Fracture Mechanics Simple Calculations to Explain Small Reduction of the Real Contact Area Under Shear

Ciavarella, M.

doi:10.22190/fume180108007c

Cited by 7 publications

(21 citation statements)

References 21 publications

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“…friction, plasticity, dislocation emission) and cannot be ascribed to a single phenomenon [16]. Since then, a few phenomenological models have been proposed ( [17], [18], [19], [20], [21], [22], [23]) which require a Mode-Mixity Function (MMF) f (ψ) [26] to describe the critical condition for propagation G c = G Ic f (ψ) (1) where G Ic is mode I critical factor (or surface energy, if we assume Griffith's concept), G c is the critical energy release rate in mixed mode conditions and finally ψ is the "phase angle"…”

Section: Introductionmentioning

confidence: 99%

“…Experimental measurements of contact area evolution show that the shape of contact area is circular, according to JKR theory, at zero tangential force and shrinks in an elliptical-like fashion while the shear force is increased ( [8], [15], [19]). So far, all LEFM models proposed ( [14], [17], [18], [19], [22], [23]) make the approximation to consider the contact as circular, even when sheared. This requires an averaging of the effects of mode II and mode III around the periphery.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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“…the effective surface energy (or toughness of the interface) is increased, rather than decreased in Savkoor's theory (5), and curiously of a very similar quantity, perhaps even exactly the same since τ 0 = τ m , if Y = 2 π . This should not be confused from the result of the theories using the mode-mixity functions of the type (1), like (Ciavarella, 2018, since in the latter case, there is no size-effect associated to the contact area a, as there is in (13), and this has profoundly different implications, as we shall explore.…”

Section: The Area Enhancement MCD Theorymentioning

confidence: 82%

“…In particular, Johnson (1997) attempts also to model slip explicitly with cohesive models (as well as the mode I corresponding part), and even in this case, the conclusion remains of the contact area reduction. Various recent other papers (Ciavarella, 2018 have shown that the size and even the elliptical shape of the contact under shear are reasonably found by these LEFM models over a wide range of loads and geometrical features, despite the mixed-mode function strictly requires a complex functional form to replicate faithfully the results and hence empirical fitting at least over one set of results. Also, they suggested there is no obvious advantage in trying to model the slip displacements (which correspond to recur to a cohesive model, in the context of fracture mechanics), since this effect is essentially included in the mixed-mode function.…”

Section: Introductionmentioning

confidence: 79%

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

Ciavarella

Cricrı̀²

2019

Bioinspir. Biomim.

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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.

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On the Degree of Irreversibility of Friction in Sheared Soft Adhesive Contacts

Ciavarella

Papangelo

2020

Tribol Lett

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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.

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Fracture Mechanics Simple Calculations to Explain Small Reduction of the Real Contact Area Under Shear

Abstract: Abstract. In a very recent paper, Sahli and coauthors [12] (R.Sahli

Cited by 7 publications

References 21 publications

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

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

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

On the Degree of Irreversibility of Friction in Sheared Soft Adhesive Contacts

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