arXiv subjects

M. Ciavarella

Publications and source records attributed to M. Ciavarella.

At least 19 recordsLinked to original sources

arXiv2020

Crack propagation at the interface between viscoelastic and elastic materials

Crack propagation in viscoelastic materials has been understood with the use of Barenblatt cohesive models by many authors since the 1970's. In polymers and metal creep, it is customary to assume that the relaxed modulus is zero, so that we have typically a crack speed which depends on some power of the stress intensity factor. Generally, when there is a finite relaxed modulus, it has been shown that the toughness increases between a value at very low speeds at a threshold toughness G0, to a very fast fracture value at Ginf, and that the enhancement factor in infinite systems (where the classical singular fracture mechanics field dominates) simply corresponds to the ratio of instantaneous to relaxed elastic moduli. Here, we apply a cohesive model for the case of a bimaterial interface between an elastic and a viscoelastic material, assuming the crack remains at the interface, and neglect the details of bimaterial singularity. For the case of a Maxwell material at low speeds the crack propagates with a speed which depends only on viscosity, and the fourth power of the stress intensity factor, and not on the elastic moduli of either material. For the Schapery type of power law material with no relaxation modulus, there are more general results. For arbitrary viscoelastic materials with nonzero relaxed modulus, we show that the maximum toughness enhancement will be reduced with respect to that of a classical viscoelastic crack in homogeneous material.

cond-mat.mtrl-sci↗

arXiv2020

Stickiness of randomly rough surfaces with high fractal dimension: is there a fractal limit?

Two surfaces are "sticky" if breaking their mutual contact requires a finite tensile force. At low fractal dimensions D, there is consensus stickiness does not depend on the upper truncation frequency of roughness spectrum (or "magnification"). As debate is still open for the case at high D, we exploit BAM theory of Ciavarella and Persson-Tosatti theory, to derive criteria for all fractal dimensions. For high D, we show that stickiness is more influenced by short wavelength roughness with respect to the low D case. BAM converges at high magnifications to a simple criterion which depends only on D, in agreement with theories that includes Lennard-Jones traction-gap law, while Persson-Tosatti disagrees because of its simplifying approximations.

cond-mat.mtrl-sci↗

arXiv2020

Improved Muller approximate solution of the pull-off of a sphere from a viscoelastic substrate

The detachment of a sphere from a viscoelastic substrate is clearly a fundamental problem. In the case viscoelastic dissipation is concentrated at the contact edge, and the work of adhesion follows a quite popular simplified model, Muller has suggested an approximate solution, which however is based on an empirical observation. We revisit Muller's solution and show it leads to very poor fitting of the actual full numerical results, particularly for the radius of contact at pull-off, and we suggest an improved fitting of the pull-off which works extremely well over a very wide range of withdrawing speeds, and correctly converges to the JKR value at very low speeds.

cond-mat.mtrl-sci↗

arXiv2020

A comment on "Discussion on the use of the strain energy release rate for fatigue delamination characterization"

In a recent very interesting and illuminating proposal, Yao et al. (2014) have discussed the use of the strain energy release rate (SERR) as a parameter to characterize fatigue delamination growth in composite materials. They consider fatigue delamination data strongly affected by R-curve behaviour due to fibres bridging and argue that a better approach is to correlate the crack advance with the total work per cycle measured in the testing machine. This seems to work better than estimating the compliance as a linear fit of experimental curves from Modified Compliance Calibration ASTM standards equations for the SERR in the classical Linear Elastic Fracture Mechanics framework. We show however that if we assume indeed linear behaviour (i.e. LEFM), the approach they introduce is perfectly equivalent to the SERR one, i.e. Paris type of laws. As well known form Barenblatt and Botvina, fatigue crack growth is a weak form of scaling, and it gives Paris classical dependence only when the crack is much longer than any other characteristic sizes. Paris' law is not a fundamental law of physics, is not an energy balance equation like Griffith, and strong size effects due to cohesive zones have been found already in concrete by Bazant. The proposal is very simple, and interesting as it would seem to suggest that a proper scaling with a cohesive model at crack tip could be predicted, although this doesn't seem to have been attempted in the Literature. The main drawback of the present proposal is that it is not predictive, but purely observational, as it requires the actual measurement of work input during the fatigue process.

cond-mat.mtrl-sci↗

arXiv2020

On the Afferrante-Carbone theory of ultratough peeling

In an elegant and interesting theory of ultratough peeling of an elastic tape from a viscoelastic substrate, Afferrante and Carbone (2016) find that, in contrast to the classic elastic Kendall's theory, there are conditions for which the load for steady state peeling could be arbitrarily large in steady state peeling, at low angles of peeling - what they call "ultratough" peeling. It is here shown in fact that this occurs near critical speeds where the elastic energy term of Kendall's equation is balanced by the viscoelastic dissipation. Surprisingly, this seems to lead to toughness enhancement higher than the limit value observed in a very large crack in a infinite viscoelastic body, possibly even considering a limit on the stress transmitted. Kendall's experiments in turn had considered viscoelastic tapes (rather than substrates), and his viscoelastic findinds seem to lead to a much simpler picture. The Afferrante-Carbone theory suggests the viscoelastic effect to be an on-off mechanism, since for large angles of peeling it is almost insignificant, while only below a certain threshold, this "ultratough" peeling seems to appear. Experimental and/or numerical verification would be most useful.

cond-mat.soft↗

arXiv2020

On the interaction of viscoelasticity and waviness in enhancing the pull-off force in sphere/flat contacts

Motivated by roughness-induced adhesion enhancement (toughening and strengthening) in low modulus materials, we study the detachment of a sphere from a substrate in the presence of both viscoelastic dissipation at the contact edge, and roughness in the form of a single axisymmetric waviness. We show that the roughness-induced enhancement found by Guduru and coworkers for the elastic case (i.e. at very small detachment speeds) tends to disappear with increasing speeds, where the viscoelastic effect dominates and the problem approaches that of a smooth sphere. This is in qualitative agreement with the original experiments of Guduru's group with gelatin. The cross-over velocity is where the two separate effects are comparable. Viscoelasticity effectively damps roughness-induced elastic instabilities, and make their effects much less important.

cond-mat.soft↗

arXiv2019

A simplified theory of "stickiness" due to electroadhesion between rough surfaces

Building on theories of Persson, we derive a simpler theory for electroadhesion between rough surfaces using BAM (Bearing Area Model) of Ciavarella, or previous ideas by Persson and Tosatti. Rather surprisingly, in terms of stickiness, we obtain very simple and similar results for pure power law power spectrum density (PSD), confirming stickiness to be mainly dependent on macroscopic quantities. We define a new dimensionless parameter for electroadhesive stickiness.

cond-mat.soft↗

arXiv2019

The interaction of frictional slip and adhesion for a stiff sphere on a compliant substrate

How friction affects adhesion is addressed. The problem is considered in the context of a very stiff sphere adhering to a compliant, isotropic, linear elastic substrate, and experiencing adhesion and frictional slip relative to each other. The adhesion is considered to be driven by very large attractive tractions between the sphere and the substrate that can act only at very small distances between them. As a consequence, the adhesion behavior can be represented by the Johnson-Kendall-Roberts model, and this is assumed to prevail also when frictional slip is occurring. Frictional slip is considered to be resisted by a uniform, constant shear traction at the slipping interface, a model that is considered to be valid for small asperities and for compliant elastomers in contact with stiff material. A model for the interaction of friction and adhesion, known to agree with some experimental data, is utilized. This model is due to Johnson, and its adhesion-friction interaction is assumed to stem, upon shrinkage of the contact area, from a postulated reversible energy release associated with frictional slip. This behavior is considered to arise from surface microstructures generated or eliminated by frictional slip, where these microstructures store some elastic strain energy in a reversible manner. The associated reversible energy release rate is derived from the energy exchanges that occur in the system. The Johnson model, and an asymptotic analysis of it for small amounts of frictional slip, is shown to be consistent with the reversible energy release rate that we identify.

cond-mat.soft↗

arXiv2019

Resolving a controversy about adhesion in sliding contacts

An interesting recent paper by Menga, Carbone & Dini (MCD, 2018, [1]), suggests that in sliding adhesive contacts, the contact area should increase due to tangential shear stresses at the interface, assumed to be constant and corresponding to a material constant. This is not observed in the known experiments, and is in sharp contrast with all the classical theories about the transition from stick to sliding, both in the JKR (Griffith like) conditions which involve singular pressure and shear, as well as in full general cohesive models. We offer a rigorous thermodynamics calculation, which suggests in fact there is no qualitative contrast but a very close quantitative agreement, with previous theories. Actually, the model predicts an even stronger reduction of contact area than predicted by Savkoor and Briggs, contrary to experimental observations, so would certainly require some adjustements to consider dissipative effects.

cond-mat.soft↗

arXiv2019

On the application of fracture mechanics mixed-mode models of sliding with friction and adhesion

As recently suggested in an interestring and stimulating paper 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.

cond-mat.soft↗

arXiv2019

Shear-induced contact area anisotropy explained by a fracture mechanics model

This paper gives a theoretical analysis for the fundamental problem of anisotropy induced by shear forces onan adhesive contact, discussing the experimental data of the companion Letter. We present a fracture mechanicsmodel where two phenomenological mode-mixity functions are introduced to describe the weak couplingbetween modes I and II or I and III, which changes the effective toughness of the interface. The mode-mixityfunctions have been interpolated using the data of a single experiment and then used to predict the behavior of thewhole set of experimental observations. The model extends an idea by Johnson and Greenwood, to solve purelymode I problems of adhesion in the presence of a nonaxisymmetric Hertzian geometry, to the case of ellipticalcontacts sheared along their major or minor axis. Equality between the stress intensity factors and their criticalvalues is imposed solely at the major and minor axes. We successfully validate our model against experimentaldata. The model predicts that the punch geometry will affect both the shape and the overall decay of the shearedcontact area.

cond-mat.soft↗

arXiv2019

Shear-Induced Anisotropy in Rough Elastomer Contact

True contact between randomly rough solids consists of myriad individual micro-junctions. 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 micro-junctions. Here we show that, in rough elastomer contacts, the shape of micro-junctions 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 macroscopic sliding regime. We show that smooth sphere/plane contacts have the same shear-induced anisotropic behaviour as individual micro-junctions, with a common scaling law over four orders of magnitude in initial area. We discuss the physical origin of the observations in the 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.

cond-mat.soft↗

arXiv2018

On stickiness of multiscale randomly rough surfaces

We derive a very simple and effective stickiness criterion for solids having random roughness using a new asymptotic theory, which we validate with that of Persson and Scaraggi and independent numerical experiments. Previous claims that stickiness may depend on small scale quantities such as rms slopes and/or curvatures, obtained by making oversimplified assumptions on the contact area geometry, are largely incorrect, as the truncation of the PSD spectrum of roughness at short wavelengths is irrelevant. We find stickiness is destroyed typically at roughness amplitudes up to three orders of magnitude larger than the range of attractive forces. With typical nanometer values of the latter, the criterion gives justification to the qualitative well known empirical Dalhquist criterion for stickiness which demands adhesives to have elastic modulus lower than about 1MPa. The results clarifies a much debated question in both the scientific and technological world of adhesion, and may serve as benchmark for better comprehension of the role of roughness.

cond-mat.soft↗

arXiv2018

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems.

nlin.PS↗

arXiv2018

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 analyzing contact problems involving adhesive tractions, with particular reference to the effect of the inevitable roughness of the contacting surfaces.

cond-mat.soft↗

arXiv2018

On mixed-mode fracture mechanics models for contact area reduction under shear load in soft materials

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, there could be 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. The idea that the mixed mode function and parameter should be an interface property may be erroneous.

cond-mat.soft↗

arXiv2018

Ultrastrong adhesion in the contact with thin elastic layers on a rigid foundation

In the present short note, we generalize simple approximate Johnson-Jaffar-Barber solutions for the indentation by a rigid punch of a thin elastic layer on a rigid foundation to the case of adhesion. This could be an interesting geometry for an adhesive system, a limit case of the more general class of layered systems, or FGMs (Functionally Graded Materials). We show that ultrastrong adhesion (up to theoretical strength) can be reached both in line contact or in axisymmetric contact for thin layers (typically of nanoscale size), which suggests a new possible strategy for "optimal adhesion". In particular, in line contact adhesion enhancement occurs as an increase of the actual pull-off force, while in axisymmetric case the latter is apparently very close to the classical JKR case. However, it appears in closer examination that also for axisymmetric case, the enhancement occurs by reducing the size of contact needed to sustain the pull-off force. These effects are further enhanced by Poisson's ratio effects in the case of nearly incompressible layer.

cond-mat.mtrl-sci↗

arXiv2018

Some further validations and comparison of the Bearing Area Model (BAM) for adhesion of rough surfaces

In the present short note, we attempt further validations and comparisons of a recent simple model for the estimate for adhesion between elastic (hard) rough solids with Gaussian multiple scales of roughness, BAM (Bearing Area Model) belonging to a DMT class of models. In one case, we use the GJP (Generalized Johnson Parameter) model, which is an empirical fit validated on the same (and so far most extensive) set of data on which BAM was validated, namely that of Pastewka and Robbins. In the second case, we compare with another approximate DMT theory, that of Persson and Scaraggi, which turns out extremely close to the BAM model, despite much more complex: GJP however can lead to significant discrepancies.

cond-mat.mtrl-sci↗