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.
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.
The Tabor parameter μ is conventionally assumed to determine the range of applicability of the classical ‘JKR’ solution for adhesive elastic contact of a sphere and a plane, with the variation of the ...contact area and approach with load, and in particular the maximum tensile force (the pull-off force) being well predicted for μ>5. Here we show that the hysteretic energy loss during a contact separation cycle is significantly overestimated by the JKR theory, even at quite large values of μ. This stems from the absence of long-range tensile forces in the JKR theory, which implies that jump into contact is delayed until the separation α=0. We develop an approximate solution based on the use of Wu's solution with van der Waals interactions for jump-in, and the JKR theory for jump out of contact, and show that for μ>5, the predicted hysteresis loss is then close to that found by direct numerical solutions using the Lennard-Jones force law. We also show how the same method can be adapted to allow for contact between bodies with finite support stiffness.
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.
With an appropriate combination of constant and varying loads, a punch may “walk” or “ratchet”, if rigid body motion is allowed. Here, a full numerical analysis is conducted to study the effect of ...material dissimilarity on a simple configuration. It is found that walking starts from much lower loads than in the case of similar materials, and higher shift per cycle is predicted with the same load and rocking motion, even accounting for the change of the plane strain modulus. Both elastic shakedown or cyclic dissipation are found, and convergence in these cases is relatively slow, whereas it occurs after 2 cycles of oscillations, in the walking case.
•With a constant tangential load, but a rocking normal load, a punch may “walk” or “ratchet”.•With elastic dissimilarity, we find much higher shift per cycle for given loads, or lower loads to start walking.•Both elastic shakedown or cyclic dissipation are found, and convergence in this cases is relatively slow.
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