The role of adhesion in contact mechanics Ciavarella, M; Joe, J; Papangelo, A ...
Journal of the Royal Society interface,
02/2019, Volume:
16, Issue:
151
Journal Article
Peer reviewed
Open access
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.
The fundamental problem of friction in the presence of macroscopic adhesion, as in soft bodies, is receiving interest from many experimentalists. Since the first fracture mechanics ‘purely brittle’ ...model of Savkoor and Briggs, models have been proposed where the mixed mode toughness is interpreted with phenomenological fitting coefficients introducing weaker coupling between modes than expected by the “purely brittle” model. We compare here two such previously proposed models and introduce a third one to show that the transition to sliding is very sensitive to the form of the mixed-mode model. In particular, after a quadratic decay of the contact area with load for modest tangential loads, depending on the exact form of the mixed mode function, there is an inflexion point and an asymptotic limit, or a jump to the Hertzian contact area. We find also that the unstable points are different under load or displacement control. Hence, the form of the mixed mode function, and not only its parameter, is an extremely sensitive choice.
Simple exact solutions are known for the indentation problem of a viscoelastic halfspace by a rigid sphere only as long as the contact area is growing. We consider instead a more general cyclic ...repeated indentation with a pulsating load with a period of zero load. We show that a combination of exact with empirical relaxation solutions coming from simple uniaxial cases is sufficiently accurate to estimate the energy dissipated per cycle, which we report for the standard ”3-elements” solid and periodic half-sine loading for various parameters. The theoretical predictions favourably compare with boundary element numerical simulations. We find more energy is dissipated during the first indentation cycle with respect to the subsequent ones, due to the residual indentation left in the viscoelastic half-space. In load controlled systems, the maximum dissipation is reached at an angular frequency that is close to the reciprocal of the relaxation time of the material both for the first and subsequent cycles, but this is in general not true when displacement controlled systems are considered, when dissipation is much lower for subsequent cycles.
•Friction-induced vibrations may arise in viscoelastic contacts.•Contact interactions depend on the relative speed and on the indentation depth.•Instability may occur due to negative damping ...terms.•In plane and out-of-plane motion are coupled through the contact interface.•Multiple stable solutions exist in certain range of system parameters.
Self-excited vibrations represent a big concern in engineering, particularly in automotive, railway and aeronautic industry. Many lumped models have been proposed over the years to analyze the stability of such systems. Among the instability mechanisms a falling characteristic of the friction law and mode coupling have been shown to give friction-excited oscillations. The mass-on-moving-belt system has been studied extensively in Literature, very often adopting a prescribed form of the friction law and linearizing the contact stiffness. Instead, in this work, the case of a spherical oscillator excited by a moving viscoelastic halfspace is considered. The friction law and the nonlinear normal contact stiffness have been computed via boundary element numerical simulations for varying substrate velocity and indentation depth, then they have been adopted in time-marching dynamical numerical simulations. It is shown that the horizontal and vertical dynamics of the oscillator are tightly connected each other through the viscoelastic substrate. Furthermore, for certain normal forces/substrate velocity, the system has multiple stable solutions, which may include lift-off of the oscillator, which are selected based solely on the system initial conditions.
A number of authors have experimentally assessed the influence of friction on adhesive contacts, and generally the contact area has been found to decrease due to tangential shear stresses at the ...interface. The decrease is however generally much smaller than that predicted already by the Savkoor and Briggs 1977 classical theory using “brittle” fracture mechanics mixed mode model extending the JKR (Griffith like) solution to the contact problem. The Savkoor and Briggs theory has two strong assumptions, namely that (i) shear tractions are also singular at the interface, whereas they have been found to follow a rather constant distribution, and that (ii) no dissipation occurs in the contact. While assumption (ii) has been extensively discussed in the Literature the role of assumption (i) remained unclear. We show that assuming entirely reversible slip at the interface with a constant shear stress fracture mechanics model leads to results almost indistinguishable from the Savkoor and Briggs model (and further in disagreement with experiments), hence it is assumption (ii) that critically affects the results. We analyze a large set of experimental data from Literature and show that the degree of irreversibility of friction can vary by orders of magnitude, despite similar materials and geometries, depending on the velocity at which the tangential load is applied.
Crack propagation in viscoelastic materials is a problem of considerable importance, now relatively well understood after early paradoxical results have been addressed with the use of cohesive ...models. However, finite size effects have received limited theoretical attention so far. Here, following suggestions of Persson (2017), we derive simple results for a crack propagating in a finite size specimen for a model of a single relaxation time material (but extension to many relaxation times is trivial). We show results for the maximum velocity above which the crack may become unstable and the toughness enhancement reduction with respect to that of the infinite system, which corresponds to the ratio of instantaneous to relaxed elastic moduli. Agreement with the literature is dubious, since de Gennes (1996) predicts instability but same amplification as the infinite system, whereas a more recent theory of Persson (2021) suggests same amplification of that of the infinite system, but without instability. A clarification of these qualitative differences is hoped for the future.
•Crack propagation finite size effects in viscoelastic materials have received limited theoretical attention so far.•We derive simple results of Persson’s 2017 theory.•We show that there is a maximum velocity above which the crack may become unstable in Persson’s 2017 theory.•The toughness enhancement seems reduced with respect to that of the infinite system•Agreement with literature is dubious.
The dynamical behavior of a single-degree-of-freedom system that experiences friction-induced vibrations is studied with particular interest on the possibility of the so-called hard effect of a ...subcritical Hopf bifurcation, using a velocity weakening–strengthening friction law. The bifurcation diagram of the system is numerically evaluated using as bifurcation parameter the velocity of the belt. Analytical results are provided using standard linear stability analysis and nonlinear stability analysis to large perturbations. The former permits to identify the lowest belt velocity
(
v
lw
)
at which the full sliding solution is stable, the latter allows to estimate a priori the highest belt velocity at which large amplitude stick–slip vibrations exist. Together the two boundaries
v
lw
,
v
up
define the range where two equilibrium solutions coexist, i.e., a stable full sliding solution and a stable stick–slip limit cycle. The model is used to fit recent experimental observations.
True contact between randomly rough solids consists of myriad individual microjunctions. While their total area controls the adhesive friction force of the interface, other macroscopic features, ...including viscoelastic friction, wear, stiffness, and electric resistance, also strongly depend on the size and shape of individual microjunctions. We show that, in rough elastomer contacts, the shape of microjunctions significantly varies as a function of the shear force applied to the interface. This process leads to a growth of anisotropy of the overall contact interface, which saturates in the macroscopic sliding regime. We show that smooth sphere-plane contacts have the same shear-induced anisotropic behavior as individual microjunctions, with a common scaling law over 4 orders of magnitude in the initial area. We discuss the physical origin of the observations in light of a fracture-based adhesive contact mechanics model, described in the companion article, which captures the smooth sphere-plane measurements. Our results shed light on a generic, overlooked source of anisotropy in rough elastic contacts, not taken into account in current rough contact mechanics models.
There is ample evidence of ThermoElastic Instabilities (TEI) occurring in sliding contacts. The very first experiments of JR Barber in 1969 suggested wear interacts in the process of localization of ...contact into “hot spots”. However, studies on the interaction of TEI with wear are scarce. We consider the case of two sliding halfspaces and make a perturbation analysis permitting the formation of waves migrating over the two bodies, in presence of wear. We find that for exactly identical bodies wear does not affect the stability boundary. In the other limit case of bad conductor against a good conductor, wear tends to suppress TEI completely. Intermediate cases show a complex range of possible effects: for certain thermomechanical properties wear may even reduce the critical speed.
•The effect of wear on thermoelastic instability in presence of wear is studied.•For two dissimilar material sliding wear can completely suppress thermoelastic Instabilities.•For similar material sliding wear does not affect the stability boundary.•In certain ranges wear can be detrimental reducing the critical speed for instability.
We study the adhesion of a surface with a ‘dimple’ which shows a mechanism for a bi-stable adhesive system in surfaces with spaced patterns of depressions, leading to adhesion enhancement, high ...dissipation and hysteresis. Recent studies were limited mainly to the very short range of adhesion (the so-called JKR regime), while we generalize the study to a Maugis cohesive model. A ‘generalized Tabor parameter’, given by the ratio of theoretical strength to elastic modulus, multiplied by the ratio of dimple width to depth has been found. It is shown that bistability disappears for generalized Tabor parameter less than about 2. Introduction of the theoretical strength is needed to have significant results when the system has gone in full contact, unless one postulates alternative limits to full contact, such as air entrapment, contaminants or fine scale roughness. Simple equations are obtained for the pull-off and for the full contact pressure in the entire set of the two governing dimensionless parameters. A qualitative comparison with results of recent experiments with nanopatterned bioinspired dry adhesives is attempted in light of the present model.
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