Papers by michele ciavarella
Friction-induced vibrations are known to affect many engineering applications. Here, we study a c... more Friction-induced vibrations are known to affect many engineering applications. Here, we study a chain of friction-excited oscillators with nearest neighbor elastic coupling. The excitation is provided by a moving belt which moves at a certain velocity v d while friction is modelled with an exponentially decaying friction law. It is shown that in a certain range of driving velocities, multiple stable spatially localized solutions exist whose dynamical behavior (i.e. regular or irregular) depends on the number of oscillators involved in the vibration. The classical non-repeatability of friction-induced vibration problems can be interpreted in light of those multiple stable dynamical states. These states are found within a "snaking-like" bifurcation pattern. Contrary to the classical Anderson localization phenomenon, here the underlying linear system is perfectly homogeneous and localization is solely triggered by the friction nonlinearity.
We consider a series of flat contact spots distributed over a half-space, for which the pull-off ... more We consider a series of flat contact spots distributed over a half-space, for which the pull-off force is proportional to the square root of the total contact area over the elastic compliance. By using an electro-mechanical analogy to compute the compliance using the well-known Greenwood-Holm equation, we show how the pull-off decays for fractal patterns of contact spots with simple scaling laws, tending to zero in a fractal limit, as the contact area goes to zero. Moreover, a qualitative assessment is made for contact of fractal rough surfaces, and it is shown that pull-off in this case is dominated by the value of the contact area reached during the loading process, which depends on the applied load, suggesting pressure-sensitive adhesion.
Snaking bifurcations in a chain of mechanical oscillators are studied. The individual oscillators... more Snaking bifurcations in a chain of mechanical oscillators are studied. The individual oscillators are weakly nonlinear and subject to self-excitation and subcritical Hopf-bifurcations with some parameter ranges yielding bistability. When the oscillators are coupled to their neighbours, snaking bifurcations result, corresponding to localised vibration states. The snaking patterns do seem to be more complex than in previously studied continuous systems, comprising a plethora of isolated branches and also a large number of similar but not identical states, originating from the weak coupling of the phases of the individual oscillators.
Wedge-shaped frictional dampers are widely used in civil, mechanical and aeronautical engineering... more Wedge-shaped frictional dampers are widely used in civil, mechanical and aeronautical engineering with the purpose to limit and damp vibrations, increase component fatigue life, or resist seismic loads. The wedge shape induces normal load variations which complicates the analysis. Here, we study a model which can be considered a generalization of the Griffin model, originally devised for underplatform dampers in turbine blade attachments. The model has a mass element (the body whose vibrations are to be damped) linked to the wall by means of a spring and to a massless Coulomb damper via a ''contact stiffness". In Griffin's work the normal load acting on the Coulomb damper was kept constant. We introduce cyclic amplitude of the normal load, and phase shift between tangential and normal load. It is found that the optimization curves maintain the minimum for the mean normal load expected by Griffin's model. However, a lower vibration amplitude is found for in-phase loading with respect to the constant load, over the entire frequency range. When the ''contact stiffness" is higher than the structure stiffness (as it is generally expected), the maximum vibration decrement for in-phase loading is around 40%.
Recently, a simple and elegant "dimple" model was introduced by to show a mechanism for a bistabl... more Recently, a simple and elegant "dimple" model was introduced by to show a mechanism for a bistable adhesive system involving a surface with a shallow depression. The system shows, at least for intermediate levels of stickiness, that external pressure can switch the system into a "strong adhesive" regime of full contact, or into weak adhesion and complete pull-off, similarly to the contact of surfaces with a single scale of periodical waviness. We add to this model the effect of roughness, in the simple form of axisymmetric single scale of waviness, and we show that this induces a resistance to jumping into full contact on one hand (limiting the "strong adhesion" regime), and an enhancement of pull-off and of hysteresis starting from the partial contact state on the other (enhancing the "weak adhesion" regime). We show the system depends only on two dimensionless parameters, and becomes pressure-sensitive. The model obviously is specular to the Guduru model of rough spheres , with which it shares the limitations of the analysis assuming a connected contact (crack) area, and serves also the purpose of showing the effect of a depression into an otherwise periodic rough contact, towards the understanding of adhesion with multiple scales of roughness.
We study the adhesion of a surface with a 'dimple' which shows a mechanism for a bi-stable adhesi... more 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.
In the present paper we investigate indentation of a power-law axisymmetric rigid probe in adhesi... more In the present paper we investigate indentation of a power-law axisymmetric rigid probe in adhesive contact with a "thin layer" laying on a rigid foundation for both frictionless unbounded and bounded compressible cases. The investigation relies on the "thin layer" assumption proposed by Johnson, i.e. the layer thickness being much smaller than the radius of the contact area, and it makes use of the previous solutions proposed by Jaffar and Barber for the adhesiveless case. We give analytical predictions of the loading curves and provide indentation, load and contact radius at the pull-off. It is shown that the adhesive behavior is strongly affected by the indenter shape; nevertheless below a critical thickness of the layer (typically below 1 µm) the theoretical strength of the material is reached. This is in contrast with the Hertzian case, which has been shown to be insensitive to the layer thickness. Two cases are investigated, namely, the case of a free layer and the case of a compressible confined layer, the latter being more "efficient", as, due to Poisson effects, the same detachment force is reached with a smaller contact area. It is suggested that high sensitive micro-/nanoindentation tests may be performed using probes with different power law profiles for characterization of adhesive and elastic properties of micro-/nanolayers.
We study the contact between a rigid flat punch and an elastic half-space using Coulomb friction ... more We study the contact between a rigid flat punch and an elastic half-space using Coulomb friction for a normal load followed by a tangential load applied at a certain height above the interface line. The study is inspired by recent experiments by the group of Jay Fineberg in Israel. Three regimes are found in the evolution of slip at the interface depending on a dimensionless parameter ¼ a 2h , the ratio between the halfwidth of the contact and the product of twice friction coefficient and height of the loading point. Normal pressure and shear tractions are plotted for each case. It is shown that the effect of height does not collapse the data, contrary to the experimental data of Fineberg's setup. However, this is not surprising given the many deviations from the ideal configuration we have studied, namely the finite thickness of the bottom block, the presence of vertical surfaces on the upper block (both not permitting the assumption of halfspace elasticity) and finally local effects due to concentrated tangential load which give rise to local and not only global induced moment.
In a recent paper in Science, namely, "The Contact Sport of Rough Surfaces", Carpick summarizes r... more In a recent paper in Science, namely, "The Contact Sport of Rough Surfaces", Carpick summarizes recent efforts in a "contact challenge" to predict in detail an elastic contact between the mathematically defined fractal rough surfaces under (very little) adhesion. He also suggests the next steps that are needed to "fulfill da Vinci's dream of understanding what causes friction". However, this is disappointing as friction has been studied since the times of Leonardo and in 500 years, no predictive model has emerged, nor any significant improvement from rough contact models. Similarly, a very large effort we have spent on the "sport" of studying rough surfaces has not made us any closer to being able to predict the coefficient of proportionality between wear loss and friction dissipation which was already observed by Reye in 1860. Recent nice simulations by Aghababaei, Warner and Molinari have confirmed the criterion for the formation of debris of a single particle, proposed in 1958 by Rabinowicz, as well as Reye's assumption for the proportionality with frictional loss, which is very close to Archard anyway. More recent investigations under variable loads suggest that Reye's assumption is probably much more general than Archard's law. The attempts to obtain exact coefficients with rough surfaces models are very far from predictive, essentially because for fractals most authors fail to recognize that resolution-dependence of the contact area makes the models very ill-defined. We also suggest that in the models of wear, rough contacts should be considered "plastic" and "adhesive" and introduce a new length scale in the problem.
By integrating the simple deterministic Paris' law from a distribution of initial defects, in the... more By integrating the simple deterministic Paris' law from a distribution of initial defects, in the form of a Frechet extreme value distribution, it was known that a distribution of Weibull distribution of fatigue lives follows exactly. However, it had escaped previous researchers that the shape parameter of this distribution tends to very high values (meaning the scatter is extremely reduced) when Paris' exponent m approaches 2, leading to the exponential growth of cracks with number of cycles. In view of the fact that values close to m = 2 are of great importance in materials for example used for primary aircraft structures as recognized by some certification requirements (and the so-called "lead crack" methodology), we believe this conclusion may have some immediate relevance for damage tolerance procedures, or certification methods where accurate description of scatter is required. Indeed, we extend the result also to the case when Paris' constant C is distributed, and give also an estimate of the level of scatter expected in propagation life in the most general case when C, m are both random variate alongwith the defect size distribution, based on first transforming them to uncorrelated form C 0 , m, and validate this with the famous Virkler set of data. We finally discuss that from known typical values of fatigue life scatter of aeronautical alloys, it is very likely that an important contribution comes from short crack growth. of extreme values (here, the largest cracks) bears the name of Frechet, having Cumulative Distribution Function (CDF)
AbstractThere has been a long debate about the validity of asperity models in the contact between... more AbstractThere has been a long debate about the validity of asperity models in the contact between rough surfaces, much of it concentrated on relatively minor aspects of the solution for the special case of Gaussian random processes for roughness, like the exact value of the areaload slope or the extent of the linear regime. It is shown here that in the case of adhesion, the behavior is extremely sensitive to the shape of the height distribution. We show for example results for Weibull distributions, which has been suggested in a number of practical cases from macroscopic to nanoscopic roughness. Pull-off force is found to vary by several orders of magnitude both lower and higher than in the Gaussian case, whereas the stickiness criterion on the adhesion parameter changes by an order of magnitude. Additionally, in some operations like chemical-mechanical polishing, tails are almost completely removed and a sharp peak develops instead of a tail: modeling this with contact on the bounded side of the Weibull distribution, stickiness seems to occur for any level of roughness. Some qualitative comparison with recent numerical experiments is attempted.
a center of excellence in computational Mechanics, Politecnico di Bari, Bari, italy; b department... more a center of excellence in computational Mechanics, Politecnico di Bari, Bari, italy; b department of Mechanical engineering, hamburg university of Technology, hamburg, germany ABSTRACT A simple asperity model using random process theory is developed in the presence of adhesion, using the Derjaguin, Muller and Toporov model for each individual asperity. A new adhesion parameter is found, which perhaps improves the previous parameter proposed by Fuller and Tabor which assumed identical asperities -the model in all his variants for the radius always gives a finite pull-off force, as in Fuller and Tabor, and contrary to the exponential asperity height distribution, where the force is either always compressive, or always tensile. It is shown that a model with spheres having a radius only dependent on height is a reasonable approximation with respect to models having also a distribution of radius curvatures -the three models differ considerably, as opposed to the adhesionless case where these details did not matter. The important surface parameters in the theory determining the pull-off force are the three moments m 0 , m 2 , m 4 . The asymptotic form of the model at large separation is solved in closed form. As the theoretical pull-off of aligned asperities having the same radius (the average value) increases with the square root of the Nayak bandwidth of the roughness, and as asperity models are known to describe less well the surface at large bandwidth parameters, the limit behavior at large bandwidths remains uncertain.
Recent numerical investigation on self-affine Gaussian surfaces by Pastewka and Robbins (PR) has ... more Recent numerical investigation on self-affine Gaussian surfaces by Pastewka and Robbins (PR) has led to a criterion for "stickiness" based on when the slope of the (repulsive) area-load relationship appears to become vertical in numerical simulations at a ratio of contact area to nominal one (rather arbitrarily) fixed to 1%. Since pull-off and slope of the area-load are two faces of the same medal, a simple check of the results in terms of pull-off shows that PR have many more data which fail their criterion than the ones that satisfy it, and this is evident even in their own figures. As a small improvement, a proposal to modify the criterion to better fit their own data is put forward. However, the pull-off decay seems rather exponential so that it is unclear if their slope criterion really corresponds to a "thermodynamic" limit, and consequently their conclusion that stickiness should depend only on slopes and curvature may be an artifact of their assumption of defining a secant at 1% contact area ratio and of using truncated potentials, rather than a true important property of rough contact. Both the PR criterion and the present modified one imply that for fractal dimension D < 2:4, stickiness should increase with resolution, so the problem of truncation of the spectrum seems ill-defined: in fact, PR define rigid self-affine surfaces with rather smooth and well-defined slopes, and not a realistic atomic roughness as first studied by Luan and Robbins.
AbstractThere is no simple theory at present to predict accurately the decay of pull-off in the a... more AbstractThere is no simple theory at present to predict accurately the decay of pull-off in the adhesion of randomly rough surfaces. The asperity model of .uller and Tabor has shown significant error in recent numerical investigations by Pastewka and Robbins of self-affine random roughness from micrometer to atomic scale which corresponds to low values of Tabor parameter. .or sinusoidal contact, the Johnson parameter, originally introduced for the JKR regime (from JohnsonKendallRoberts) is the dominant parameter ruling the pull-off at intermediate Tabor values. Hence, we define a generalized Johnson parameter as the ratio between the adhesive energy to the elastic strain energy to flatten the surface in the case of multiscale roughness and find that it correlates very well with the data of Pastewka and Robbins spanning almost five orders of magnitude of reduction from theoretical strength, improving significantly with respect to other possible single parameter criteria. .or the most important case in practice, that of low fractal dimensions, this suggests the product of amplitude and slope of the largest wavelength components of roughness dominate pull-off decay, and not small scales features like slopes and curvatures, as suggested by Pastewka and Robbins.
In the present article, we study the development of a wear profile in an axially symmetric contac... more In the present article, we study the development of a wear profile in an axially symmetric contact under conditions of gross slip and assumption of the Reye-Archard wear criterion. Simulations are carried out using the method of dimensionality reduction and a full finite element method (FEM) formulation. The calculation time of the proposed model is several orders lower than that of FEM-based models and allows for much higher spatial resolution.
There are two main approximate theories in the contact of rough solids: Greenwood-Williamson aspe... more There are two main approximate theories in the contact of rough solids: Greenwood-Williamson asperity theories (GW) and Persson theories. Neither of them has been fully assessed so far with respect to load-separation curves. Focusing on the most important case of low fractal dimension (D f = 2.2) with extensive numerical studies we find that: (i) Persson's theory describes well the regime of intermediate pressures/contact area, but requires significant corrective factors: the latter depend also on upper wavevector cutoff of the roughness; hence, (ii) Persson's theory does not predict the correct functional dependence on magnification; (iii) asperity theories in the discrete version even neglecting interaction effects are more appropriate in the range of relatively large separations, also to take into consideration of the large scatter in actual realization of the surface.
The classical Cattaneo-Mindlin problem for elastic halfplanes is extended for a Griffith conditio... more The classical Cattaneo-Mindlin problem for elastic halfplanes is extended for a Griffith condition for inception of slip, and otherwise following the standard Coulomb law in the sliding zone. A general solution is found using the idea of superposing normal contact pressure distributions for arbitrary 2D geometry. In particular, the full sliding component of shear is corrected with a distribution in the stick region which is formally equivalent to a JKR solution for the normal contact problem insisting on the stick area. We show that geometry affects the apparent friction coefficient (the maximum tangential load at the inception of slip), since a sudden transition to slip occurs when the stick region reaches a critical size which corresponds to the phenomenon of pull-off in the JKR solution. Example solutions are given for Hertzian geometry, power law punches and a sinusoidal profile.
Recently, the observation of ''slow fronts'' in Fineberg's group beautiful experiments in the tra... more Recently, the observation of ''slow fronts'' in Fineberg's group beautiful experiments in the transition from stick to slip has motivated some interesting mesoscopic models for friction, introduced along the lines of rate-state dependent models, but with a key role played by a viscous strengthening term in the friction law. In particular two models, proposed by Bar Sinai, Brener and Bouchbinder (BSBB), are considered in this work which differ in the strengthening term: the first introduces a logarithmic strengthening, the second a linear strengthening. The models aim to show that the velocity of the slip propagating fronts can be related to the much smaller slip velocities in the friction steady state curve. With the logarithmic strengthening model the increase in the local friction coefficient remains negligible if compared with the experimental results. When a stronger-than-logarithmic strengthening friction model is considered an order of magnitude increase of friction coefficient is observed in steady state friction curves, nevertheless when the local shear/pressure ratio is related with the front velocity, the results are inconsistent with the experiments. Some closed form equations are obtained to show the main results of the BSBB models, not shown in the original papers. The results and the limitations of the present models are presented.
Under rolling contact fatigue (RCF) existing multiaxial fatigue criteria are not well validated a... more Under rolling contact fatigue (RCF) existing multiaxial fatigue criteria are not well validated and predict significantly different results. Results for simple typical Hertzian RCF pure rolling are shown as previously remarked by the authors, the Dang Van criterion applied to RCF gives over-optimistic fatigue limits, due to the large influence of the hydrostatic component of the stress, particularly under some conditions. It is here shown that the ''simpler'' Crossland criterion gives a more realistic fatigue limit of Hertzian peak pressure, and the more ''elaborate'' Papadopoulos criterion gives an even more conservative value, of about 3-3.5 times higher than the fatigue limit under pure shear. It is suggested that the multiaxial criteria per se do not give a reliable estimate of the fatigue limit, and perhaps an integration within Weibull-like theories should be attempted in the future, as well as a more ''unified'' approach and mix of criteria taken from gears design, rolling contact in railways, and in rolling bearings.
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Papers by michele ciavarella
by Menga, Carbone & Dini (MCD), applying fracture mechanics energy concepts for the case of a sliding adhesive contact, imposing also the shear stress is constant at the interface and equal to a material constant (as it seems in experiments), leads to a increase of contact area which instead is never observed.
We add that the rigorous MCD theory also predict a size effect and hence a distortion of the JKR curve during sliding which is also not observed in experiments. Finally, a simpler example with the pure mode I contact case, leads in the MCD theory to an unbounded contact area, which is difficult to interpret, rather than a perhaps more correct limit of the Maugis-Dugdale solution for the adhesive sphere when Tabor parameter is zero, that is DMT’s solution. We discuss therefore the implications of the MCD theory, although they may be rather academic: recent semi-empirical models, with an appropriate choice of
the empirical parameters, seem more promising and robust in modelling actual experiments.