mathematical model containing multiple exponential terms suggested that the material behaviour may be adequately described by the generalized Maxwell model

Evaluation of elastic modulus and hardness of highly inhomogeneous materials by nanoindentation

The experimental and numerical techniques for evaluation of mechanical properties of highly inhomogeneous materials are discussed. The techniques are applied to coal as an example of such a material. Characterization of coals is a very difficult task because they are composed of a number of distinct organic entities called macerals and some amount of inorganic substances along with internal pores and cracks. It is argued that to avoid the influence of the pores and cracks, the samples of the materials have to be prepared as very thin and very smooth sections, and the depth-sensing nanoindentation (DSNI) techniques has to be employed rather than the conventional microindentation. It is shown that the use of the modern nanoindentation techniques integrated with transmitted light microscopy is very effective for evaluation of elastic modulus and hardness of coal macerals. However, because the thin sections are glued to the substrate and the glue thickness is approximately equal to the thickness of the section, the conventional DSNI techniques show the effective properties of the section/substrate system rather than the properties of the material. As the first approximation, it is proposed to describe the sample/substrate system using the classic exponential weight function for the dependence of the equivalent elastic contact modulus on the depth of indentation. This simple approach allows us to extract the contact modulus of the material constitutes from the data measured on a region occupied by a specific component of the material. The proposed approach is demonstrated on application to the experimental data obtained by Berkovich nanoindentation with varying maximum depth of indentation

Hierarchical models of engineering rough surfaces and bio-inspired adhesives

Friction, wear, adhesion and energy dissipation during sliding are strongly influenced by deformations of asperities, which, in turn, depend on the surface profile. At the nanoscale, the effects of surface roughness and the underlying physical phenomena, such as adhesion between contacting objects, have a considerable influence on the interaction between surfaces. Here various models of rough surfaces, including multi-level models, hierarchically structured models, and appropriate multi-scale models of contact interactions between rough surfaces are reviewed and discussed. A new model for numerical simulations of dry friction between rough engineering surfaces is introduced. The main features of the new model based on the use of a multi-level and multi-scale, hierarchically structured slider are described. Although the surface topography of the biological attachment devices is rather different from the topography of engineering surfaces, some existing models of bio-inspired adhesives are classified using terminology introduced for models of engineering rough surfaces

Frictional Indentation of an Elastic Half-Space

In this chapter, we study the axisymmetric indentation problem for a transversely isotropic elastic half-space with finite friction. By treating the indentation problem incrementally, its general solution is reduced to that of the problem for a flat-ended cylindrical indenter with an unknown stick-slip radius. The solution to the latter problem in the transversely isotropic case is obtained via Turner?s equivalence principle Turner (Int J Solids Struct 16:409?419, 1980 [15]), from the analytical solution given by Spence (J Elast 5:297?319, 1975 [12]) in the case of isotropy. The generalization, due to Stor?kers and Elaguine (J Mech Phys Solids 53:1422?1447, 2005 [14]), of the BASh relation for incremental indentation stiffness, and also accounting for the friction effects, is presented. The case of self-similar contact with friction is considered in more detai