This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among ...the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano- and microscales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions.
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In classical experiments, it has been found that a rigid cylinder can roll both on and
under
an inclined rubber plane with a friction force that depends on a power law of velocity, independent of the ...sign of the normal force. Further, contact area increases significantly with velocity with a related power law. We try to model qualitatively these experiments with a numerical boundary element solution with a standard linear solid and we find for sufficiently large Maugis–Tabor parameter
λ
qualitative agreement with experiments. However, friction force increases linearly with velocity at low velocities (like in the case with no adhesive hysteresis) and then decays at large speeds. Quantitative agreement with the Persson–Brener theory of crack propagation is found for the two power law regimes, but when Maugis–Tabor parameter
λ
is small, the cut-off stress in Persson–Brener theory depends on all the other dimensionless parameters of the problem.
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 “apparent” toughness in a semi-infinite crack increases between a value at very low speeds at a threshold toughness w0, to a very fast fracture value at w∞, 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 “effective” toughness enhancement will be reduced with respect to that of a classical viscoelastic crack in homogeneous material.
•A bimaterial elastic–viscoelastic interface is studied using a cohesive model.•For Maxwell material we provide closed form approximate results.•The highest toughness enhancement is reduced with respect to the homogeneous case.
In the present paper, we consider a recent very simple model for the estimate of adhesion between elastic (hard) rough solids with Gaussian multiple scales of roughness (BAM, Bearing Area Model), and ...compare it in particular with very recent extensive results from the numerical method of Joe, Thouless and Barber (JTB theory), in the range of non-hysteretic behaviour. BAM shows no sensitiveness to rms slopes and curvatures for the pull-off load or the apparent surface energy, in agreement with the JTB theory, but in contrast with the criterion proposed by Pastewka and Robbins for stickiness, especially in the fractal limit. Results show also reasonable accuracy with the JTB theory, and BAM theory is simpler than that of Persson and Scaraggi which involves convolution of adhesion tractions in the regions of separation.
•We make validations of a recent model for adhesion between elastic (hard) rough solids, namely BAM (Bearing Area Model).•We compare BAM with another approximate theory, that of Joe-Thouless-Barber (JTB) theory.•BAM shows that pull-off and effective energy of adhesion depend on macroscopic well-defined quantities.
A new stickiness criterion for solids having random fractal roughness is derived using Persson's theory with DMT-type adhesion. As expected, we find that stickiness, i.e. the possibility to sustain ...macroscopic tensile pressures or else non-zero contact area without load, is not affected by the truncation of the PSD spectrum of roughness at short wavelengths and can persist up to roughness amplitude orders of magnitude larger than the range of attractive forces. With typical nanometre values of the latter, the criterion gives justification to the well-known empirical Dalhquist criterion for stickiness that demands adhesives to have elastic modulus lower than about 1 MPa.
The interaction between contact area and frictional forces in adhesive soft contacts is receiving much attention in the scientific community due to its implications in many areas of engineering such ...as surface haptics and bioinspired adhesives. In this work, we consider a soft adhesive sphere that is pressed against a rigid substrate and is sheared by a tangential force where the loads are transferred to the sphere through a normal and a tangential spring, representing the loading apparatus stiffness. We derive a general linear elastic fracture mechanics solution, taking into account also the interaction between modes, by adopting a simple but effective mixed-mode model that has been recently validated against experimental results in similar problems. We discuss how the spring stiffness affects the stability of the equilibrium contact solution, i.e. the transition to separation or to sliding.
•A Frechet distribution of defects and of Paris constant C, leads to a Weibull distribution of fatigue lives.•The scatter tends to very low values for Paris m = 2.•We deal with the most general form ...of Paris’ power law with random C, m.
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 C0, 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.
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.
•We study the stickiness of randomly rough surfaces for the case at high fractal dimension.•We exploit BAM theory and Persson-Tosatti theory to derive two stickiness criteria in the case of high fractal dimension.•We show that stickiness is reduced by increasing the fractal dimension.•We obtain BAM stickiness criterion that holds for any fractal dimensions, showing converging results in the fractal limit.•BAM theory is in qualitatively agreement with rough contact theories where Lennard-Jones adhesive law is considered.
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.
The classical Palmgren‐Miner (PM) rule, despite clearly approximation, is commonly applied for the case of variable amplitude loading, and to date, there is no simple alternative. In the literature, ...previous authors have commented that the PM hypothesis is based on an exponential fatigue crack growth law, ie, when da/dN is proportional to the crack size a, the case that includes also Paris law for m=2, in particular. This is because they applied it by updating the damage estimate during the crack growth.
It is here shown that applying PM to the “initial” and nominal (Stress vs Number of cycles) curve of a cracked structure results exactly in the integration of the simple Paris power law equation and more in general to any crack law in the form da/dN=HΔσhan. This leads to an interesting new interpretation of PM rule. Indeed, the fact that PM rule is often considered to be quite inaccurate pertains more to the general case when propagation cannot be simplified to this form (like when there are distinct initiation and propagation phases), rather than in long crack propagation. Indeed, results from well‐known round‐robin experiments under spectrum loading confirm that even using modified Paris laws for crack propagation, the results of the “noninteraction” models, neglecting retardation and other crack closure or plasticity effects due to overloads, are quite satisfactory, and these correspond indeed very closely to applying PM, at least when geometrical factors can be neglected. The use of generalized exponential crack growth, even in the context of spectrum loading, seems to imply the PM rule applies. Therefore, this seems closely related to the so‐called lead crack fatigue lifing framework. The connection means however that the same sort of accuracy is expected from PM rule and from assuming exponential crack growth for the entire lifetime.
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